Simon Colton
Professor in Digital Games Technologies (Falmouth)
and Computational Creativity (Goldsmiths)
About me
Hello there – I’m Simon Colton. I hold an ERA Chair in Digital Games Technology at Falmouth University. I’m also a Professor of Computational Creativity in the Department of Computing of Goldsmiths College, University of London, and I hold an EPSRC Leadership Fellowship. Previously, I was a Reader in Computational Creativity in the Department of Computing at Imperial College, London.
I’m an Artificial Intelligence researcher, specialising in questions of Computational Creativity. In particular, I lead the Computational Creativity Group. We develop and investigate novel AI techniques and apply them to creative tasks in domains such as pure mathematics, graphic design, video game design, creative language and the visual arts. By taking an overview of creativity in such domains, we also add to the philosophical discussion of creativity, by addressing issues raised by the idea of autonomously creative software. This has enabled us to drive forward various formalism projects aimed at bringing more rigour to the assessment of creativity in software.
At Imperial, I taught courses on Artificial Intelligence and Ludic Computing to both undergraduate and postgraduate classes. I have also given a course at the Helsinki Autumn School on Computational Creativity. Please see our group’s teaching pages for materials.
I’m the guy behind The Painting Fool, which is a computer program that we hope will one day be taken seriously as a creative artist in its own right. www.thepaintingfool.com.
I’m on a number of programme committees for AI events each year, and often I’m involved in organising an event or two. Please see our group’s blog for more information.
You can contact me on .[at]...
Academic CV
You can find my academic CV here.
Recent Talks
Recent talks will be added here soon.
Publications
We investigate three principal areas of research. Firstly, we have developed and continue to improve upon a novel machine learning algorithm called Automated Theory Formation (ATF), which invents concepts, discovers regularities in data, and uses third party reasoning systems to prove and disprove hypotheses. Secondly, we investigate fruitful ways in which to combine disparate AI methods so that the whole is more than the sum of the parts. Thirdly, we apply ATF and various combined reasoning systems to intelligent tasks involving the simulation of creative behaviour in pure mathematics, bioinformatics, graphic design, visual arts and video game design. We are particularly interested in the technical and sociological challenges involved in building AI software which is independently creative. Our research can be broadly categorised into the eight areas described below.
Books
Theses
Colton, Simon Automated Theory Formation in Pure Mathematics PhD Thesis 2001. @phdthesis{colton2001d, title = {Automated Theory Formation in Pure Mathematics}, author = {Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/colton_phd01.pdf}, year = {2001}, date = {2001-01-01}, publisher = {Springer}, institution = {University of Edinburgh}, keywords = {}, pubstate = {published}, tppubtype = {phdthesis} } |
Colton, Simon Involving Computers with Mathematics, Minimum Distances of Quadratic Residue Codes Masters Thesis 1996. @mastersthesis{colton96, title = {Involving Computers with Mathematics, Minimum Distances of Quadratic Residue Codes}, author = {Simon Colton}, url = {http://ccg.doc.gold.ac.uk/papers/colton_msc96.pdf}, year = {1996}, date = {1996-01-01}, institution = {University of Liverpool}, keywords = {}, pubstate = {published}, tppubtype = {mastersthesis} } |
Papers
Please click on category to expand.
The Development of Automated Theory Formation
Automated Theory Formation (ATF) is a novel machine learning technique which has been developed over 12 years, and which is implemented in the HR system. Given some background knowledge, HR forms new concepts from old ones using a set of production rules, and then makes conjectures which relate the concepts, by appealing to empirical patterns in the examples of the concepts. HR then uses third party systems to prove/disprove the conjectures (usually the Otter theorem prover and the MACE model generator). HR also interacts with computer algebra systems such as Maple and Gap, in order to calculate values for concepts. To drive a heuristic search, HR uses a weighted sum – with the weights set by the user – of measures of interestingness for concepts, i.e., having decided which concept is most interesting, HR builds new concepts from this. My book is the main reference text for Automated Theory Formation.
The following papers describe some of the fundamental aspects of automated theory formation. The first paper is the main reference for ATF as an Inductive Logic Programming system, the other papers are from quite early on in the development of ATF.
Colton, Simon; Ramezani, Ramin; Llano, Maria Teresa The HR3 discovery system: Design decisions and implementation details Inproceedings In: Proceedings of the AISB symposium on Computational Scientific Discovery, 2014. @inproceedings{colton2014hr3, title = {The HR3 discovery system: Design decisions and implementation details}, author = { Simon Colton and Ramin Ramezani and Maria Teresa Llano}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/07/colton_aisb14b.pdf}, year = {2014}, date = {2014-01-01}, booktitle = {Proceedings of the AISB symposium on Computational Scientific Discovery}, abstract = {Automated Theory Formation is a hybrid AI technique which has been implemented in two scientific discovery systems, HR1 and HR2, both of which have been used successfully in vari- ous applications. We describe here the latest iteration in the HR se- ries, in terms of the lessons learned from the successes and failures of the previous versions, and how these lessons have informed our design choices and the implementation details of the new version. We also present two case studies: a synthetic domain mirroring an aspect of medical diagnosis, and invariant discovery in formal meth- ods. In each case, we compare HR3 with HR2 to highlight various improvements in the new version.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Automated Theory Formation is a hybrid AI technique which has been implemented in two scientific discovery systems, HR1 and HR2, both of which have been used successfully in vari- ous applications. We describe here the latest iteration in the HR se- ries, in terms of the lessons learned from the successes and failures of the previous versions, and how these lessons have informed our design choices and the implementation details of the new version. We also present two case studies: a synthetic domain mirroring an aspect of medical diagnosis, and invariant discovery in formal meth- ods. In each case, we compare HR3 with HR2 to highlight various improvements in the new version. |
Colton, Simon; Muggleton, Stephen Mathematical applications of inductive logic programming Journal Article In: Machine Learning, 64 (1-3), pp. 25–64, 2006. @article{colton2006mathematical, title = {Mathematical applications of inductive logic programming}, author = { Simon Colton and Stephen Muggleton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/07/colton_mlj06.pdf}, year = {2006}, date = {2006-01-01}, journal = {Machine Learning}, volume = {64}, number = {1-3}, pages = {25--64}, publisher = {Springer}, abstract = {The application of Inductive Logic Programming to scientific datasets has been highly successful. Such applications have led to breakthroughs in the domain of interest and have driven the development of ILP systems. The application of AI techniques to mathemat- ical discovery tasks, however, has largely involved computer algebra systems and theorem provers rather than machine learning systems. We discuss here the application of the HR and Progol machine learning programs to discovery tasks in mathematics. While Progol is an established ILP system, HR has historically not been described as an ILP system. However, many applications of HR have required the production of first order hypotheses given data expressed in a Prolog-style manner, and the core functionality of HR can be expressed in ILP terminology. In Colton (2003), we presented the first partial description of HR as an ILP system, and we build on this work to provide a full description here. HR performs a novel ILP routine called Automated Theory Formation, which combines inductive and deductive reasoning to form clausal theories consisting of classification rules and association rules. HR generates definitions using a set of production rules, interprets the definitions as classification rules, then uses the success sets of the definitions to induce hypotheses from which it extracts association rules. It uses third party theorem provers and model generators to check whether the association rules are entailed by a set of user supplied axioms. HR has been applied successfully to a number of predictive, descriptive and subgroup discovery tasks in domains of pure mathematics. We survey various applications of HR which have led to it producing number theory results worthy of journal publication, graph theory results rivalling those of the highly successful Graffiti program and algebraic results leading to novel classification theorems. To further promote mathematics as a challenge domain for ILP systems, we present the first application of Progol to an algebraic domain—we use Progol to find algebraic properties of quasigroups, semigroups and magmas (groupoids) of varying sizes which differentiate pairs of non-isomorphic objects. This development is particularly interesting because algebraic domains have been an important proving ground for both deduction systems and constraint solvers. We believe that AI programs written for discovery tasks will need to simultaneously employ a variety of reasoning techniques such as induction, abduction, deduction, calculation and invention. We argue that mathematics is not only a challenging domain for the application of ILP systems, but that mathematics could be a good domain in which to develop a new generation of systems which integrate various reasoning techniques. }, keywords = {}, pubstate = {published}, tppubtype = {article} } The application of Inductive Logic Programming to scientific datasets has been highly successful. Such applications have led to breakthroughs in the domain of interest and have driven the development of ILP systems. The application of AI techniques to mathemat- ical discovery tasks, however, has largely involved computer algebra systems and theorem provers rather than machine learning systems. We discuss here the application of the HR and Progol machine learning programs to discovery tasks in mathematics. While Progol is an established ILP system, HR has historically not been described as an ILP system. However, many applications of HR have required the production of first order hypotheses given data expressed in a Prolog-style manner, and the core functionality of HR can be expressed in ILP terminology. In Colton (2003), we presented the first partial description of HR as an ILP system, and we build on this work to provide a full description here. HR performs a novel ILP routine called Automated Theory Formation, which combines inductive and deductive reasoning to form clausal theories consisting of classification rules and association rules. HR generates definitions using a set of production rules, interprets the definitions as classification rules, then uses the success sets of the definitions to induce hypotheses from which it extracts association rules. It uses third party theorem provers and model generators to check whether the association rules are entailed by a set of user supplied axioms. HR has been applied successfully to a number of predictive, descriptive and subgroup discovery tasks in domains of pure mathematics. We survey various applications of HR which have led to it producing number theory results worthy of journal publication, graph theory results rivalling those of the highly successful Graffiti program and algebraic results leading to novel classification theorems. To further promote mathematics as a challenge domain for ILP systems, we present the first application of Progol to an algebraic domain—we use Progol to find algebraic properties of quasigroups, semigroups and magmas (groupoids) of varying sizes which differentiate pairs of non-isomorphic objects. This development is particularly interesting because algebraic domains have been an important proving ground for both deduction systems and constraint solvers. We believe that AI programs written for discovery tasks will need to simultaneously employ a variety of reasoning techniques such as induction, abduction, deduction, calculation and invention. We argue that mathematics is not only a challenging domain for the application of ILP systems, but that mathematics could be a good domain in which to develop a new generation of systems which integrate various reasoning techniques. |
Colton, Simon The HR program for theorem generation Inproceedings In: International Conference on Automated Deduction, pp. 285–289, Springer 2002. @inproceedings{colton2002hr, title = {The HR program for theorem generation}, author = { Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/07/colton_cade02.pdf}, year = {2002}, date = {2002-01-01}, booktitle = {International Conference on Automated Deduction}, pages = {285--289}, organization = {Springer}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } |
Colton, Simon An application-based comparison of ATF and ILP Journal Article In: Electron. Trans. Artif. Intell., 4 (B), pp. 97–117, 2000, ISSN: 1401-9841. @article{colton2000application, title = {An application-based comparison of ATF and ILP}, author = { Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/07/colton_etai00.pdf}, issn = {1401-9841}, year = {2000}, date = {2000-01-01}, journal = {Electron. Trans. Artif. Intell.}, volume = {4}, number = {B}, pages = {97--117}, abstract = {Automated theory formation involves the production of exam- ples, concepts and hypotheses. The HR program performs au- tomated theory formation and has been used to form theories in mathematical domains. In addition to providing a plausible model for automated theory formation, HR has been applied to some applications in machine learning. We discuss HR’s applica- tion to inducing definitions from examples, scientific discovery, problem solving and puzzle generation. For each problem, we look at how theory formation was applied, and mention some initial results from using HR. Our aim is not to describe the applications in great detail, but rather to provide an overview of how HR is used for these prob- lems. We do this to facilitate a comparison of HR and the Progol Inductive Logic Programming program. We compare both the concept formation these programs perform and by how they are (or could be) applied to the four problems discussed.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Automated theory formation involves the production of exam- ples, concepts and hypotheses. The HR program performs au- tomated theory formation and has been used to form theories in mathematical domains. In addition to providing a plausible model for automated theory formation, HR has been applied to some applications in machine learning. We discuss HR’s applica- tion to inducing definitions from examples, scientific discovery, problem solving and puzzle generation. For each problem, we look at how theory formation was applied, and mention some initial results from using HR. Our aim is not to describe the applications in great detail, but rather to provide an overview of how HR is used for these prob- lems. We do this to facilitate a comparison of HR and the Progol Inductive Logic Programming program. We compare both the concept formation these programs perform and by how they are (or could be) applied to the four problems discussed. |
Colton, Simon; Bundy, Alan; Walsh, Toby Automatic identification of mathematical concepts Inproceedings In: ICML, pp. 183–190, 2000. @inproceedings{colton2000automatic, title = {Automatic identification of mathematical concepts}, author = { Simon Colton and Alan Bundy and Toby Walsh}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/07/colton_icml00.pdf}, year = {2000}, date = {2000-01-01}, booktitle = {ICML}, pages = {183--190}, abstract = {The HR program by Colton et al. (1999) performs theory formation in mathematics by exploring a space of mathematical concepts. By enabling HR to determine when it has found a particular concept, and by adding a forward looking mechanism, we have applied HR to the problem of identifying mathematical concepts. We illustrate this by using HR to identify and extrapolate integer sequences and by performing a qualitative comparison with the machine learning program Progol.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } The HR program by Colton et al. (1999) performs theory formation in mathematics by exploring a space of mathematical concepts. By enabling HR to determine when it has found a particular concept, and by adding a forward looking mechanism, we have applied HR to the problem of identifying mathematical concepts. We illustrate this by using HR to identify and extrapolate integer sequences and by performing a qualitative comparison with the machine learning program Progol. |
Colton, Simon; Bundy, Alan; Walsh, Toby Automatic concept formation in pure mathematics Inproceedings In: Proceedings of IJCAI, 1999. @inproceedings{colton1999automatic, title = {Automatic concept formation in pure mathematics}, author = { Simon Colton and Alan Bundy and Toby Walsh}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/07/colton_ijcai99.pdf}, year = {1999}, date = {1999-01-01}, booktitle = {Proceedings of IJCAI}, journal = {IJCAI}, abstract = {The HR program forms concepts and makes conjectures in domains of pure mathematics and uses theorem prover OTTER and model generator MACE to prove or disprove the conjectures. HR measures properties of concepts and assesses the theorems and proofs involving them to estimate the interestingness of each concepts and employ a best first search. This approach has led HR to the discovery of interesting new mathematics and enables it to build theories from just the axioms of finite algebras.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } The HR program forms concepts and makes conjectures in domains of pure mathematics and uses theorem prover OTTER and model generator MACE to prove or disprove the conjectures. HR measures properties of concepts and assesses the theorems and proofs involving them to estimate the interestingness of each concepts and employ a best first search. This approach has led HR to the discovery of interesting new mathematics and enables it to build theories from just the axioms of finite algebras. |
Colton, Simon HR-automatic concept formation in finite algebras Inproceedings In: AAAI/IAAI, pp. 1170, Technical Report 920,(Presented at the Machine Discovery Workshop at ECAI 98) Department of Artificial Intelligence, University of Edinburgh 1998. @inproceedings{colton1998hrb, title = {HR-automatic concept formation in finite algebras}, author = { Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/07/colton_aaai98.pdf}, year = {1998}, date = {1998-01-01}, booktitle = {AAAI/IAAI}, pages = {1170}, organization = {Technical Report 920,(Presented at the Machine Discovery Workshop at ECAI 98) Department of Artificial Intelligence, University of Edinburgh}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } |
Bundy, Alan; Colton, Simon; Walsh, Toby HR-a system for machine discovery in finite algebras Inproceedings In: Proceedings of the Machine Discovery Workshop at ECAI, Citeseer, 1998. @inproceedings{bundy1998hr, title = {HR-a system for machine discovery in finite algebras}, author = { Alan Bundy and Simon Colton and Toby Walsh}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/07/bundy_ecai98.pdf}, year = {1998}, date = {1998-01-01}, booktitle = {Proceedings of the Machine Discovery Workshop at ECAI}, journal = {DAI RESEARCH PAPER}, publisher = {Citeseer}, abstract = {We describe the HR concept formation program which invents mathematical definitions and conjectures in finite algebras such as group theory and ring theory. We give the methods behind and the reasons for the concept formation in HR, an evaluation of its performance in its training domain, group theory, and a look at HR in domains other than group theory.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We describe the HR concept formation program which invents mathematical definitions and conjectures in finite algebras such as group theory and ring theory. We give the methods behind and the reasons for the concept formation in HR, an evaluation of its performance in its training domain, group theory, and a look at HR in domains other than group theory. |
Colton, Simon; Cresswell, Stephen; Bundy, Alan The use of classification in automated mathematical concept formation Book University of Edinburgh, Department of Artificial Intelligence, 1997. @book{colton1997use, title = {The use of classification in automated mathematical concept formation}, author = { Simon Colton and Stephen Cresswell and Alan Bundy}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/07/colton_simcat97.pdf}, year = {1997}, date = {1997-01-01}, publisher = {University of Edinburgh, Department of Artificial Intelligence}, organization = {Citeseer}, abstract = {Concept formation programs aim to produce a high yield of concepts which are considered interesting. One intelligent way to do this is to base a new concept on one or more concepts which are already known to be interesting. This requires a concrete notion of the ‘interestingness’ of a particular concept. Restricting the concepts formed to mathematical definitions in finite group theory, we derive three measures of the interest- ingness of a concept. These measures are based on how much the concept improves a classification of finite groups.}, keywords = {}, pubstate = {published}, tppubtype = {book} } Concept formation programs aim to produce a high yield of concepts which are considered interesting. One intelligent way to do this is to base a new concept on one or more concepts which are already known to be interesting. This requires a concrete notion of the ‘interestingness’ of a particular concept. Restricting the concepts formed to mathematical definitions in finite group theory, we derive three measures of the interest- ingness of a concept. These measures are based on how much the concept improves a classification of finite groups. |
More Sophisticated Mathematical Theory Formation Models
We have taken Automated Theory Formation as the basis for more in-depth studies into how mathematical theories can be formed automatically. In addition to providing extensions to the basic automated theory formation model and providing more background to the subject, these projects have led to more sophisticated systems for mathematical invention and machine learning in general, which take into account philosophical and psychological perspectives on theory formation. The following papers describe some of our projects in this area:
Schorlemmer, Marco; Smaill, Alan; Kühnberger, Kai-Uwe; Kutz, Oliver; Colton, Simon; Cambouropoulos, Emilios; Pease, Alison COINVENT: Towards a Computational Concept Invention Theory Inproceedings In: Proceedings of the Fifth International Conference on Computational Creativity, 2014. @inproceedings{schorlemmer2014coinvent, title = {COINVENT: Towards a Computational Concept Invention Theory}, author = { Marco Schorlemmer and Alan Smaill and Kai-Uwe Kühnberger and Oliver Kutz and Simon Colton and Emilios Cambouropoulos and Alison Pease}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/shorlemmer_iccc2014.pdf}, year = {2014}, date = {2014-01-01}, booktitle = {Proceedings of the Fifth International Conference on Computational Creativity}, journal = {ICCC}, abstract = {We aim to develop a computationally feasible, cognitively- inspired, formal model of concept invention, drawing on Fauconnier and Turner’s theory of conceptual blending, and grounding it on a sound mathematical theory of concepts. Conceptual blending, although successfully applied to de- scribing combinational creativity in a varied number of fields, has barely been used at all for implementing creative compu- tational systems, mainly due to the lack of sufficiently precise mathematical characterisations thereof. The model we will define will be based on Goguen’s proposal of a Unified Con- cept Theory, and will draw from interdisciplinary research results from cognitive science, artificial intelligence, formal methods and computational creativity. To validate our model, we will implement a proof of concept of an autonomous computational creative system that will be evaluated in two testbed scenarios: mathematical reasoning and melodic har- monisation. We envisage that the results of this project will be significant for gaining a deeper scientific understanding of creativity, for fostering the synergy between understand- ing and enhancing human creativity, and for developing new technologies for autonomous creative systems.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We aim to develop a computationally feasible, cognitively- inspired, formal model of concept invention, drawing on Fauconnier and Turner’s theory of conceptual blending, and grounding it on a sound mathematical theory of concepts. Conceptual blending, although successfully applied to de- scribing combinational creativity in a varied number of fields, has barely been used at all for implementing creative compu- tational systems, mainly due to the lack of sufficiently precise mathematical characterisations thereof. The model we will define will be based on Goguen’s proposal of a Unified Con- cept Theory, and will draw from interdisciplinary research results from cognitive science, artificial intelligence, formal methods and computational creativity. To validate our model, we will implement a proof of concept of an autonomous computational creative system that will be evaluated in two testbed scenarios: mathematical reasoning and melodic har- monisation. We envisage that the results of this project will be significant for gaining a deeper scientific understanding of creativity, for fostering the synergy between understand- ing and enhancing human creativity, and for developing new technologies for autonomous creative systems. |
Colton, Simon; Charnley, John; Pease, Alison Automated Theory Formation: The Next Generation Journal Article In: IFCOLOG Journal Proceedings in Computational Logic, 2013. @article{pease2013automated, title = {Automated Theory Formation: The Next Generation}, author = {Simon Colton and John Charnley and Alison Pease}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_ifcolog15.pdf}, year = {2013}, date = {2013-01-01}, journal = {IFCOLOG Journal Proceedings in Computational Logic}, abstract = {Automated Theory Formation was introduced as a compu- tational model for how mathematical theories could be formed from the bare minimum such as a set of axioms or some background concepts in a domain of pure mathematics such as group theory, graph theory or num- ber theory. The approach consists of using production rules to form new concepts from old ones, and employing a set of measures of interesting- ness to drive a heuristic search. Empirical pattern-based conjecture mak- ing techniques are used to find relationships between concepts, and third party automated reasoning systems are employed to prove the truth of the conjectures or find counterexamples. Automated Theory Formation has been applied to a number of discovery tasks which have led to the publication of mathematical results in the literature. In recent years, the approach has been extended, improved and generalised. This has been done via appeals to the philosophy of mathematics, namely Lakatos’s suggestions in the book Proofs and Refutations describing ways in which mathematicians find and respond to counterexamples, using them to evolve concepts, conjectures and proofs within a mathematical theory. The resulting computational approach extends Automated Theory For- mation by modelling ways in which mathematicians discuss counterex- amples and their implications for the conjecture at hand. The recent extensions also appeal to cognitive science results, in particular Baar’s suggestions in the Global Workspace Architecture theory of mammalian consciousness. The resulting computational approach involves configur- ing a framework for the combination of reasoning systems leading to more sophisticated and applied theory formation approaches. We sur- vey these extensions here, in addition to other projects that have added to our understanding of Automated Theory Formation. We also frame these approaches within a broader picture, specifically with reference to Mathematical Theory Exploration approaches. We end with a discussion of future applications and extensions of Automated Theory Formation.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Automated Theory Formation was introduced as a compu- tational model for how mathematical theories could be formed from the bare minimum such as a set of axioms or some background concepts in a domain of pure mathematics such as group theory, graph theory or num- ber theory. The approach consists of using production rules to form new concepts from old ones, and employing a set of measures of interesting- ness to drive a heuristic search. Empirical pattern-based conjecture mak- ing techniques are used to find relationships between concepts, and third party automated reasoning systems are employed to prove the truth of the conjectures or find counterexamples. Automated Theory Formation has been applied to a number of discovery tasks which have led to the publication of mathematical results in the literature. In recent years, the approach has been extended, improved and generalised. This has been done via appeals to the philosophy of mathematics, namely Lakatos’s suggestions in the book Proofs and Refutations describing ways in which mathematicians find and respond to counterexamples, using them to evolve concepts, conjectures and proofs within a mathematical theory. The resulting computational approach extends Automated Theory For- mation by modelling ways in which mathematicians discuss counterex- amples and their implications for the conjecture at hand. The recent extensions also appeal to cognitive science results, in particular Baar’s suggestions in the Global Workspace Architecture theory of mammalian consciousness. The resulting computational approach involves configur- ing a framework for the combination of reasoning systems leading to more sophisticated and applied theory formation approaches. We sur- vey these extensions here, in addition to other projects that have added to our understanding of Automated Theory Formation. We also frame these approaches within a broader picture, specifically with reference to Mathematical Theory Exploration approaches. We end with a discussion of future applications and extensions of Automated Theory Formation. |
Cavallo, Flaminia; Colton, Simon; Pease, Alison Uncertainty Modelling in Automated Concept Formation Inproceedings In: Proceedings of the Automated Reasoning Workshop, pp. 53, Citeseer, 2012. @inproceedings{cavallo2012uncertainty, title = {Uncertainty Modelling in Automated Concept Formation}, author = { Flaminia Cavallo and Simon Colton and Alison Pease}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/cavallo_arw12.pdf}, year = {2012}, date = {2012-01-01}, booktitle = {Proceedings of the Automated Reasoning Workshop}, journal = {ARW 2012}, pages = {53}, publisher = {Citeseer}, abstract = {Categorisation and classification are areas that have been well studied in machine learning. How- ever, the use of cognitive theories in psychology as a basis to implement a category formation system designed for creative purposes and based on human behaviour is still largely unexplored. Our aim in this project is to verify how some of the ideas on uncertainty and ambiguity in classification could influence concept classifica- tion in an automated theory formation system.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Categorisation and classification are areas that have been well studied in machine learning. How- ever, the use of cognitive theories in psychology as a basis to implement a category formation system designed for creative purposes and based on human behaviour is still largely unexplored. Our aim in this project is to verify how some of the ideas on uncertainty and ambiguity in classification could influence concept classifica- tion in an automated theory formation system. |
Pease, Alison; Smaill, Alan; Colton, Simon; Ireland, Andrew; Llano, Maria Teresa; Ramezani, Ramin; Grov, Gudmund; Guhe, Markus Applying Lakatos-style reasoning to AI problems Book Chapter In: Thinking Machines and the philosophy of computer science: Concepts and principles., Chapter 10, pp. 149–174, Information Science Reference, 2010, ISBN: 9781616920142. @inbook{pease2010applying, title = {Applying Lakatos-style reasoning to AI problems}, author = {Alison Pease and Alan Smaill and Simon Colton and Andrew Ireland and Maria Teresa Llano and Ramin Ramezani and Gudmund Grov and Markus Guhe}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/pease_tm10-1.pdf}, doi = {10.4018/978-1-61692-014-2.ch010}, isbn = {9781616920142}, year = {2010}, date = {2010-01-01}, booktitle = {Thinking Machines and the philosophy of computer science: Concepts and principles.}, journal = {Thinking Machines and the philosophy of computer science: Concepts and principles}, pages = {149--174}, publisher = {Information Science Reference}, chapter = {10}, abstract = {One current direction in AI research is to focus on combining different reasoning styles such as deduction, induction, abduction, analogical reasoning, non-monotonic reasoning, vague and uncertain reasoning. The philosopher Imre Lakatos produced one such theory of how people with different reasoning styles collaborate to develop mathematical ideas. Lakatos argued that mathematics is a quasi-empirical, flexible, fallible, human endeavour, involving negotiations, mistakes, vague concept definitions and disagreements, and he outlined a heuristic approach towards the subject. In this chapter we apply these heuristics to the AI domains of evolving requirement specifi- cations, planning and constraint satisfaction problems. In drawing analogies between Lakatos’s theory and these three domains we identify areas of work which correspond to each heuristic, and suggest extensions and further ways in which Lakatos’s philoso- phy can inform AI problem solving. Thus, we show how we might begin to produce a philosophically-inspired AI theory of combined reasoning.}, keywords = {}, pubstate = {published}, tppubtype = {inbook} } One current direction in AI research is to focus on combining different reasoning styles such as deduction, induction, abduction, analogical reasoning, non-monotonic reasoning, vague and uncertain reasoning. The philosopher Imre Lakatos produced one such theory of how people with different reasoning styles collaborate to develop mathematical ideas. Lakatos argued that mathematics is a quasi-empirical, flexible, fallible, human endeavour, involving negotiations, mistakes, vague concept definitions and disagreements, and he outlined a heuristic approach towards the subject. In this chapter we apply these heuristics to the AI domains of evolving requirement specifi- cations, planning and constraint satisfaction problems. In drawing analogies between Lakatos’s theory and these three domains we identify areas of work which correspond to each heuristic, and suggest extensions and further ways in which Lakatos’s philoso- phy can inform AI problem solving. Thus, we show how we might begin to produce a philosophically-inspired AI theory of combined reasoning. |
Pease, Alison; Colton, Simon; Ramezani, Ramin; Smaill, Alan; Guhe, Markus Using Analogical Representations for Mathematical Concept Formation Incollection In: Model-Based Reasoning in Science and Technology, 314 , pp. 301–314, Springer Berlin Heidelberg, 2010, ISBN: 978-3-642-15222-1. @incollection{pease2010using, title = {Using Analogical Representations for Mathematical Concept Formation}, author = { Alison Pease and Simon Colton and Ramin Ramezani and Alan Smaill and Markus Guhe}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/pease_mbr10.pdf}, doi = {10.1007/978-3-642-15223-8}, isbn = {978-3-642-15222-1}, year = {2010}, date = {2010-01-01}, booktitle = {Model-Based Reasoning in Science and Technology}, volume = {314}, pages = {301--314}, publisher = {Springer Berlin Heidelberg}, abstract = {We argue that visual, analogical representations of mathematical concepts can be used by automated theory formation systems to develop fur- ther concepts and conjectures in mathematics. We consider the role of visual reasoning in human development of mathematics, and consider some aspects of the relationship between mathematics and the visual, including artists us- ing mathematics as inspiration for their art (which may then feed back into mathematical development), the idea of using visual beauty to evaluate math- ematics, mathematics which is visually pleasing, and ways of using the visual to develop mathematical concepts. We motivate an analogical representation of number types with examples of “visual” concepts and conjectures, and present an automated case study in which we enable an automated theory formation program to read this type of visual, analogical representation.}, keywords = {}, pubstate = {published}, tppubtype = {incollection} } We argue that visual, analogical representations of mathematical concepts can be used by automated theory formation systems to develop fur- ther concepts and conjectures in mathematics. We consider the role of visual reasoning in human development of mathematics, and consider some aspects of the relationship between mathematics and the visual, including artists us- ing mathematics as inspiration for their art (which may then feed back into mathematical development), the idea of using visual beauty to evaluate math- ematics, mathematics which is visually pleasing, and ways of using the visual to develop mathematical concepts. We motivate an analogical representation of number types with examples of “visual” concepts and conjectures, and present an automated case study in which we enable an automated theory formation program to read this type of visual, analogical representation. |
Colton, Simon Three Next Generation Approaches to Automated Mathematical Theory Formation Inproceedings In: Proceedings of the Model Based Reasoning Conference, 2009. @inproceedings{Colton2009, title = {Three Next Generation Approaches to Automated Mathematical Theory Formation}, author = {Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_mbr09.pdf}, year = {2009}, date = {2009-08-01}, booktitle = {Proceedings of the Model Based Reasoning Conference}, abstract = {Around a decade ago, we introduced Automated Theory Formation as a technique for mathematical discovery, implemented in the HR system. Starting with some basic background information such as a set of axioms for an algebraic domain, or fundamental concepts such as addition and multiplication in number theory, HR forms concepts which categorise the examples; makes conjectures which relate the concepts; and generates proofs which explain the conjectures (or counterexamples which disprove them). In addition to inventing concepts and discovering theorems which have been published in the mathematical literature, HR has been applied successfully to AI tasks including constraint solving and machine learning. In the talk, I will describe three PhD projects which have been influenced by the Automated Theory Formation approach.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Around a decade ago, we introduced Automated Theory Formation as a technique for mathematical discovery, implemented in the HR system. Starting with some basic background information such as a set of axioms for an algebraic domain, or fundamental concepts such as addition and multiplication in number theory, HR forms concepts which categorise the examples; makes conjectures which relate the concepts; and generates proofs which explain the conjectures (or counterexamples which disprove them). In addition to inventing concepts and discovering theorems which have been published in the mathematical literature, HR has been applied successfully to AI tasks including constraint solving and machine learning. In the talk, I will describe three PhD projects which have been influenced by the Automated Theory Formation approach. |
Torres, Pedro; Colton, Simon First-Order Logic Concept Symmetry for Theory Formation Inproceedings In: Automated Reasoning Workshop 2009 Bridging the Gap between Theory and Practice, pp. 41, 2009. @inproceedings{torres2009first, title = {First-Order Logic Concept Symmetry for Theory Formation}, author = { Pedro Torres and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/torres_arw09.pdf}, year = {2009}, date = {2009-01-07}, booktitle = {Automated Reasoning Workshop 2009 Bridging the Gap between Theory and Practice}, pages = {41}, abstract = {SURICATA (Torres and Colton, 2008) is a hybrid automated theory formation system which uses both production rules and structured language biased search to produce new concepts and make conjectures about those concepts. The idea of implementing a highly-configurable theory formation system able to work with arbitrary first-order production rules started from the observation that it was helpful for users of automated theory formation systems to be able to define their own production rules. We implemented a generic first-order production rule (Torres and Colton, 2006) for the HR system (Colton, 2002) and showed how new user-defined production rules led to the discovery of novel conjectures in quasigroup theory.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } SURICATA (Torres and Colton, 2008) is a hybrid automated theory formation system which uses both production rules and structured language biased search to produce new concepts and make conjectures about those concepts. The idea of implementing a highly-configurable theory formation system able to work with arbitrary first-order production rules started from the observation that it was helpful for users of automated theory formation systems to be able to define their own production rules. We implemented a generic first-order production rule (Torres and Colton, 2006) for the HR system (Colton, 2002) and showed how new user-defined production rules led to the discovery of novel conjectures in quasigroup theory. |
Pease, Alison; Crook, Paul; Smaill, Alan; Colton, Simon; Guhe, Markus Towards a Computational Model of Embodied Mathematical Language Book Chapter In: Proceedings of the Second Symposium on Computing and Philosophy, pp. 35–37, Society for the Study of Artificial Intelligence and Simulation of Behaviour, 2009, ISBN: 1902956826. @inbook{Pease2009, title = {Towards a Computational Model of Embodied Mathematical Language}, author = { Alison Pease and Paul Crook and Alan Smaill and Simon Colton and Markus Guhe}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/pease_aisb09.pdf}, isbn = {1902956826}, year = {2009}, date = {2009-01-01}, booktitle = {Proceedings of the Second Symposium on Computing and Philosophy}, pages = {35--37}, publisher = {Society for the Study of Artificial Intelligence and Simulation of Behaviour}, abstract = {We outline two theories of mathematical language acquisition and development, and discuss how a computational model of these theories may help to bridge the gap between automated theory formation and situated embodied agents. Finally, we briefly describe a simple theoretical case study of how such a model could work in the arithmetic domain.}, keywords = {}, pubstate = {published}, tppubtype = {inbook} } We outline two theories of mathematical language acquisition and development, and discuss how a computational model of these theories may help to bridge the gap between automated theory formation and situated embodied agents. Finally, we briefly describe a simple theoretical case study of how such a model could work in the arithmetic domain. |
Torres, Pedro; Colton, Simon Automated Meta-Theory Induction in Pure Mathematics Incollection In: Proceedings of the 2008 Automated Reasoning Workshop, 8 , Citeseer, 2008. @incollection{torres2008automated, title = {Automated Meta-Theory Induction in Pure Mathematics}, author = { Pedro Torres and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/torres_arw08.pdf}, year = {2008}, date = {2008-01-01}, booktitle = {Proceedings of the 2008 Automated Reasoning Workshop}, journal = {Proceedings of ARW}, volume = {8}, publisher = {Citeseer}, abstract = {HR [1] is an Automated Theory Formation (ATF) system which has been described as a Descriptive Inductive Logic Programming system [4]. Given a set of initial concepts, each provided with a definition and a set of examples, HR forms a theory about them. HR uses a set of production rules to form new concepts and forms conjectures according to the examples it finds for new concepts.}, keywords = {}, pubstate = {published}, tppubtype = {incollection} } HR [1] is an Automated Theory Formation (ATF) system which has been described as a Descriptive Inductive Logic Programming system [4]. Given a set of initial concepts, each provided with a definition and a set of examples, HR forms a theory about them. HR uses a set of production rules to form new concepts and forms conjectures according to the examples it finds for new concepts. |
Colton, Simon; Wagner, Daniel Using Formal Concept Analysis in Mathematical Discovery Incollection In: Towards Mechanized Mathematical Assistants, pp. 205–220, Springer, 2007. @incollection{colton2007using, title = {Using Formal Concept Analysis in Mathematical Discovery}, author = { Simon Colton and Daniel Wagner}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_mkm07.pdf}, year = {2007}, date = {2007-01-01}, booktitle = {Towards Mechanized Mathematical Assistants}, pages = {205--220}, publisher = {Springer}, abstract = {Formal concept analysis (FCA) comprises a set of powerful algorithms which can be used for data analysis and manipulation, and a set of visualisation tools which enable the discovery of meaningful re- lationships between attributes of the data. We explore the potential of combining FCA and mathematical discovery tools in order to better fa- cilitate discovery tasks. In particular, we propose a novel lookup method for the Encyclopedia of Integer Sequences, and we show how conjectures from the Graffiti discovery program can be better understood using FCA visualisation tools. We argue that, not only can FCA tools greatly en- hance the management and visualisation of mathematical knowledge, but they can also be used to drive exploratory processes.}, keywords = {}, pubstate = {published}, tppubtype = {incollection} } Formal concept analysis (FCA) comprises a set of powerful algorithms which can be used for data analysis and manipulation, and a set of visualisation tools which enable the discovery of meaningful re- lationships between attributes of the data. We explore the potential of combining FCA and mathematical discovery tools in order to better fa- cilitate discovery tasks. In particular, we propose a novel lookup method for the Encyclopedia of Integer Sequences, and we show how conjectures from the Graffiti discovery program can be better understood using FCA visualisation tools. We argue that, not only can FCA tools greatly en- hance the management and visualisation of mathematical knowledge, but they can also be used to drive exploratory processes. |
Torres, Pedro; Colton, Simon Proving Producibility of Concepts Journal Article In: 2007. @article{producibilityproving, title = {Proving Producibility of Concepts}, author = {Pedro Torres and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/torres_arw07.pdf}, year = {2007}, date = {2007-01-01}, publisher = {Citeseer}, abstract = {In a previous study (Torres and Colton, 2006a), we presented a general framework for using model generation to implement generic first-order production rules. We have taken this idea one step further by designing a general automated theory formation system which is able to deal with arbitrary sets of first-order production rules. In the same study, we also sketched a method of backwards proof to prove concept producibility which we will here put to practice. In this workshop we will address both unsolved problems mentioned above by (i) presenting an algorithm for proving producibility of concepts by our theory formation system and (ii) putting forward ideas on how this algorithm may be useful to induce production rules from examples of produced concepts.}, keywords = {}, pubstate = {published}, tppubtype = {article} } In a previous study (Torres and Colton, 2006a), we presented a general framework for using model generation to implement generic first-order production rules. We have taken this idea one step further by designing a general automated theory formation system which is able to deal with arbitrary sets of first-order production rules. In the same study, we also sketched a method of backwards proof to prove concept producibility which we will here put to practice. In this workshop we will address both unsolved problems mentioned above by (i) presenting an algorithm for proving producibility of concepts by our theory formation system and (ii) putting forward ideas on how this algorithm may be useful to induce production rules from examples of produced concepts. |
Torres, Pedro; Colton, Simon Towards Meta-Level Descriptive ILP Inproceedings In: Proceedings of the 16th International Conference on Inductive Logic Programming, 2006. @inproceedings{torres2006towards, title = {Towards Meta-Level Descriptive ILP}, author = { Pedro Torres and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/torres_ilp06poster.pdf}, year = {2006}, date = {2006-01-01}, booktitle = {Proceedings of the 16th International Conference on Inductive Logic Programming}, abstract = {We introduce a formal setting for a first-order production rule approach to descriptive learning and we consider searching for sets of production rules as opposed to a direct search for concepts. We sketch the Parrot algorithm which generates a basic set of production rules capable of producing a set of user-given concepts and present some pre- liminary ideas on how to enrich this set.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We introduce a formal setting for a first-order production rule approach to descriptive learning and we consider searching for sets of production rules as opposed to a direct search for concepts. We sketch the Parrot algorithm which generates a basic set of production rules capable of producing a set of user-given concepts and present some pre- liminary ideas on how to enrich this set. |
Colton, Simon; Torres, Pedro; Cairns, Paul; Sorge, Volker Managing Automatically Formed Mathematical Theories Inproceedings In: International Conference on Mathematical Knowledge Management, pp. 237–250, Springer 2006. @inproceedings{colton2006managing, title = {Managing Automatically Formed Mathematical Theories}, author = { Simon Colton and Pedro Torres and Paul Cairns and Volker Sorge}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_mkm06.pdf}, year = {2006}, date = {2006-01-01}, booktitle = {International Conference on Mathematical Knowledge Management}, pages = {237--250}, organization = {Springer}, abstract = {The HR system forms scientific theories, and has found par- ticularly successful application in domains of pure mathematics. Starting with only the axioms of an algebraic system, HR can generate dozens of example algebras, hundreds of concepts and thousands of conjectures, many of which have first order proofs. Given the overwhelming amount of knowledge produced, we have provided HR with sophisticated tools for handling this data. We present here the first full description of these management tools. Moreover, we describe how careful analysis of the theories produced by HR – which is enabled by the management tools – has led us to make interesting discoveries in algebraic domains. We demonstrate this with some illustrative results from HR’s theories about an algebra of one axiom. The results fueled further developments, and led us to discover and prove a fundamental theorem about this domain.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } The HR system forms scientific theories, and has found par- ticularly successful application in domains of pure mathematics. Starting with only the axioms of an algebraic system, HR can generate dozens of example algebras, hundreds of concepts and thousands of conjectures, many of which have first order proofs. Given the overwhelming amount of knowledge produced, we have provided HR with sophisticated tools for handling this data. We present here the first full description of these management tools. Moreover, we describe how careful analysis of the theories produced by HR – which is enabled by the management tools – has led us to make interesting discoveries in algebraic domains. We demonstrate this with some illustrative results from HR’s theories about an algebra of one axiom. The results fueled further developments, and led us to discover and prove a fundamental theorem about this domain. |
Torres, Pedro; Colton, Simon Using Model Generation in Automated Concept Formation Inproceedings In: Proceedings of the Automated Reasoning Workshop, pp. 41, Citeseer, 2006. @inproceedings{torres2006using, title = {Using Model Generation in Automated Concept Formation}, author = { Pedro Torres and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/torres_arw06.pdf}, year = {2006}, date = {2006-01-01}, booktitle = {Proceedings of the Automated Reasoning Workshop}, journal = {Specification and Verification of Reconfiguration Protocols in Grid Component Systems}, pages = {41}, publisher = {Citeseer}, abstract = {HR (Colton, 2002) is an Automated Theory Formation (ATF) system which makes extensive use of automated reasoning tools, in particular, the Otter theorem prover (McCune, 1990) and MACE model generator (McCune, 1994). Given a set of initial concepts, each provided with a definition and a set of examples, HR forms a theory about them. HR uses a set of production rules to form new concepts and forms conjectures according to the examples it finds for new concepts. For instance, if the set of examples for the new concept is contained in the set of examples of some old concept, an implication conjecture is generated. Similarly, equivalence and non-existence conjectures can be made. We present here a general first order setting for concept production in ATF, explain a recently implemented user-customisable generic production rule, and report on results in pure mathematics obtained using the new rule. The new concept production method make novel use of MACE, thus extending the combination of reasoning techniques employed in theory formation.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } HR (Colton, 2002) is an Automated Theory Formation (ATF) system which makes extensive use of automated reasoning tools, in particular, the Otter theorem prover (McCune, 1990) and MACE model generator (McCune, 1994). Given a set of initial concepts, each provided with a definition and a set of examples, HR forms a theory about them. HR uses a set of production rules to form new concepts and forms conjectures according to the examples it finds for new concepts. For instance, if the set of examples for the new concept is contained in the set of examples of some old concept, an implication conjecture is generated. Similarly, equivalence and non-existence conjectures can be made. We present here a general first order setting for concept production in ATF, explain a recently implemented user-customisable generic production rule, and report on results in pure mathematics obtained using the new rule. The new concept production method make novel use of MACE, thus extending the combination of reasoning techniques employed in theory formation. |
Pease, Alison; Colton, Simon; Smaill, Alan; Lee, John A Model of Lakatos’s Philosophy of Mathematics Book College Publications, 2004. @book{pease2004model, title = {A Model of Lakatos’s Philosophy of Mathematics}, author = { Alison Pease and Simon Colton and Alan Smaill and John Lee}, editor = {Lorenzo Magnani and Riccardo Dossena}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/pease_ecap04.pdf}, year = {2004}, date = {2004-01-01}, booktitle = {Computing, Philosophy and Cognition}, publisher = {College Publications}, series = {Texts in philosophy}, abstract = {Lakatos attacked the view that mathematical knowledge is timeless, certain and a priori (Lakatos, 1976). Lakatos's work in the philosophy of mathematics is a controversial mathematical analogy of Hume's problem of induction combined with Popper's theory of falsification. That is, Lakatos both identified the problem of the impossibility of mathematical knowledge, and suggested a solution. His solution consisted of heuristic methods which guide the development of mathematical conjectures, concepts and proofs. These evolve through dialectic and analysis sparked by counterexamples. Counterexamples therefore, play a vital role in (Lakatos, 1976), though they are a starting, rather than finishing point: criticism has to be constructive if it is to be valuable. }, keywords = {}, pubstate = {published}, tppubtype = {book} } Lakatos attacked the view that mathematical knowledge is timeless, certain and a priori (Lakatos, 1976). Lakatos's work in the philosophy of mathematics is a controversial mathematical analogy of Hume's problem of induction combined with Popper's theory of falsification. That is, Lakatos both identified the problem of the impossibility of mathematical knowledge, and suggested a solution. His solution consisted of heuristic methods which guide the development of mathematical conjectures, concepts and proofs. These evolve through dialectic and analysis sparked by counterexamples. Counterexamples therefore, play a vital role in (Lakatos, 1976), though they are a starting, rather than finishing point: criticism has to be constructive if it is to be valuable. |
Colton, Simon; Pease, Alison Lakatos-style Methods in Automated Reasoning Inproceedings In: In Proceedings of the IJCAI’03 workshop on Agents and Reasoning, Citeseer 2003. @inproceedings{colton2003lakatos, title = {Lakatos-style Methods in Automated Reasoning}, author = { Simon Colton and Alison Pease}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_ijcai03_agents.pdf}, year = {2003}, date = {2003-01-01}, booktitle = {In Proceedings of the IJCAI’03 workshop on Agents and Reasoning}, organization = {Citeseer}, abstract = {We advocate increased flexibility in automated reasoning, whereby a reasoning agent is able to correct the statement of a given faulty conjec-ture in order to prove that the modified the-orem is true. Such alterations are common in mathematics. In particular, in his book 'Proofs and Refutations', Imre Lakatos prescribes var-ious techniques for the modification of a faulty conjecture within a social setting (a hypothe-sised mathematics class). This has inspired a multi-agent approach to automating Lakatos-style techniques, and we give details of the implementation of these methods within (and on top of) the HR automated theory forma-tion system. We report on the progress of this project and supply illustrative results from ses-sions using the enhanced system. }, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We advocate increased flexibility in automated reasoning, whereby a reasoning agent is able to correct the statement of a given faulty conjec-ture in order to prove that the modified the-orem is true. Such alterations are common in mathematics. In particular, in his book 'Proofs and Refutations', Imre Lakatos prescribes var-ious techniques for the modification of a faulty conjecture within a social setting (a hypothe-sised mathematics class). This has inspired a multi-agent approach to automating Lakatos-style techniques, and we give details of the implementation of these methods within (and on top of) the HR automated theory forma-tion system. We report on the progress of this project and supply illustrative results from ses-sions using the enhanced system. |
Bundy, Alan; Colton, Simon; Huczynska, Sophie; McCasland, Roy New Directions in Automated Conjecture Making Inproceedings In: Proceedings of the Automated Reasoning Workshop, 2003. @inproceedings{Bundy2003, title = {New Directions in Automated Conjecture Making}, author = {Alan Bundy and Simon Colton and Sophie Huczynska and Roy McCasland}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/bundy_arw03.pdf}, year = {2003}, date = {2003-01-01}, booktitle = {Proceedings of the Automated Reasoning Workshop}, abstract = {The HR system has been developed to form scientific theories automatically, with special application to mathematical conjecture making [1]. Two projects with HR are currently coming to an end and within both, there have been recent studies of the potential application of HR to research mathematics. These studies have led to some criticisms about the current limitations of HR and suggestions for improvements. Furthermore, a new project with a goal of extending HR in order to test its application to an area of research mathematics is about to start. Hence, now is a ideal time to look at these criticisms and recommendations and suggest directions for the future development of the system, which we do here. To appreciate the recommendations, we first give a brief overview of the theory formation HR undertakes. }, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } The HR system has been developed to form scientific theories automatically, with special application to mathematical conjecture making [1]. Two projects with HR are currently coming to an end and within both, there have been recent studies of the potential application of HR to research mathematics. These studies have led to some criticisms about the current limitations of HR and suggestions for improvements. Furthermore, a new project with a goal of extending HR in order to test its application to an area of research mathematics is about to start. Hence, now is a ideal time to look at these criticisms and recommendations and suggest directions for the future development of the system, which we do here. To appreciate the recommendations, we first give a brief overview of the theory formation HR undertakes. |
Pease, Alison; Colton, Simon; Smaill, Alan; Lee, John Semantic Negotiation: Modelling Ambiguity in Dialogue Inproceedings In: Proceedings of Edilog 2002, the 6th Workshop on the semantics and pragmatics of dialogue, 2002. @inproceedings{pease2002semantic, title = {Semantic Negotiation: Modelling Ambiguity in Dialogue}, author = { Alison Pease and Simon Colton and Alan Smaill and John Lee}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/pease_edilog02.pdf}, year = {2002}, date = {2002-01-01}, booktitle = {Proceedings of Edilog 2002, the 6th Workshop on the semantics and pragmatics of dialogue}, abstract = {We argue that negotiation over the meaning of terms in a statement is part of human discussion and that it can lead to richer theories. We describe our pre-liminary model of semantic negotiation and discuss theoretical examples which we hope to implement. Finally we consider how semantic negotiation fits into existing work on argumentation. }, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We argue that negotiation over the meaning of terms in a statement is part of human discussion and that it can lead to richer theories. We describe our pre-liminary model of semantic negotiation and discuss theoretical examples which we hope to implement. Finally we consider how semantic negotiation fits into existing work on argumentation. |
Pease, Alison; Colton, Simon; Smaill, Alan; Lee, John Lakatos-style Reasoning Book Chapter In: Proceedings of the Automated Reasoning Workshop, Imperial College, London, Society for the Study of Artificial Intelligence and Simulation of Behaviour, 2002, ISBN: 1902956265. @inbook{Pease2002, title = {Lakatos-style Reasoning}, author = {Alison Pease and Simon Colton and Alan Smaill and John Lee}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/pease_arw02.pdf}, isbn = {1902956265}, year = {2002}, date = {2002-01-01}, booktitle = {Proceedings of the Automated Reasoning Workshop, Imperial College, London}, publisher = {Society for the Study of Artificial Intelligence and Simulation of Behaviour}, abstract = {A problem in modelling mathematics is that few people have analysed and reported the way in which mathematicians work. Lakatos(4) is a welcome exception. He presents a rational recon-struction of the evolution of Euler's conjecture that for all polyhedra, the number of vertices (V) minus the number of edges (E) plus the number of faces (F) is two, and its proof. This work spans 200 years of concepts, conjectures, counter-examples and 'proofs' and is invaluable to AI researchers trying to model mathematical reasoning. Such models might serve to (a) illuminate aspects of human mathematics, and (b) improve existing automated reasoning programs.}, keywords = {}, pubstate = {published}, tppubtype = {inbook} } A problem in modelling mathematics is that few people have analysed and reported the way in which mathematicians work. Lakatos(4) is a welcome exception. He presents a rational recon-struction of the evolution of Euler's conjecture that for all polyhedra, the number of vertices (V) minus the number of edges (E) plus the number of faces (F) is two, and its proof. This work spans 200 years of concepts, conjectures, counter-examples and 'proofs' and is invaluable to AI researchers trying to model mathematical reasoning. Such models might serve to (a) illuminate aspects of human mathematics, and (b) improve existing automated reasoning programs. |
Pease, Alison; Colton, Simon; Smaill, Alan; Lee, John A Multi-agent Approach to Modelling Interaction in Human Mathematical Reasoning Inproceedings In: Proceedings of Intelligent Agent Technology, 2001. @inproceedings{pease2001multi, title = {A Multi-agent Approach to Modelling Interaction in Human Mathematical Reasoning}, author = { Alison Pease and Simon Colton and Alan Smaill and John Lee}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/pease_iat01.pdf}, year = {2001}, date = {2001-01-01}, booktitle = {Proceedings of Intelligent Agent Technology}, journal = {Intelligent Agent Technology Research and Development}, abstract = {Current work in automated reasoning does not in general model social aspects of human mathematics, with a few exceptions, for example [1]. We are inter-ested in modelling concept and conjecture refinement, i.e. the way in which the definition of a concept evolves as a conjecture develops. Modelling this process is important because (a) it will illuminate aspects of the social nature of mathematics and (b) it may be useful for improving existing automated reasoning programs. In V we outline descriptions by Devlin and Lakatos of the human process. In 9 we describe an agent architecture for this task and how it could be implemented using the HR theory formation system[2]. }, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Current work in automated reasoning does not in general model social aspects of human mathematics, with a few exceptions, for example [1]. We are inter-ested in modelling concept and conjecture refinement, i.e. the way in which the definition of a concept evolves as a conjecture develops. Modelling this process is important because (a) it will illuminate aspects of the social nature of mathematics and (b) it may be useful for improving existing automated reasoning programs. In V we outline descriptions by Devlin and Lakatos of the human process. In 9 we describe an agent architecture for this task and how it could be implemented using the HR theory formation system[2]. |
Colton, Simon Experiments in Meta-theory Formation Inproceedings In: Proceedings of the AISB’01 Symposium on Artificial Intelligence and Creativity in Arts and Science, pp. 100–109, 2001. @inproceedings{colton2001experiments, title = {Experiments in Meta-theory Formation}, author = { Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_aisb01.pdf}, year = {2001}, date = {2001-01-01}, booktitle = {Proceedings of the AISB’01 Symposium on Artificial Intelligence and Creativity in Arts and Science}, pages = {100--109}, abstract = {An ability to reason at a meta-level is widely regarded as an important aspect of human creativity which is often missing from creative computer programs. We discuss recent experiments with the HR theory formation program where it formed meta-theories about previously formed theories. We report how HR re-invented aspects of how it forms theories and reflected on the nature of the theories it produces. Additionally, the meta-theories contains higher level concepts than those produced using HR normally. We discuss how HR’s meta-level abilities were enabled by changing domains, rather than writing new programs, which was the model previously employed in the Meta-DENDRAL and Eurisko programs. These experiments suggest an improved model of theory formation where meta-theories are produced alongside theories, with information from the meta-theory being used to improve the search in the original theory.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } An ability to reason at a meta-level is widely regarded as an important aspect of human creativity which is often missing from creative computer programs. We discuss recent experiments with the HR theory formation program where it formed meta-theories about previously formed theories. We report how HR re-invented aspects of how it forms theories and reflected on the nature of the theories it produces. Additionally, the meta-theories contains higher level concepts than those produced using HR normally. We discuss how HR’s meta-level abilities were enabled by changing domains, rather than writing new programs, which was the model previously employed in the Meta-DENDRAL and Eurisko programs. These experiments suggest an improved model of theory formation where meta-theories are produced alongside theories, with information from the meta-theory being used to improve the search in the original theory. |
Colton, Simon Automated "Plugging and Chugging" Inproceedings In: Symbolic computation and automated reasoning, pp. 247–248, AK Peters, Ltd. 2001. @inproceedings{colton2001automated, title = {Automated "Plugging and Chugging"}, author = { Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_calculemus00.pdf}, year = {2001}, date = {2001-01-01}, booktitle = {Symbolic computation and automated reasoning}, pages = {247--248}, organization = {AK Peters, Ltd.}, abstract = {In [1], Paul Zeitz discusses how to solve mathematical problems. One tech-nique he proposes is to calculate some examples of objects in the problem statement and try to spot a pattern or property which provides insight into the nature of the problem.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } In [1], Paul Zeitz discusses how to solve mathematical problems. One tech-nique he proposes is to calculate some examples of objects in the problem statement and try to spot a pattern or property which provides insight into the nature of the problem. |
Colton, Simon Assessing Exploratory Theory Formation Programs Inproceedings In: Proceedings of the AAAI-2000 workshop on new research directions in machine learning, 2000. @inproceedings{colton2000assessing, title = {Assessing Exploratory Theory Formation Programs}, author = { Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_aaai00w.pdf}, year = {2000}, date = {2000-01-01}, booktitle = {Proceedings of the AAAI-2000 workshop on new research directions in machine learning}, abstract = {Broadly speaking, machine learning programs are asked to identify a single concept given a set of examples and some background knowledge. Mathematical theory form- ation programs, such as the AM program, (Davis & Lenat 1982) and the HR program, (Colton, Bundy, & Walsh 1999), are also given a set of examples and some background know- ledge. However, they are not asked to find a single concept, but rather to explore the domain and attempt to gain some understanding of it. Because the domain is mathematics, there are a range of ways by which the program can gain an understanding of the domain, including inventing concepts, performing calculations, making conjectures, proving theor- ems and finding counterexamples. The HR system is able to perform all of these activities in domains such as group the- ory, where it employs the Otter theorem prover, (McCune 1990), and MACE counterexample finder, (McCune 1994), to prove and disprove theorems.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Broadly speaking, machine learning programs are asked to identify a single concept given a set of examples and some background knowledge. Mathematical theory form- ation programs, such as the AM program, (Davis & Lenat 1982) and the HR program, (Colton, Bundy, & Walsh 1999), are also given a set of examples and some background know- ledge. However, they are not asked to find a single concept, but rather to explore the domain and attempt to gain some understanding of it. Because the domain is mathematics, there are a range of ways by which the program can gain an understanding of the domain, including inventing concepts, performing calculations, making conjectures, proving theor- ems and finding counterexamples. The HR system is able to perform all of these activities in domains such as group the- ory, where it employs the Otter theorem prover, (McCune 1990), and MACE counterexample finder, (McCune 1994), to prove and disprove theorems. |
Colton, Simon; Bundy, Alan; Walsh, Toby Agent Based Cooperative Theory Formation in Pure Mathematics Inproceedings In: Proceedings of AISB 2000 symposium on creative and cultural aspects and applications of AI and cognitive science, pp. 11–18, 2000. @inproceedings{colton2000agent, title = {Agent Based Cooperative Theory Formation in Pure Mathematics}, author = { Simon Colton and Alan Bundy and Toby Walsh}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_aisb00.pdf}, year = {2000}, date = {2000-01-01}, booktitle = {Proceedings of AISB 2000 symposium on creative and cultural aspects and applications of AI and cognitive science}, pages = {11--18}, abstract = {The HR program, Colton et al. (1999), performs theory formation in domains of pure mathematics. Given only minimal information about a domain, it invents concepts, make conjectures, proves theorems and finds counterexamples to false conjectures. We present here a multi-agent version of HR which may provide a model for how individual mathematicians perform separate investigations but communicate their results to the mathematical community, learning from others as they do. We detail the exhaustive categorisation problem to which we have applied a multi-agent approach.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } The HR program, Colton et al. (1999), performs theory formation in domains of pure mathematics. Given only minimal information about a domain, it invents concepts, make conjectures, proves theorems and finds counterexamples to false conjectures. We present here a multi-agent version of HR which may provide a model for how individual mathematicians perform separate investigations but communicate their results to the mathematical community, learning from others as they do. We detail the exhaustive categorisation problem to which we have applied a multi-agent approach. |
Steel, Graham; Colton, Simon; Bundy, Alan; Walsh, Toby Cross Domain Mathematical Concept Formation Technical Report The University of Edinburgh 2000. @techreport{steel2000cross, title = {Cross Domain Mathematical Concept Formation}, author = { Graham Steel and Simon Colton and Alan Bundy and Toby Walsh}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/steel_aisb00.pdf}, year = {2000}, date = {2000-01-01}, institution = {The University of Edinburgh}, abstract = {Many interesting concepts in mathematics are essentially ‘cross-domain’ in nature, relating objects from more than one area of mathematics, e.g. prime order groups. These concepts are often vital to the formation of a mathematical theory. Often, the introduction of cross-domain concepts to an investigation seems to exercise a mathematician’s creative ability. The HR program, (Colton et al., 1999), proposes new concepts in mathematics. Its original implementation was limited to working in one mathematical domain at a time, so it was unable to create cross-domain concepts. Here, we describe an extension of HR to multiple domains. Cross-domain concept formation is facilitated by generalisation of the data structures and heuristic measures employed by the program, and the implementation of a new production rule. Results achieved include generation of the concepts of prime order groups, graph nodes of maximal degree and an interesting class of graph.}, keywords = {}, pubstate = {published}, tppubtype = {techreport} } Many interesting concepts in mathematics are essentially ‘cross-domain’ in nature, relating objects from more than one area of mathematics, e.g. prime order groups. These concepts are often vital to the formation of a mathematical theory. Often, the introduction of cross-domain concepts to an investigation seems to exercise a mathematician’s creative ability. The HR program, (Colton et al., 1999), proposes new concepts in mathematics. Its original implementation was limited to working in one mathematical domain at a time, so it was unable to create cross-domain concepts. Here, we describe an extension of HR to multiple domains. Cross-domain concept formation is facilitated by generalisation of the data structures and heuristic measures employed by the program, and the implementation of a new production rule. Results achieved include generation of the concepts of prime order groups, graph nodes of maximal degree and an interesting class of graph. |
The Combination of Reasoning Systems
As described above, the HR system for theory formation routinely appeals to third party software as part of its core routine. This led us to address the more general question of when it is possible to combine AI techniques so that the whole is more than a sum of the parts. In total, we have experimented with various combinations of around 20 different AI systems, including descriptive and predictive machine learning systems, model generators, constraint solvers, satisfiability solvers, theorem provers and computer algebra systems. Many of the applications described below make use of a combination of reasoning systems. We have also looked at some more generic ways to combine AI systems. The following papers describe some of our projects in this area:
Colton, Simon Joined-Up Reasoning for Automated Scientific Discovery: A Position Statement and Research Agenda Inproceedings In: AAAI Fall Symposium: Automated Scientific Discovery, pp. 18–19, 2008. @inproceedings{colton2008joined, title = {Joined-Up Reasoning for Automated Scientific Discovery: A Position Statement and Research Agenda}, author = { Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/FS08-03-004.pdf}, year = {2008}, date = {2008-01-01}, booktitle = {AAAI Fall Symposium: Automated Scientific Discovery}, pages = {18--19}, abstract = {We use the phrase “joined-up” here with a double mean- ing: to convey two aspects of scientific discovery which we believe are essential, yet under-researched with respect to automating scientific discovery processes. Firstly, from an Artificial Intelligence perspective, the majority of ap- proaches to using AI techniques involve a disjointed se- quential application of different problem solving methods, with the user providing the glue in various ways. These in- clude routine logistical aspects such as the pre-processing of data and knowledge, translating outputs into input, choos- ing parameter settings for running AI methods, etc. More importantly, however, the user performs various aspects of meta-level reasoning, including asking the most pertinent questions, determining what it means if a process terminates with success and identifying – and investigating – anoma- lies. This approach tends to lead to auto-assisted discov- eries where the user knows what they are looking for, but not what it looks like, rather than the deeper discoveries of examples/concepts/hypotheses/explanations that the user didn’t even know he or she was looking for. While AI meth- ods promise the discovery of such surprising and novel sci- entific artefacts, they rarely deliver on this promise, as their application is too regimented within the problem solving paradigm of AI.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We use the phrase “joined-up” here with a double mean- ing: to convey two aspects of scientific discovery which we believe are essential, yet under-researched with respect to automating scientific discovery processes. Firstly, from an Artificial Intelligence perspective, the majority of ap- proaches to using AI techniques involve a disjointed se- quential application of different problem solving methods, with the user providing the glue in various ways. These in- clude routine logistical aspects such as the pre-processing of data and knowledge, translating outputs into input, choos- ing parameter settings for running AI methods, etc. More importantly, however, the user performs various aspects of meta-level reasoning, including asking the most pertinent questions, determining what it means if a process terminates with success and identifying – and investigating – anoma- lies. This approach tends to lead to auto-assisted discov- eries where the user knows what they are looking for, but not what it looks like, rather than the deeper discoveries of examples/concepts/hypotheses/explanations that the user didn’t even know he or she was looking for. While AI meth- ods promise the discovery of such surprising and novel sci- entific artefacts, they rarely deliver on this promise, as their application is too regimented within the problem solving paradigm of AI. |
Charnley, John; Colton, Simon A Global Workspace Framework for Combining Reasoning Systems Inproceedings In: International Conference on Intelligent Computer Mathematics, pp. 261–265, Springer Springer Berlin Heidelberg, Berlin, Heidelberg, 2008, ISBN: 978-3-540-85110-3. @inproceedings{charnley2008global, title = {A Global Workspace Framework for Combining Reasoning Systems}, author = { John Charnley and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/charnley_calculemus08.pdf}, doi = {10.1007/978-3-540-85110-3_21}, isbn = {978-3-540-85110-3}, year = {2008}, date = {2008-01-01}, booktitle = {International Conference on Intelligent Computer Mathematics}, journal = {9th International Conference, AISC 2008, 15th Symposium, Calculemus 2008, 7th International Conference, MKM 2008, Birmingham, UK, July 28 - August 1, 2008. Proceedings}, pages = {261--265}, publisher = {Springer Berlin Heidelberg}, address = {Berlin, Heidelberg}, organization = {Springer}, abstract = {Stand-alone Artificial Intelligence systems for performing specific types of reasoning - such as automated theorem proving and symbolic manipulation in computer algebra systems - are numerous, highly capable and constantly improving. Moreover, systems which combine various forms of reasoning have repeatedly been shown to be more effective than stand-alone systems. For example, the ICARUS system for reformulating constraint satisfaction problems [1] and the HOMER system for conjecture making in number theory [2]. However, in general, such combinations have been ad-hoc in nature and designedwith a specific task in mind. With little general design consideration or a suitable framework for combining reasoning, in general every new combination has to be built from scratch and the resulting system is often inflexible and difficult to manage. We believe it is imperative that generic frameworks are developed if the field of combining reasoning systems is to progress. Such generic frameworkswould provide standardised rule sets and toolkits to simplify the development of combined systems.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Stand-alone Artificial Intelligence systems for performing specific types of reasoning - such as automated theorem proving and symbolic manipulation in computer algebra systems - are numerous, highly capable and constantly improving. Moreover, systems which combine various forms of reasoning have repeatedly been shown to be more effective than stand-alone systems. For example, the ICARUS system for reformulating constraint satisfaction problems [1] and the HOMER system for conjecture making in number theory [2]. However, in general, such combinations have been ad-hoc in nature and designedwith a specific task in mind. With little general design consideration or a suitable framework for combining reasoning, in general every new combination has to be built from scratch and the resulting system is often inflexible and difficult to manage. We believe it is imperative that generic frameworks are developed if the field of combining reasoning systems is to progress. Such generic frameworkswould provide standardised rule sets and toolkits to simplify the development of combined systems. |
Charnley, John; Colton, Simon Applications of a Global Workspace Framework to Mathematical Discovery Inproceedings In: Proceedings of the Conferences on Intelligent Computer Mathematics workshop on Empirically Successful Automated Reasoning for Mathematics, 2008. @inproceedings{charnley2008applications, title = {Applications of a Global Workspace Framework to Mathematical Discovery}, author = { John Charnley and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/22874493.pdf}, year = {2008}, date = {2008-01-01}, booktitle = {Proceedings of the Conferences on Intelligent Computer Mathematics workshop on Empirically Successful Automated Reasoning for Mathematics}, abstract = {Systems which combine various forms of reasoning such as deductive inference and symbolic manipulation have repeatedly been shown to be more effective than stand-alone systems. In general, however, the combined systems are ad-hoc and designed for a single task. We present a generic framework for combining reasoning processes which is based on the theory of the Global Workspace Architecture. Within this blackboard-style framework, processes attached to a workspace propose information to be broadcast, along with a rating of the importance of the information, and only the most important is broadcast to all the processes, which react accordingly. To begin to demonstrate the value of the framework, we show that the tasks undertaken by previous ad-hoc systems can be performed by a configuration of the framework. To this end, we describe configurations for theorem discovery and conjecture making respectively, which produce comparable results to the previous ICARUS and HOMER systems. We further describe a novel application where we use a configuration of the framework to identify potentially interesting specialisations of finite algebras.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Systems which combine various forms of reasoning such as deductive inference and symbolic manipulation have repeatedly been shown to be more effective than stand-alone systems. In general, however, the combined systems are ad-hoc and designed for a single task. We present a generic framework for combining reasoning processes which is based on the theory of the Global Workspace Architecture. Within this blackboard-style framework, processes attached to a workspace propose information to be broadcast, along with a rating of the importance of the information, and only the most important is broadcast to all the processes, which react accordingly. To begin to demonstrate the value of the framework, we show that the tasks undertaken by previous ad-hoc systems can be performed by a configuration of the framework. To this end, we describe configurations for theorem discovery and conjecture making respectively, which produce comparable results to the previous ICARUS and HOMER systems. We further describe a novel application where we use a configuration of the framework to identify potentially interesting specialisations of finite algebras. |
Sorge, Volker; Meier, Andreas; McCasland, Roy; Colton, Simon Integrating AI Systems for Classification in Non-Associative Algebra Inproceedings In: Proceedings of the 13th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning , Elsevier, 2006. @inproceedings{Sorge2006, title = {Integrating AI Systems for Classification in Non-Associative Algebra}, author = {Volker Sorge and Andreas Meier and Roy McCasland and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/sorge_calculemus06.pdf}, year = {2006}, date = {2006-01-01}, booktitle = {Proceedings of the 13th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning }, journal = {Electronic Notes in Theoretical Computer Science}, publisher = {Elsevier}, abstract = {The automatic construction of mathematical theorems is a challenging task for Arti-ficial Intelligence systems, which has pushed many research boundaries in different branches of AI. We describe how the construction of classification theorems in algebraic domains of mathematics has driven research not only on the individual mathematical reasoning techniques, but also the integration of these techniques. We have developed a bootstrapping algorithm for the automatic generation of such theorems which relies on the power of model generation, first order theorem proving, computer algebra, machine learning and satisfiability solving. In particular, the con-struction of algebraic invariants demands an intricate interplay of these techniques. We demonstrate the effectiveness of this approach by generating novel theorems which have so far been beyond the reach of automated reasoning systems.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } The automatic construction of mathematical theorems is a challenging task for Arti-ficial Intelligence systems, which has pushed many research boundaries in different branches of AI. We describe how the construction of classification theorems in algebraic domains of mathematics has driven research not only on the individual mathematical reasoning techniques, but also the integration of these techniques. We have developed a bootstrapping algorithm for the automatic generation of such theorems which relies on the power of model generation, first order theorem proving, computer algebra, machine learning and satisfiability solving. In particular, the con-struction of algebraic invariants demands an intricate interplay of these techniques. We demonstrate the effectiveness of this approach by generating novel theorems which have so far been beyond the reach of automated reasoning systems. |
Sorge, Volker; Colton, Simon; Meier, Andreas A Grid-based Application of Machine Learning to Model Generation Inproceedings In: Poster Proceedings of KI'04, pp. 204, 2004. @inproceedings{sorge2004grid, title = {A Grid-based Application of Machine Learning to Model Generation}, author = { Volker Sorge and Simon Colton and Andreas Meier}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/sorge_ki04.pdf}, year = {2004}, date = {2004-01-01}, booktitle = {Poster Proceedings of KI'04}, pages = {204}, abstract = {The classification of mathematical structures is a driving force in pure mathematics. A first step in producing algebraic classification theorems is to de-termine for which sizes certain algebras exist. Computational approaches to solv-ing such existence problems using constraint satisfaction and model generation approaches have had much success. We look here at the question of distributing the model generation process using Grid technology. We present a novel distri-bution approach which involves using the HR machine learning program to intel-ligently suggest specialisations of the problem which are given to separate pro-cessors. Using the MACE, FINDER and SEM model generators, we demonstrate how this approach provides greater efficiency over a single-process approach for a series of quasigroup existence problems. We compare several approaches for the production and choice of specialisations, including the generation of proved classification theorems for algebraic structures of small sizes. We discuss how this approach could be used for more general problems. }, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } The classification of mathematical structures is a driving force in pure mathematics. A first step in producing algebraic classification theorems is to de-termine for which sizes certain algebras exist. Computational approaches to solv-ing such existence problems using constraint satisfaction and model generation approaches have had much success. We look here at the question of distributing the model generation process using Grid technology. We present a novel distri-bution approach which involves using the HR machine learning program to intel-ligently suggest specialisations of the problem which are given to separate pro-cessors. Using the MACE, FINDER and SEM model generators, we demonstrate how this approach provides greater efficiency over a single-process approach for a series of quasigroup existence problems. We compare several approaches for the production and choice of specialisations, including the generation of proved classification theorems for algebraic structures of small sizes. We discuss how this approach could be used for more general problems. |
Meier, Andreas; Sorge, Volker; Colton, Simon Employing Theory Formation to Guide Proof Planning Incollection In: Artificial Intelligence, Automated Reasoning, and Symbolic Computation, pp. 275–289, Springer, 2002. @incollection{meier2002employing, title = {Employing Theory Formation to Guide Proof Planning}, author = { Andreas Meier and Volker Sorge and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/meier_calculemus02.pdf}, year = {2002}, date = {2002-01-01}, booktitle = {Artificial Intelligence, Automated Reasoning, and Symbolic Computation}, pages = {275--289}, publisher = {Springer}, abstract = {The invention of suitable concepts to characterise mathe-matical structures is one of the most challenging tasks for both human mathematicians and automated theorem provers alike. We present an approach where automatic concept formation is used to guide non-iso-morphism proofs in the residue class domain. The main idea behind the proof is to automatically identify discriminants for two given structures to show that they are not isomorphic. Suitable discriminants are gen-erated by a theory formation system; the overall proof is constructed by a proof planner with the additional support of traditional automated theorem provers and a computer algebra system. }, keywords = {}, pubstate = {published}, tppubtype = {incollection} } The invention of suitable concepts to characterise mathe-matical structures is one of the most challenging tasks for both human mathematicians and automated theorem provers alike. We present an approach where automatic concept formation is used to guide non-iso-morphism proofs in the residue class domain. The main idea behind the proof is to automatically identify discriminants for two given structures to show that they are not isomorphic. Suitable discriminants are gen-erated by a theory formation system; the overall proof is constructed by a proof planner with the additional support of traditional automated theorem provers and a computer algebra system. |
Applications to Discovery Tasks in Pure Mathematics
Pure mathematics is a unique domain for AI research, as mathematical enquiry involves many diverse forms of reasoning, hence we can look at the question of theory formation in pure mathematics and study computational systems which combine different AI techniques. In addition, the data in pure mathematics is usually error free, hence we can concentrate on pure forms of reasoning without (usually) requiring statistical interpretations. On numerous occasions, we have shown that HR and other systems can make mathematical discoveries of genuine value in graph theory, number theory and various algebraic domains of pure mathematics. In addition, by combining HR with multiple other AI systems, we have achieved new partial classifications of algebraic domains, which were previously beyond any computer (or human). The following papers describe some of our projects in this area:
Sorge, Volker; Meier, Andreas; McCasland, Roy; Colton, Simon Automatic Construction and Verification of Isotopy Invariants Journal Article In: Journal of Automated Reasoning, 40 (2-3), pp. 221–243, 2008. @article{sorge2008automatic, title = {Automatic Construction and Verification of Isotopy Invariants}, author = { Volker Sorge and Andreas Meier and Roy McCasland and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/sorge_jar08.pdf}, year = {2008}, date = {2008-01-01}, journal = {Journal of Automated Reasoning}, volume = {40}, number = {2-3}, pages = {221--243}, publisher = {Springer}, abstract = {We extend our previous study of the automatic construction of iso- morphic classification theorems for algebraic domains by considering the isotopy equivalence relation, which is of more importance than isomorphism in certain domains. This extension was not straightforward, and we had to solve two major technical problems, namely generating and verifying isotopy invariants. Concentrat- ing on the domain of loop theory, we have developed three novel techniques for generating isotopic invariants, by using the notion of universal identities and by using constructions based on sub-blocks. In addition, given the complexity of the theorems which verify that a conjunction of the invariants form an isotopy class, we have developed ways of simplifying the problem of proving these theorems. Our techniques employ an intricate interplay of computer algebra, model generation, theorem proving and satisfiability solving methods. To demonstrate the power of the approach, we generate an isotopic classification theorem for loops of size 6, which extends the previously known result that there are 22. This result was previously beyond the capabilities of automated reasoning techniques.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We extend our previous study of the automatic construction of iso- morphic classification theorems for algebraic domains by considering the isotopy equivalence relation, which is of more importance than isomorphism in certain domains. This extension was not straightforward, and we had to solve two major technical problems, namely generating and verifying isotopy invariants. Concentrat- ing on the domain of loop theory, we have developed three novel techniques for generating isotopic invariants, by using the notion of universal identities and by using constructions based on sub-blocks. In addition, given the complexity of the theorems which verify that a conjunction of the invariants form an isotopy class, we have developed ways of simplifying the problem of proving these theorems. Our techniques employ an intricate interplay of computer algebra, model generation, theorem proving and satisfiability solving methods. To demonstrate the power of the approach, we generate an isotopic classification theorem for loops of size 6, which extends the previously known result that there are 22. This result was previously beyond the capabilities of automated reasoning techniques. |
Sorge, Volker; Colton, Simon; McCasland, Roy; Meier, Andreas Classification Results in Quasigroup and Loop Theory via a Combination of Automated Reasoning Tools Journal Article In: Commentationes Mathematicae Universitatis Carolinae, 49 (2), pp. 319–340, 2008. @article{sorge2008classification, title = {Classification Results in Quasigroup and Loop Theory via a Combination of Automated Reasoning Tools}, author = { Volker Sorge and Simon Colton and Roy McCasland and Andreas Meier}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/sorge_carolinae08.pdf}, year = {2008}, date = {2008-01-01}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {49}, number = {2}, pages = {319--340}, publisher = {Prague [Mathematical Institute of the Charles University]}, abstract = {Abstract. We present some novel partial classification results in quasigroup and loop theory. For quasigroups up to size XXX and loops up to size YYY, we describe a unique property which determines the isomorphism (and in the case of loops, the isotopism) class for any example. These invariant properties were generated using a variety of automated techniques – including machine learning and computer algebra – which we present here. Moreover, each result has been automatically verified, again using a variety of techniques – including automated theorem proving, computer algebra and satisfiability solving – and we describe our bootstrapping approach to the generation and verification of these classification results.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Abstract. We present some novel partial classification results in quasigroup and loop theory. For quasigroups up to size XXX and loops up to size YYY, we describe a unique property which determines the isomorphism (and in the case of loops, the isotopism) class for any example. These invariant properties were generated using a variety of automated techniques – including machine learning and computer algebra – which we present here. Moreover, each result has been automatically verified, again using a variety of techniques – including automated theorem proving, computer algebra and satisfiability solving – and we describe our bootstrapping approach to the generation and verification of these classification results. |
Colton, Simon; Sorge, Volker Automated Parameterisation of Finite Algebras Inproceedings In: Workshop on Empirical Successful Automated Reasoning in Mathematics, 2008. @inproceedings{colton2008automated, title = {Automated Parameterisation of Finite Algebras}, author = { Simon Colton and Volker Sorge}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_esarm08.pdf}, year = {2008}, date = {2008-01-01}, booktitle = {Workshop on Empirical Successful Automated Reasoning in Mathematics}, abstract = {In previous work we have designed an automatic bootstrap- ping algorithm to classify finite algebraic structures by generating prop- erties that uniquely describe and discriminate different equivalence classes. One of the drawbacks of the approach was that during the classification a large number different discriminating properties were generated. This made it particularly difficult to compare classifying properties for dif- ferent sizes of algebraic structures. To minimise the overall number of properties needed we have now experimented with parameterising struc- tures by counting the number of elements with particular properties. Isomorphism classes are then discriminated by the different number of elements with the same property. With this new approach we can now classify large numbers of algebraic structures using only a small number of properties. We were able to construct and prove parameterisations for algebraic structures like loops of size 6 and groups of size 8. However, the approach is currently limited as translating counting arguments into pure first order or propositional logic, often makes for prohibitively long problem formulations. }, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } In previous work we have designed an automatic bootstrap- ping algorithm to classify finite algebraic structures by generating prop- erties that uniquely describe and discriminate different equivalence classes. One of the drawbacks of the approach was that during the classification a large number different discriminating properties were generated. This made it particularly difficult to compare classifying properties for dif- ferent sizes of algebraic structures. To minimise the overall number of properties needed we have now experimented with parameterising struc- tures by counting the number of elements with particular properties. Isomorphism classes are then discriminated by the different number of elements with the same property. With this new approach we can now classify large numbers of algebraic structures using only a small number of properties. We were able to construct and prove parameterisations for algebraic structures like loops of size 6 and groups of size 8. However, the approach is currently limited as translating counting arguments into pure first order or propositional logic, often makes for prohibitively long problem formulations. |
Colton, Simon Computational Discovery in Pure Mathematics Book Chapter In: Dzeroski, Saso; Todorowski, Ljupco (Ed.): Computational Discovery of Scientific Knowledge, 4660 , pp. 175–201, Springer, 2007. @inbook{colton2007computational, title = {Computational Discovery in Pure Mathematics}, author = { Simon Colton}, editor = {Saso Dzeroski and Ljupco Todorowski}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_cdck07.pdf}, year = {2007}, date = {2007-01-01}, booktitle = {Computational Discovery of Scientific Knowledge}, journal = {Communicable Scientific Discovery, LNAI}, volume = {4660}, pages = {175--201}, publisher = {Springer}, abstract = {We discuss what constitutes knowledge in pure mathemat- ics and how new advances are made and communicated. We describe the impact of computer algebra systems, automated theorem provers, programs designed to generate examples, mathematical databases, and theory formation programs on the body of knowledge in pure mathemat- ics. We discuss to what extent the output from certain programs can be considered a discovery in pure mathematics. This enables us to assess the state of the art with respect to Newell and Simon’s prediction that a computer would discover and prove an important mathematical theorem.}, keywords = {}, pubstate = {published}, tppubtype = {inbook} } We discuss what constitutes knowledge in pure mathemat- ics and how new advances are made and communicated. We describe the impact of computer algebra systems, automated theorem provers, programs designed to generate examples, mathematical databases, and theory formation programs on the body of knowledge in pure mathemat- ics. We discuss to what extent the output from certain programs can be considered a discovery in pure mathematics. This enables us to assess the state of the art with respect to Newell and Simon’s prediction that a computer would discover and prove an important mathematical theorem. |
Colton, Simon Automated Conjecture Making In Number Theory Using HR, Otter and Maple Journal Article In: Journal of Symbolic Computation, 39 (5), pp. 593–615, 2005. @article{colton2005automated, title = {Automated Conjecture Making In Number Theory Using HR, Otter and Maple}, author = { Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_jsc05.pdf}, year = {2005}, date = {2005-01-01}, journal = {Journal of Symbolic Computation}, volume = {39}, number = {5}, pages = {593--615}, publisher = {Elsevier}, abstract = {One of the main applications of computational techniques to pure math- ematics has been the use of computer algebra systems to perform cal- culations which mathematicians cannot perform by hand. Because the data is produced within the computer algebra system, this becomes an environment for the exploration of new functions and the data produced is often analysed in order to make conjectures empirically. We add some automation to this discovery process by using the HR theory formation system to make conjectures about Maple functions supplied by the user. HR forms theories by inventing concepts, making conjectures empirically which relate the concepts, and appealing to third party theorem provers and model generators to prove/disprove the conjectures. It has been used with success in number theory, graph theory and various algebraic do- mains such as group theory and ring theory. Experience has shown that HR produces too many conjectures which can be easily proven from the definitions of the functions involved. Hence, we use the Otter theorem prover to discard any theorems which can be easily proven, leaving behind the more interesting ones which are empiri- cally plausible but not easily provable. We describe the core functionality of HR which enables it to form a theory, and the additional functionality implemented in order for HR to work with Maple functions. We present two experiments where we have applied HR’s theory formation in number theory. We discuss the modes of operation for the user and provide some of the results produced in this way. We hope to show that using HR, Ot- ter and Maple in this fashion has much potential for the advancement of computer algebra systems.}, keywords = {}, pubstate = {published}, tppubtype = {article} } One of the main applications of computational techniques to pure math- ematics has been the use of computer algebra systems to perform cal- culations which mathematicians cannot perform by hand. Because the data is produced within the computer algebra system, this becomes an environment for the exploration of new functions and the data produced is often analysed in order to make conjectures empirically. We add some automation to this discovery process by using the HR theory formation system to make conjectures about Maple functions supplied by the user. HR forms theories by inventing concepts, making conjectures empirically which relate the concepts, and appealing to third party theorem provers and model generators to prove/disprove the conjectures. It has been used with success in number theory, graph theory and various algebraic do- mains such as group theory and ring theory. Experience has shown that HR produces too many conjectures which can be easily proven from the definitions of the functions involved. Hence, we use the Otter theorem prover to discard any theorems which can be easily proven, leaving behind the more interesting ones which are empiri- cally plausible but not easily provable. We describe the core functionality of HR which enables it to form a theory, and the additional functionality implemented in order for HR to work with Maple functions. We present two experiments where we have applied HR’s theory formation in number theory. We discuss the modes of operation for the user and provide some of the results produced in this way. We hope to show that using HR, Ot- ter and Maple in this fashion has much potential for the advancement of computer algebra systems. |
Colton, Simon; Meier, Andreas; Sorge, Volker; McCasland, Roy Automatic Generation of Classification Theorems for Finite Algebras Inproceedings In: International Joint Conference on Automated Reasoning, pp. 400–414, Springer 2004. @inproceedings{colton2004automatic, title = {Automatic Generation of Classification Theorems for Finite Algebras}, author = { Simon Colton and Andreas Meier and Volker Sorge and Roy McCasland}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_ijcar04.pdf}, year = {2004}, date = {2004-01-01}, booktitle = {International Joint Conference on Automated Reasoning}, pages = {400--414}, organization = {Springer}, abstract = {Classifying finite algebraic structures has been a major mo- tivation behind much research in pure mathematics. Automated tech- niques have aided in this process, but this has largely been at a quan- titative level. In contrast, we present a qualitative approach which pro- duces verified theorems, which classify algebras of a particular type and size into isomorphism classes. We describe both a semi-automated and a fully automated bootstrapping approach to building and verifying clas- sification theorems. In the latter case, we have implemented a procedure which takes the axioms of the algebra and produces a decision tree em- bedding a fully verified classification theorem. This has been achieved by the integration (and improvement) of a number of automated reasoning techniques: we use the Mace model generator, the HR and C4.5 machine learning systems, the Spass theorem prover, and the Gap computer al- gebra system to reduce the complexity of the problems given to Spass. We demonstrate the power of this approach by classifying loops, groups, monoids and quasigroups of various sizes.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Classifying finite algebraic structures has been a major mo- tivation behind much research in pure mathematics. Automated tech- niques have aided in this process, but this has largely been at a quan- titative level. In contrast, we present a qualitative approach which pro- duces verified theorems, which classify algebras of a particular type and size into isomorphism classes. We describe both a semi-automated and a fully automated bootstrapping approach to building and verifying clas- sification theorems. In the latter case, we have implemented a procedure which takes the axioms of the algebra and produces a decision tree em- bedding a fully verified classification theorem. This has been achieved by the integration (and improvement) of a number of automated reasoning techniques: we use the Mace model generator, the HR and C4.5 machine learning systems, the Spass theorem prover, and the Gap computer al- gebra system to reduce the complexity of the problems given to Spass. We demonstrate the power of this approach by classifying loops, groups, monoids and quasigroups of various sizes. |
Colton, Simon; Muggleton, Stephen ILP for Mathematical Discovery Inproceedings In: International Conference on Inductive Logic Programming, pp. 93–111, Springer 2003. @inproceedings{colton2003ilp, title = {ILP for Mathematical Discovery}, author = { Simon Colton and Stephen Muggleton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_ilp03.pdf}, year = {2003}, date = {2003-01-01}, booktitle = {International Conference on Inductive Logic Programming}, pages = {93--111}, organization = {Springer}, abstract = {We believe that AI programs written for discovery tasks will need to simultaneously employ a variety of reasoning techniques such as induction, abduction, deduction, calculation and invention. We describe the HR system which performs a novel ILP routine called automated the- ory formation. This combines inductive and deductive reasoning to form clausal theories consisting of classification rules and association rules. HR generates definitions using a set of production rules, interprets the definitions as classification rules, then uses the success sets of the defi- nitions to induce hypotheses from which it extracts association rules. It uses third party theorem provers and model generators to check whether the association rules are entailed by a set of user supplied axioms. HR has been applied to a range of predictive, descriptive and subgroup discovery tasks in domains of pure mathematics. We describe these applications and how they have led to some interesting mathematical discoveries. Our main aim here is to provide a thorough overview of automated theory for- mation. A secondary aim is to promote mathematics as a worthy domain for ILP applications, and we provide pointers to mathematical datasets.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We believe that AI programs written for discovery tasks will need to simultaneously employ a variety of reasoning techniques such as induction, abduction, deduction, calculation and invention. We describe the HR system which performs a novel ILP routine called automated the- ory formation. This combines inductive and deductive reasoning to form clausal theories consisting of classification rules and association rules. HR generates definitions using a set of production rules, interprets the definitions as classification rules, then uses the success sets of the defi- nitions to induce hypotheses from which it extracts association rules. It uses third party theorem provers and model generators to check whether the association rules are entailed by a set of user supplied axioms. HR has been applied to a range of predictive, descriptive and subgroup discovery tasks in domains of pure mathematics. We describe these applications and how they have led to some interesting mathematical discoveries. Our main aim here is to provide a thorough overview of automated theory for- mation. A secondary aim is to promote mathematics as a worthy domain for ILP applications, and we provide pointers to mathematical datasets. |
Colton, Simon; Huczynska, Sophie The HOMER System Inproceedings In: International Conference on Automated Deduction, pp. 289–294, Springer 2003. @inproceedings{colton2003homer, title = {The HOMER System}, author = { Simon Colton and Sophie Huczynska}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_cade03.pdf}, year = {2003}, date = {2003-01-01}, booktitle = {International Conference on Automated Deduction}, pages = {289--294}, organization = {Springer}, abstract = {The Homer system combines the HR automated theory formation program, the Otter theorem prover, and the Maple computer algebra package [1] to make intelligent conjectures about number theory functions supplied by the user. The integration is as follows: given Maple code for some functions the user is in-terested in, Maple is used to calculate values for those functions. HR then forms a theory using the functions as background knowledge, calling Maple when-ever necessary to perform additional calculations. The theory formation process makes conjectures empirically and the user is initially asked to prove or disprove each conjecture. As the theory formation progresses, however, Homer uses the theorems it has found (namely those proved by the user) as axioms in attempts to prove the conjectures itself using Otter. Any conjectures proved in this way are likely to follow easily from the theorems already known to the user, so Homer does not present them, in order to keep the quality of the output high. Using Otter in this extreme way is not meant to indicate that Otter can only prove trivial theorems, nor that HR produces too many dull conjectures. Rather, we wish to emphasise the power of the combined system (Homer) at discovering interesting conjectures by generate (HR) and quick test (Otter). }, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } The Homer system combines the HR automated theory formation program, the Otter theorem prover, and the Maple computer algebra package [1] to make intelligent conjectures about number theory functions supplied by the user. The integration is as follows: given Maple code for some functions the user is in-terested in, Maple is used to calculate values for those functions. HR then forms a theory using the functions as background knowledge, calling Maple when-ever necessary to perform additional calculations. The theory formation process makes conjectures empirically and the user is initially asked to prove or disprove each conjecture. As the theory formation progresses, however, Homer uses the theorems it has found (namely those proved by the user) as axioms in attempts to prove the conjectures itself using Otter. Any conjectures proved in this way are likely to follow easily from the theorems already known to the user, so Homer does not present them, in order to keep the quality of the output high. Using Otter in this extreme way is not meant to indicate that Otter can only prove trivial theorems, nor that HR produces too many dull conjectures. Rather, we wish to emphasise the power of the combined system (Homer) at discovering interesting conjectures by generate (HR) and quick test (Otter). |
Colton, Simon Making Conjectures About Maple Functions Incollection In: Artificial Intelligence, Automated Reasoning, and Symbolic Computation, pp. 259–274, Springer, 2002. @incollection{colton2002making, title = {Making Conjectures About Maple Functions}, author = { Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_calculemus02.pdf}, year = {2002}, date = {2002-01-01}, booktitle = {Artificial Intelligence, Automated Reasoning, and Symbolic Computation}, pages = {259--274}, publisher = {Springer}, abstract = {One of the main applications of computational techniques to pure mathematics has been the use of computer algebra systems to perform calculations which mathematicians cannot perform by hand. Because the data is produced within the computer algebra system, this becomes an environment for the exploration of new functions and the data produced is often analysed in order to make conjectures empirically. We add some automation to this by using the HR theory formation system to make conjectures about Maple functions supplied by the user. Experience has shown that HR produces too many conjectures which are easily proven from the definitions of the functions involved. Hence, we use the Otter theorem prover to discard any theorems which can be easily proven, leaving behind the more interesting ones which are empirically true but not trivially provable. By providing an application of HR's theory formation in number theory, we show that using Otter to prune HR's dull conjectures has much potential for producing interesting conjectures about standard computer algebra functions. }, keywords = {}, pubstate = {published}, tppubtype = {incollection} } One of the main applications of computational techniques to pure mathematics has been the use of computer algebra systems to perform calculations which mathematicians cannot perform by hand. Because the data is produced within the computer algebra system, this becomes an environment for the exploration of new functions and the data produced is often analysed in order to make conjectures empirically. We add some automation to this by using the HR theory formation system to make conjectures about Maple functions supplied by the user. Experience has shown that HR produces too many conjectures which are easily proven from the definitions of the functions involved. Hence, we use the Otter theorem prover to discard any theorems which can be easily proven, leaving behind the more interesting ones which are empirically true but not trivially provable. By providing an application of HR's theory formation in number theory, we show that using Otter to prune HR's dull conjectures has much potential for producing interesting conjectures about standard computer algebra functions. |
Colton, Simon; Dennis, Louise Abigail The NumbersWithNames Program Inproceedings In: Proceedings of the Seventh AI and Maths Symposium, 2002. @inproceedings{colton2002numberswithnames, title = {The NumbersWithNames Program}, author = { Simon Colton and Louise Abigail Dennis}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_aim02_1.pdf}, year = {2002}, date = {2002-01-01}, booktitle = {Proceedings of the Seventh AI and Maths Symposium}, abstract = {We present the NumbersWithNames program which performs data-mining on the Encyclopedia of Integer Sequences to find interesting conjectures in number theory. The program forms conjec-tures by finding empirical relationships between a sequence chosen by the user and those in the Encyclopedia. Furthermore, it transforms the chosen sequence into another set of sequences about which conjectures can also be formed. Finally, the program prunes and sorts the conjectures so that the most plausible ones are presented first. We describe here the many improvements to the previous Prolog implementation which have enabled us to provide NumbersWithNames as an online program. We also present some new results from using NumbersWithNames, including details of an automated proof plan of a conjecture NumbersWithNames helped to discover. }, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We present the NumbersWithNames program which performs data-mining on the Encyclopedia of Integer Sequences to find interesting conjectures in number theory. The program forms conjec-tures by finding empirical relationships between a sequence chosen by the user and those in the Encyclopedia. Furthermore, it transforms the chosen sequence into another set of sequences about which conjectures can also be formed. Finally, the program prunes and sorts the conjectures so that the most plausible ones are presented first. We describe here the many improvements to the previous Prolog implementation which have enabled us to provide NumbersWithNames as an online program. We also present some new results from using NumbersWithNames, including details of an automated proof plan of a conjecture NumbersWithNames helped to discover. |
Colton, Simon; McCasland, Roy; Bundy, Alan; Walsh, Toby Automated Theory Formation for Tutoring Tasks in Pure Mathematics Inproceedings In: In CADE-18, Workshop on the Role of Automated Deduction in Mathematics, Citeseer 2002. @inproceedings{colton2002automated, title = {Automated Theory Formation for Tutoring Tasks in Pure Mathematics}, author = { Simon Colton and Roy McCasland and Alan Bundy and Toby Walsh}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_radm02.pdf}, year = {2002}, date = {2002-01-01}, booktitle = {In CADE-18, Workshop on the Role of Automated Deduction in Mathematics}, organization = {Citeseer}, abstract = {The HR program forms mathematical theories from as little infor-mation as the axioms of a domain. The theories include concepts with examples and definitions, conjectures, theorems and proofs. Moreover, HR uses third party mathematical software including automated theorem provers and model generators. We suggest that a potential role for theory formation systems such as HR is as an aid to mathematics lecturers. We discuss an application of HR to the generation of a set of group theory exercises. This forms part of a project using HR to make discoveries in Zariski spaces, which is also detailed. }, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } The HR program forms mathematical theories from as little infor-mation as the axioms of a domain. The theories include concepts with examples and definitions, conjectures, theorems and proofs. Moreover, HR uses third party mathematical software including automated theorem provers and model generators. We suggest that a potential role for theory formation systems such as HR is as an aid to mathematics lecturers. We discuss an application of HR to the generation of a set of group theory exercises. This forms part of a project using HR to make discoveries in Zariski spaces, which is also detailed. |
Bundy, Alan; Colton, Simon; McCasland, Roy; Walsh, Toby Semi-Automated Discovery in Zariski Spaces (A Proposal) Inproceedings In: Proceedings of the Automated Reasoning Workshop, 2002. @inproceedings{bundysemi, title = {Semi-Automated Discovery in Zariski Spaces (A Proposal)}, author = { Alan Bundy and Simon Colton and Roy McCasland and Toby Walsh}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/bundy_arw02.pdf}, year = {2002}, date = {2002-01-01}, booktitle = {Proceedings of the Automated Reasoning Workshop}, journal = {Automated Reasoning Workshop}, abstract = {Zariski Spaces were introduced in 1998 [MMS98]. In order to understand these spaces, one needs to first understand Zariski Topologies. In a broad sense, these topologies are rather like prime factorizations. For example, the Zariski topology associated with the ring of integers consists of sets (called varieties) of prime ideals, one set for each integer. In particular, the variety of the integer 12 would be the set of ideals generated by 2 and by 3, respectively, since 2 and 3 are the prime factors of 12. Note that since 2 and 3 both divide 12, then the ideal generated by 2 and the ideal generated by 3 both contain the ideal generated by 12. In the general case, let R be a commutative ring with unity, and let specR denote the collection of prime ideals of R.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Zariski Spaces were introduced in 1998 [MMS98]. In order to understand these spaces, one needs to first understand Zariski Topologies. In a broad sense, these topologies are rather like prime factorizations. For example, the Zariski topology associated with the ring of integers consists of sets (called varieties) of prime ideals, one set for each integer. In particular, the variety of the integer 12 would be the set of ideals generated by 2 and by 3, respectively, since 2 and 3 are the prime factors of 12. Note that since 2 and 3 both divide 12, then the ideal generated by 2 and the ideal generated by 3 both contain the ideal generated by 12. In the general case, let R be a commutative ring with unity, and let specR denote the collection of prime ideals of R. |
Colton, Simon Mathematics - a new Domain for Datamining? Inproceedings In: Proceedings of the IJCAI-01 Workshop on Knowledge Discovery from Distributed, Dynamic, Heterogenous, Autonomous Sources, 2001. @inproceedings{Colton2001, title = {Mathematics - a new Domain for Datamining?}, author = {Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_ijcai01.pdf}, year = {2001}, date = {2001-01-01}, booktitle = {Proceedings of the IJCAI-01 Workshop on Knowledge Discovery from Distributed, Dynamic, Heterogenous, Autonomous Sources}, journal = {International Joint Conference on Artificial Intelligence}, abstract = {With the many databases of mathematical informa-tion currently available, there is much potential for datamining techniques to find new and interesting mathematical results. Indeed, we suggest that, if we can utilise the research into dealing with dynamic, dis-tributed and heterogeneous datasets, datamining could be as successful a technique for mathematics as it is for, say, biology. We briefly survey 7 mathematical databases available online and present a motivating example and a case study. This enables us to high-light important issues and to make some suggestions for datamining mathematical information. }, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } With the many databases of mathematical informa-tion currently available, there is much potential for datamining techniques to find new and interesting mathematical results. Indeed, we suggest that, if we can utilise the research into dealing with dynamic, dis-tributed and heterogeneous datasets, datamining could be as successful a technique for mathematics as it is for, say, biology. We briefly survey 7 mathematical databases available online and present a motivating example and a case study. This enables us to high-light important issues and to make some suggestions for datamining mathematical information. |
Colton, Simon; Bundy, Alan; Walsh, Toby Automatic Invention of Integer Sequences Inproceedings In: AAAI/IAAI, pp. 558–563, 2000. @inproceedings{colton2000automaticb, title = {Automatic Invention of Integer Sequences}, author = { Simon Colton and Alan Bundy and Toby Walsh}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_aaai00.pdf}, year = {2000}, date = {2000-01-01}, booktitle = {AAAI/IAAI}, pages = {558--563}, abstract = {We report on the application of the HR program (Colton, Bundy, & Walsh 1999) to the problem of automatically in- venting integer sequences. Seventeen sequences invented by HR are interesting enough to have been accepted into the En- cyclopedia of Integer Sequences (Sloane 2000) and all were supplied with interesting conjectures about their nature, also discovered by HR. By extending HR, we have enabled it to perform a two stage process of invention and investigation. This involves generating both the definition and terms of a new sequence, relating it to sequences already in the Encyc- lopedia and pruning the output to help identify the most sur- prising and interesting results. }, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We report on the application of the HR program (Colton, Bundy, & Walsh 1999) to the problem of automatically in- venting integer sequences. Seventeen sequences invented by HR are interesting enough to have been accepted into the En- cyclopedia of Integer Sequences (Sloane 2000) and all were supplied with interesting conjectures about their nature, also discovered by HR. By extending HR, we have enabled it to perform a two stage process of invention and investigation. This involves generating both the definition and terms of a new sequence, relating it to sequences already in the Encyc- lopedia and pruning the output to help identify the most sur- prising and interesting results. |
Colton, Simon; Bundy, Alan; Walsh, Toby On the Notion of Interestingness in Automated Mathematical Discovery Journal Article In: International Journal of Human-Computer Studies, 53 (3), pp. 351–375, 2000. @article{colton2000notion, title = {On the Notion of Interestingness in Automated Mathematical Discovery}, author = { Simon Colton and Alan Bundy and Toby Walsh}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_ijhcs00.pdf}, year = {2000}, date = {2000-01-01}, journal = {International Journal of Human-Computer Studies}, volume = {53}, number = {3}, pages = {351--375}, publisher = {Elsevier}, abstract = {We survey five mathematical discovery programs by looking in detail at the discovery processes they illustrate and the success they’ve had. We focus on how they estimate the interestingness of concepts and conjectures and extract some common notions about interestingness in automated mathematical discovery. We detail how empirical evidence is used to give plausibility to conjectures, and the different ways in which a result can be thought of as novel. We also look at the ways in which the programs assess how surprising and complex a conjecture statement is, and the different ways in which the applicability of a concept or conjecture is used. Finally, we note how a user can set tasks for the program to achieve and how this affects the calculation of interestingness. We conclude with some hints on the use of interestingness measures for future developers of discovery programs in mathematics.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We survey five mathematical discovery programs by looking in detail at the discovery processes they illustrate and the success they’ve had. We focus on how they estimate the interestingness of concepts and conjectures and extract some common notions about interestingness in automated mathematical discovery. We detail how empirical evidence is used to give plausibility to conjectures, and the different ways in which a result can be thought of as novel. We also look at the ways in which the programs assess how surprising and complex a conjecture statement is, and the different ways in which the applicability of a concept or conjecture is used. Finally, we note how a user can set tasks for the program to achieve and how this affects the calculation of interestingness. We conclude with some hints on the use of interestingness measures for future developers of discovery programs in mathematics. |
Colton, Simon; Bundy, Alan; Walsh, Toby Automated Discovery in Pure Mathematics Inproceedings In: Automated Reasoning Workshop: Bridging the Gap between Theory and Practice, 1999. @inproceedings{colton1999automated, title = {Automated Discovery in Pure Mathematics}, author = { Simon Colton and Alan Bundy and Toby Walsh}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_arw99.pdf}, year = {1999}, date = {1999-01-01}, booktitle = {Automated Reasoning Workshop: Bridging the Gap between Theory and Practice}, abstract = {The HR project aims to automate two important discovery processes which occur in mathematics before theorem proving happens, namely the making of the conjecture to be proved and the invention of the definitions in the conjecture statement.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } The HR project aims to automate two important discovery processes which occur in mathematics before theorem proving happens, namely the making of the conjecture to be proved and the invention of the definitions in the conjecture statement. |
Colton, Simon Refactorable numbers-a machine invention Journal Article In: Journal of Integer Sequences, 2 (99.1), pp. 2, 1999. @article{colton1999refactorable, title = {Refactorable numbers-a machine invention}, author = { Simon Colton}, url = {http://emis.ams.org/journals/JIS/colton/joisol.html}, year = {1999}, date = {1999-01-01}, journal = {Journal of Integer Sequences}, volume = {2}, number = {99.1}, pages = {2}, keywords = {}, pubstate = {published}, tppubtype = {article} } |
Applications of ATF and Combined Reasoning to Other Domains
While pure mathematics has many advantages, other application domains also stretch the limits of AI systems and their combinations. In order to address the generic nature of the AI systems we have built, we have looked at various non-mathematical applications of ATF. In addition to the projects below, through the supervision of masters projects, we have looked at the usage of HR for musical anomaly detection, for discovery tasks in the gene ontology, for the analysis of board games and the invention of arithmetic puzzles, and for the discovery of software invariants. The following papers describe some of our projects in this area:
Colton, Simon Countdown Numbers Game: Solved, Analysed, Extended Inproceedings In: Proceedings of the AISB symposium on AI and Games, 2014. @inproceedings{colton2014countdown, title = {Countdown Numbers Game: Solved, Analysed, Extended}, author = { Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_aisb14a.pdf}, year = {2014}, date = {2014-01-01}, booktitle = {Proceedings of the AISB symposium on AI and Games}, abstract = {The Countdown Numbers Game is a popular arithmeti- cal puzzle which has been played as a two-player game on French and British television weekly for decades. We have solved this game in the sense that the optimal solution for the nearly 12 million puzzle instances has been generated and recorded. We describe here how we have achieved this using the HR3 Automated Theory Formation system. This has allowed us to analyse the space of puzzles; sug- gest gamesmanship tactics and game design improvements to the online/handheld versions of the game; and begin to investigate the potential for automatic invention of such games.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } The Countdown Numbers Game is a popular arithmeti- cal puzzle which has been played as a two-player game on French and British television weekly for decades. We have solved this game in the sense that the optimal solution for the nearly 12 million puzzle instances has been generated and recorded. We describe here how we have achieved this using the HR3 Automated Theory Formation system. This has allowed us to analyse the space of puzzles; sug- gest gamesmanship tactics and game design improvements to the online/handheld versions of the game; and begin to investigate the potential for automatic invention of such games. |
Grov, Gudmund; Farquhar, Colin; Pease, Alison; Colton, Simon Tinkering by Theory Formation Inproceedings In: Proceedings of the AIFM workshop, 2014. @inproceedings{grov2014tinkering, title = {Tinkering by Theory Formation}, author = { Gudmund Grov and Colin Farquhar and Alison Pease and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/grov_AIFM14.pdf}, year = {2014}, date = {2014-01-01}, booktitle = {Proceedings of the AIFM workshop}, abstract = {Most interactive theorem provers support encoding of common proof strategies as special func- tion called tactics. Such tactics tend to work backwards from the goal, reducing a goal to a set of simpler sub-goals. Proof strategies are then created by combining such tactics using a tactic language. Such languages are often not designed to distinguish goals in cases where tactics produce multiple sub-goals. Thus when composing tactics, one has no choice but to rely on the order in which goals arrive, thus making them brittle to minor changes. For example, consider a case where we expect three sub-goals from tactic t1, where the first two are sent to t2 and the last to t3. A small improvement of t1 may result in only two sub-goals. This “improvement” causes t2 to be applied to the second goal when it should have been t3. The tactic t2 may then fail or create unexpected new sub-goals that cause some later tactic to fail.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Most interactive theorem provers support encoding of common proof strategies as special func- tion called tactics. Such tactics tend to work backwards from the goal, reducing a goal to a set of simpler sub-goals. Proof strategies are then created by combining such tactics using a tactic language. Such languages are often not designed to distinguish goals in cases where tactics produce multiple sub-goals. Thus when composing tactics, one has no choice but to rely on the order in which goals arrive, thus making them brittle to minor changes. For example, consider a case where we expect three sub-goals from tactic t1, where the first two are sent to t2 and the last to t3. A small improvement of t1 may result in only two sub-goals. This “improvement” causes t2 to be applied to the second goal when it should have been t3. The tactic t2 may then fail or create unexpected new sub-goals that cause some later tactic to fail. |
Cavallo, Flaminia; Pease, Alison; Gow, Jeremy; Colton, Simon Using Theory Formation Techniques for the Invention of Fictional Concepts Inproceedings In: Proceedings of the Fourth International Conference on Computational Creativity, pp. 176, 2013. @inproceedings{cavallo2013using, title = {Using Theory Formation Techniques for the Invention of Fictional Concepts}, author = { Flaminia Cavallo and Alison Pease and Jeremy Gow and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/cavallo_iccc13.pdf}, year = {2013}, date = {2013-01-01}, booktitle = {Proceedings of the Fourth International Conference on Computational Creativity}, pages = {176}, abstract = {We introduce a novel method for the formation of fictional concepts based on the non-existence conjectures made by the HR automated theory formation system. We further intro- duce the notion of the typicality of an example with respect to a concept into HR, which leads to methods for ordering fic- tional concepts with respect to novelty, vagueness and stimu- lation. To test whether these measures are correlated with the way in which people similarly assess the value of fictional concepts, we ran an experiment to produce thousands of defi- nitions of fictional animals. We then compared the software’s evaluations of the non-fictional concepts with those obtained through a survey consulting sixty people. The results show that two of the three measures have a correlation with hu- man notions. We report on the experiment, and we compare our system with the well established method of conceptual blending, which leads to a discussion of automated ideation in future Computational Creativity projects.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We introduce a novel method for the formation of fictional concepts based on the non-existence conjectures made by the HR automated theory formation system. We further intro- duce the notion of the typicality of an example with respect to a concept into HR, which leads to methods for ordering fic- tional concepts with respect to novelty, vagueness and stimu- lation. To test whether these measures are correlated with the way in which people similarly assess the value of fictional concepts, we ran an experiment to produce thousands of defi- nitions of fictional animals. We then compared the software’s evaluations of the non-fictional concepts with those obtained through a survey consulting sixty people. The results show that two of the three measures have a correlation with hu- man notions. We report on the experiment, and we compare our system with the well established method of conceptual blending, which leads to a discussion of automated ideation in future Computational Creativity projects. |
Llano, Maria Teresa; Ireland, Andrew; Pease, Alison; Colton, Simon; Charnley, John Using Automated Theory Formation to Discover Invariants of Event-B Models Inproceedings In: In Proceedings of the Rodin User and Developer Workshop, 2010. @inproceedings{llano2011using, title = {Using Automated Theory Formation to Discover Invariants of Event-B Models}, author = { Maria Teresa Llano and Andrew Ireland and Alison Pease and Simon Colton and John Charnley}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/llano_rodin10.pdf}, year = {2010}, date = {2010-01-01}, booktitle = {In Proceedings of the Rodin User and Developer Workshop}, abstract = {Formal methods have been successfully used for the development of safety-critical systems; however, the need for skilled knowledge when writing formal models and reasoning about them represents a major barrier in the adoption of formal methodologies for the development of non-critical applications. A key aspect in the verification of formal models and in the development of reliable systems is the identification of invariants. However, finding correct and meaningful invariants for a model represents a significant challenge. We have used automated theory formation (ATF) techniques to automatically discover invariants of Event-B models. In particular, we use Colton’s HR system [2] to explore the domain of Event-B models and suggest potential invariants.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Formal methods have been successfully used for the development of safety-critical systems; however, the need for skilled knowledge when writing formal models and reasoning about them represents a major barrier in the adoption of formal methodologies for the development of non-critical applications. A key aspect in the verification of formal models and in the development of reliable systems is the identification of invariants. However, finding correct and meaningful invariants for a model represents a significant challenge. We have used automated theory formation (ATF) techniques to automatically discover invariants of Event-B models. In particular, we use Colton’s HR system [2] to explore the domain of Event-B models and suggest potential invariants. |
Baumgarten, Robin; Nika, Maria; Gow, Jeremy; Colton, Simon Towards the Automatic Invention of Simple Mixed Reality Games Inproceedings In: Proc. of the AISB’09 Symp. on AI and Games, 2009. @inproceedings{baumgarten2009towards, title = {Towards the Automatic Invention of Simple Mixed Reality Games}, author = { Robin Baumgarten and Maria Nika and Jeremy Gow and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_evomusart08.pdf}, year = {2009}, date = {2009-01-01}, booktitle = {Proc. of the AISB’09 Symp. on AI and Games}, abstract = {We investigate the automatic construction of visual scenes via a hybrid evolutionary/hill-climbing approach using a correlation- based fitness function. This forms part of The Painting Fool system, an automated artist which is able to render the scenes using simulated art materials. We further describe a novel method for inventing fitness functions using the HR descriptive machine learning system, and we com- bine this with The Painting Fool to generate and artistically render novel scenes. We demonstrate the potential of this approach with applications to cityscape and flower arrangement scene generation.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We investigate the automatic construction of visual scenes via a hybrid evolutionary/hill-climbing approach using a correlation- based fitness function. This forms part of The Painting Fool system, an automated artist which is able to render the scenes using simulated art materials. We further describe a novel method for inventing fitness functions using the HR descriptive machine learning system, and we com- bine this with The Painting Fool to generate and artistically render novel scenes. We demonstrate the potential of this approach with applications to cityscape and flower arrangement scene generation. |
Colton, Simon Automatic Invention of Fitness Functions, with application to Scene Generation Inproceedings In: Proceedings of the EvoMusArt Workshop, 2008. @inproceedings{Colton2008EvoMusArt, title = {Automatic Invention of Fitness Functions, with application to Scene Generation}, author = {Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/11/colton_evomusart08.pdf}, year = {2008}, date = {2008-11-01}, booktitle = {Proceedings of the EvoMusArt Workshop}, abstract = {We investigate the automatic construction of visual scenes via a hybrid evolutionary/hill-climbing approach using a correlation- based fitness function. This forms part of The Painting Fool system, an automated artist which is able to render the scenes using simulated art materials. We further describe a novel method for inventing fitness functions using the HR descriptive machine learning system, and we com- bine this with The Painting Fool to generate and artistically render novel scenes. We demonstrate the potential of this approach with applications to cityscape and flower arrangement scene generation. }, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We investigate the automatic construction of visual scenes via a hybrid evolutionary/hill-climbing approach using a correlation- based fitness function. This forms part of The Painting Fool system, an automated artist which is able to render the scenes using simulated art materials. We further describe a novel method for inventing fitness functions using the HR descriptive machine learning system, and we com- bine this with The Painting Fool to generate and artistically render novel scenes. We demonstrate the potential of this approach with applications to cityscape and flower arrangement scene generation. |
Jiang, Ning; Colton, Simon Boosting Descriptive ILP for Predictive Learning in Bioinformatics Inproceedings In: International Conference on Inductive Logic Programming, pp. 275–289, Springer 2006. @inproceedings{jiang2006boosting, title = {Boosting Descriptive ILP for Predictive Learning in Bioinformatics}, author = { Ning Jiang and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/jiang_ilp06.pdf}, year = {2006}, date = {2006-01-01}, booktitle = {International Conference on Inductive Logic Programming}, pages = {275--289}, organization = {Springer}, abstract = {Boosting is an established propositional learning method to promote the predictive accuracy of weak learning algorithms, and has achieved much empirical success. However, there have been relatively few efforts to apply boosting to Inductive Logic Programming (ILP) ap- proaches. We investigate the use of boosting descriptive ILP systems, by proposing a novel algorithm for generating classification rules which searches using a hybrid language bias/production rule approach, and a new method for converting first-order classification rules to binary clas- sifiers, which increases the predictive accuracy of the boosted classifiers. We demonstrate that our boosted approach is competitive with normal ILP systems in experiments with bioinformatics datasets.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Boosting is an established propositional learning method to promote the predictive accuracy of weak learning algorithms, and has achieved much empirical success. However, there have been relatively few efforts to apply boosting to Inductive Logic Programming (ILP) ap- proaches. We investigate the use of boosting descriptive ILP systems, by proposing a novel algorithm for generating classification rules which searches using a hybrid language bias/production rule approach, and a new method for converting first-order classification rules to binary clas- sifiers, which increases the predictive accuracy of the boosted classifiers. We demonstrate that our boosted approach is competitive with normal ILP systems in experiments with bioinformatics datasets. |
Santos, Paulo; Colton, Simon; Magee, Derek Predictive and Descriptive Approaches to Learning Game Rules from Vision Data Incollection In: Advances in Artificial Intelligence-IBERAMIA-SBIA 2006, pp. 349–359, Springer, 2006. @incollection{santos2006predictive, title = {Predictive and Descriptive Approaches to Learning Game Rules from Vision Data}, author = { Paulo Santos and Simon Colton and Derek Magee}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/santos_iberamia06.pdf}, year = {2006}, date = {2006-01-01}, booktitle = {Advances in Artificial Intelligence-IBERAMIA-SBIA 2006}, pages = {349--359}, publisher = {Springer}, abstract = {Systems able to learn from visual observations have a great deal of potential for autonomous robotics, scientific discovery, and many other fields as the necessity to generalise from visual observation (from a quotidian scene or from the results of a scientific enquiry) is inherent in various domains. We de- scribe an application to learning rules of a dice game using data from a vision system observing the game being played. In this paper, we experimented with two broad approaches: (i) a predictive learning approach with the Progol system, where explicit concept learning problems are posed and solved, and (ii) a descrip- tive learning approach with the HR system, where a general theory is formed with no specific problem solving task in mind and rules are extracted from the theory.}, keywords = {}, pubstate = {published}, tppubtype = {incollection} } Systems able to learn from visual observations have a great deal of potential for autonomous robotics, scientific discovery, and many other fields as the necessity to generalise from visual observation (from a quotidian scene or from the results of a scientific enquiry) is inherent in various domains. We de- scribe an application to learning rules of a dice game using data from a vision system observing the game being played. In this paper, we experimented with two broad approaches: (i) a predictive learning approach with the Progol system, where explicit concept learning problems are posed and solved, and (ii) a descrip- tive learning approach with the HR system, where a general theory is formed with no specific problem solving task in mind and rules are extracted from the theory. |
Colton, Simon Automated Puzzle Generation Inproceedings In: Proceedings of the AISB’02 Symposium on AI and Creativity in the Arts and Science, 2002. @inproceedings{colton2002automatedb, title = {Automated Puzzle Generation}, author = { Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_aisb02.pdf}, year = {2002}, date = {2002-01-01}, booktitle = {Proceedings of the AISB’02 Symposium on AI and Creativity in the Arts and Science}, abstract = {We give a characterisation of certain types of puzzle in terms of the structure of the question posed and the nature of the answer to the puzzle. Using this characterisation, we have extended the HR theory formation system (2) to enable it to automatically generate puzzles given background information about a set of objects of interest. The main technical difficulty to overcome was to ensure that the puzzles generated by HR had a single solution (up to a level of plausibility). We give details of the implementation and some results from its application.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We give a characterisation of certain types of puzzle in terms of the structure of the question posed and the nature of the answer to the puzzle. Using this characterisation, we have extended the HR theory formation system (2) to enable it to automatically generate puzzles given background information about a set of objects of interest. The main technical difficulty to overcome was to ensure that the puzzles generated by HR had a single solution (up to a level of plausibility). We give details of the implementation and some results from its application. |
Colton, Simon Automated Theory Formation Applied to Mutagenesis Data Inproceedings In: Proceedings of the First British-Cuban Workshop on BioInformatics, 2002. @inproceedings{colton2002automatedb, title = {Automated Theory Formation Applied to Mutagenesis Data}, author = { Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_bcwob02.pdf}, year = {2002}, date = {2002-01-01}, booktitle = {Proceedings of the First British-Cuban Workshop on BioInformatics}, abstract = {A theory learned by an inductive logic programming (ILP) system such as Progol [5] usually comprises a set of concepts, expressed as logic programs, which can be employed for a classification task. This classifying ability can, in turn, be used for prediction tasks. A scientific theory, however, comprises much more information: concepts; hypotheses relating concepts; explanations and empirical justifications of the hypotheses; representation schemes; experimental methodologies and so on. Working mainly in mathematics, we have used the HR system [1] to form theories about some objects of interest in a domain. For example, in group theory, where the objects are groups, HR invents concepts, makes conjectures about those concepts, and proves (some of) the conjectures using the Otter theorem prover [4]. Despite it’s history in mathematics, we have developed HR as a domain-independent machine learning program. In particular, the format for background information is very similar to that for Progol. Given this, we are currently exploring various possibilities for automated theory formation (ATF) using bioinformatics datasets. We describe here an application of HR to the mutagenesis data set [6] and suggest some advantages of ATF over ILP, some disadvantages, and some possibilities for the fruitful combination of the two techniques.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } A theory learned by an inductive logic programming (ILP) system such as Progol [5] usually comprises a set of concepts, expressed as logic programs, which can be employed for a classification task. This classifying ability can, in turn, be used for prediction tasks. A scientific theory, however, comprises much more information: concepts; hypotheses relating concepts; explanations and empirical justifications of the hypotheses; representation schemes; experimental methodologies and so on. Working mainly in mathematics, we have used the HR system [1] to form theories about some objects of interest in a domain. For example, in group theory, where the objects are groups, HR invents concepts, makes conjectures about those concepts, and proves (some of) the conjectures using the Otter theorem prover [4]. Despite it’s history in mathematics, we have developed HR as a domain-independent machine learning program. In particular, the format for background information is very similar to that for Progol. Given this, we are currently exploring various possibilities for automated theory formation (ATF) using bioinformatics datasets. We describe here an application of HR to the mutagenesis data set [6] and suggest some advantages of ATF over ILP, some disadvantages, and some possibilities for the fruitful combination of the two techniques. |
Improvement of AI Techniques
Given that our overall research goal is to improve the application of AI systems to intelligent tasks, it was sensible for us to question whether combined reasoning systems can improve upon stand-alone systems at standard tasks. Through our experiments with combined reasoning systems, we have shown in many cases that (a) combined reasoning systems can be more flexible in application than stand alone systems (b) combined reasoning systems can be more effective at solving traditional problems than stand alone systems, and (c) combined reasoning systems can undertake intelligent tasks that no single system can attempt. The following papers describe some of our projects in this area:
Ramezani, Ramin; Colton, Simon Automatic Generation of Dynamic Investigation Problems Inproceedings In: Proceedings of the Automated Reasoning Workshop, pp. 34, Citeseer 2010. @inproceedings{ramezani2010automatic, title = {Automatic Generation of Dynamic Investigation Problems}, author = { Ramin Ramezani and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/ramezani_arw10.pdf}, year = {2010}, date = {2010-01-01}, booktitle = {Proceedings of the Automated Reasoning Workshop}, pages = {34}, organization = {Citeseer}, abstract = {One of the ultimate goals of AI computer programs is to solve real world problems as efficiently, or even better than people; sometimes to even solve problems that cannot be solved by people. Imagine a crime case with many suspects involved where each of the suspects has various motivations for the murder which makes the case fairly complicated and the amount of information would be large for a detective to process. Considering that the knowledge about the crime may not even be sufficient for the detective to deduce the murderer, he/she may refer to previously solved cases which bear resemblance to the current one, hoping to find information that can be generalized to the present problem. Employing this new information may lead to identifying the murderer or to at least making it easier by excluding some of the suspects. We call such problems investigation problems, (IPs). These may exhibit ambiguity and complexity but AI problem solving techniques such as machine learning, constraint solving and automated theorem proving are considered as powerful tools for solving such problems. Having focused on investigation problems inspired us to initially come up with a formalized way of defining IPs where we present here. Furthermore, we will discuss an experiment in which different scenarios of a certain IP is generated and is solved by a Constraint Satisfaction Problem (CSP) solving approach.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } One of the ultimate goals of AI computer programs is to solve real world problems as efficiently, or even better than people; sometimes to even solve problems that cannot be solved by people. Imagine a crime case with many suspects involved where each of the suspects has various motivations for the murder which makes the case fairly complicated and the amount of information would be large for a detective to process. Considering that the knowledge about the crime may not even be sufficient for the detective to deduce the murderer, he/she may refer to previously solved cases which bear resemblance to the current one, hoping to find information that can be generalized to the present problem. Employing this new information may lead to identifying the murderer or to at least making it easier by excluding some of the suspects. We call such problems investigation problems, (IPs). These may exhibit ambiguity and complexity but AI problem solving techniques such as machine learning, constraint solving and automated theorem proving are considered as powerful tools for solving such problems. Having focused on investigation problems inspired us to initially come up with a formalized way of defining IPs where we present here. Furthermore, we will discuss an experiment in which different scenarios of a certain IP is generated and is solved by a Constraint Satisfaction Problem (CSP) solving approach. |
Pease, Alison; Smaill, Alan; Colton, Simon; Ireland, Andrew; Llano, Maria Teresa; Ramezani, Ramin; Grov, Gudmund; Guhe, Markus Applying Lakatos-style reasoning to AI problems Book Chapter In: Thinking Machines and the philosophy of computer science: Concepts and principles., Chapter 10, pp. 149–174, Information Science Reference, 2010, ISBN: 9781616920142. @inbook{pease2010applying, title = {Applying Lakatos-style reasoning to AI problems}, author = {Alison Pease and Alan Smaill and Simon Colton and Andrew Ireland and Maria Teresa Llano and Ramin Ramezani and Gudmund Grov and Markus Guhe}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/pease_tm10-1.pdf}, doi = {10.4018/978-1-61692-014-2.ch010}, isbn = {9781616920142}, year = {2010}, date = {2010-01-01}, booktitle = {Thinking Machines and the philosophy of computer science: Concepts and principles.}, journal = {Thinking Machines and the philosophy of computer science: Concepts and principles}, pages = {149--174}, publisher = {Information Science Reference}, chapter = {10}, abstract = {One current direction in AI research is to focus on combining different reasoning styles such as deduction, induction, abduction, analogical reasoning, non-monotonic reasoning, vague and uncertain reasoning. The philosopher Imre Lakatos produced one such theory of how people with different reasoning styles collaborate to develop mathematical ideas. Lakatos argued that mathematics is a quasi-empirical, flexible, fallible, human endeavour, involving negotiations, mistakes, vague concept definitions and disagreements, and he outlined a heuristic approach towards the subject. In this chapter we apply these heuristics to the AI domains of evolving requirement specifi- cations, planning and constraint satisfaction problems. In drawing analogies between Lakatos’s theory and these three domains we identify areas of work which correspond to each heuristic, and suggest extensions and further ways in which Lakatos’s philoso- phy can inform AI problem solving. Thus, we show how we might begin to produce a philosophically-inspired AI theory of combined reasoning.}, keywords = {}, pubstate = {published}, tppubtype = {inbook} } One current direction in AI research is to focus on combining different reasoning styles such as deduction, induction, abduction, analogical reasoning, non-monotonic reasoning, vague and uncertain reasoning. The philosopher Imre Lakatos produced one such theory of how people with different reasoning styles collaborate to develop mathematical ideas. Lakatos argued that mathematics is a quasi-empirical, flexible, fallible, human endeavour, involving negotiations, mistakes, vague concept definitions and disagreements, and he outlined a heuristic approach towards the subject. In this chapter we apply these heuristics to the AI domains of evolving requirement specifi- cations, planning and constraint satisfaction problems. In drawing analogies between Lakatos’s theory and these three domains we identify areas of work which correspond to each heuristic, and suggest extensions and further ways in which Lakatos’s philoso- phy can inform AI problem solving. Thus, we show how we might begin to produce a philosophically-inspired AI theory of combined reasoning. |
Ramezani, Ramin; Colton, Simon Solving Mutilated Problems Inproceedings In: Automated Reasoning Workshop, pp. 27, 2009. @inproceedings{ramezani2009solving, title = {Solving Mutilated Problems}, author = { Ramin Ramezani and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/ramezani_arw09.pdf}, year = {2009}, date = {2009-01-01}, booktitle = {Automated Reasoning Workshop}, pages = {27}, abstract = {Constraint solving, theorem proving and machine learning provide powerful techniques for solving AI problems. In all these approaches, information known as background knowledge needs to be provided, from which the system will infer new knowledge. Often, however, the background information may be obscure or incomplete, and is usually presented in a form suitable for only one type of problem solver, such as a first order theorem prover. In real world scenarios, there may not be enough background information for any single solver to solve the problem, and we are interested in cases where it may be possible to combine a machine learner, theorem prover and constraint solver in order to best use their incomplete background knowledge to solve the problem. We present here some preliminary experiments designed to test the feasibility of such an approach}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Constraint solving, theorem proving and machine learning provide powerful techniques for solving AI problems. In all these approaches, information known as background knowledge needs to be provided, from which the system will infer new knowledge. Often, however, the background information may be obscure or incomplete, and is usually presented in a form suitable for only one type of problem solver, such as a first order theorem prover. In real world scenarios, there may not be enough background information for any single solver to solve the problem, and we are interested in cases where it may be possible to combine a machine learner, theorem prover and constraint solver in order to best use their incomplete background knowledge to solve the problem. We present here some preliminary experiments designed to test the feasibility of such an approach |
Charnley, John; Colton, Simon Prediction using Machine Learned Constraint Satisfaction Programs Inproceedings In: Proceedings of the Automated Reasoning Workshop, 2007. @inproceedings{charnleyprediction, title = {Prediction using Machine Learned Constraint Satisfaction Programs}, author = { John Charnley and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/charnley_arw07.pdf}, year = {2007}, date = {2007-01-01}, booktitle = {Proceedings of the Automated Reasoning Workshop}, journal = {Automated Reasoning Workshop}, abstract = {Prediction is a well-researched area for Machine Learning applications. In these tasks, the aim is to predict the value for some unseen characteristic based upon the values of other, seen, characteristics for a given example. Machine learning has been extensively applied to these types of tasks by automating the derivation of a predictive function or a set of predictive rules. This predictive function can then be applied to new examples to estimate attribute values.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Prediction is a well-researched area for Machine Learning applications. In these tasks, the aim is to predict the value for some unseen characteristic based upon the values of other, seen, characteristics for a given example. Machine learning has been extensively applied to these types of tasks by automating the derivation of a predictive function or a set of predictive rules. This predictive function can then be applied to new examples to estimate attribute values. |
Charnley, John; Colton, Simon Expressing General Problems as CSPs Inproceedings In: Proceedings of the Workshop on Modelling and Solving Problems with Constraints at ECAI, Citeseer 2006. @inproceedings{charnley2006expressing, title = {Expressing General Problems as CSPs}, author = { John Charnley and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/charnley_ecai06workshop.pdf}, year = {2006}, date = {2006-01-01}, booktitle = {Proceedings of the Workshop on Modelling and Solving Problems with Constraints at ECAI}, organization = {Citeseer}, abstract = {We consider the translation of general AI problems into CSPs. In particular, we have developed a translation suite able to translate first order specifica- tions into the syntax of the Sicstus CLPFD constraint solver. We describe recent extensions to the capabilities of this suite which have enabled it to handle prob- lems outside of the algebraic domains for which it was designed. We demonstrate two of many advantages to having such a translation suite. Firstly, we show that an ability to translate between the syntaxes of different AI problem solving sys- tems enables us to make meaningful comparisons of different AI techniques, and we demonstrate this using a model generator and a constraint solver on quasi- group problems. Secondly, with an ability to express a problem in different ways, we can begin to simulate more sophisticated problem solving which uses induc- tive, deductive and constraint solving techniques. We explore such possibilities with some applications to investigative reasoning, where the aim is to identify the cause of a phenomenon from a set of candidates.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We consider the translation of general AI problems into CSPs. In particular, we have developed a translation suite able to translate first order specifica- tions into the syntax of the Sicstus CLPFD constraint solver. We describe recent extensions to the capabilities of this suite which have enabled it to handle prob- lems outside of the algebraic domains for which it was designed. We demonstrate two of many advantages to having such a translation suite. Firstly, we show that an ability to translate between the syntaxes of different AI problem solving sys- tems enables us to make meaningful comparisons of different AI techniques, and we demonstrate this using a model generator and a constraint solver on quasi- group problems. Secondly, with an ability to express a problem in different ways, we can begin to simulate more sophisticated problem solving which uses induc- tive, deductive and constraint solving techniques. We explore such possibilities with some applications to investigative reasoning, where the aim is to identify the cause of a phenomenon from a set of candidates. |
Charnley, John; Colton, Simon; Miguel, Ian Automated Reformulation of Constraint Satisfaction Problems Inproceedings In: Proceedings of the Automated Reasoning Workshop, pp. 8, Citeseer, 2006. @inproceedings{charnley2006automated, title = {Automated Reformulation of Constraint Satisfaction Problems}, author = { John Charnley and Simon Colton and Ian Miguel}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/charnley_arw06.pdf}, year = {2006}, date = {2006-01-01}, booktitle = {Proceedings of the Automated Reasoning Workshop}, journal = {Specification and Verification of Reconfiguration Protocols in Grid Component Systems}, pages = {8}, publisher = {Citeseer}, abstract = {A constraint satisfaction problem (CSP) consists of a set of variables {x1,x2,...,xn}, a set of domains of values the variables can take and a set of constraints specifying which values the variables can take simultaneously. A solution to a CSP is an assignment of values to each of the variables from their domains such that no constraints are broken. They find widespread use in science and industry and can be extremely complicated, involving a large number of variables and complex constraints. CSP solvers allow users to specify CSPs in a particular syntax, and then search for solutions to the problem, normally using a configurable search approach. Correctly formulating CSPs is a skilled and time-consuming task. Moreover, once formulated, a CSP problem can take a large amount of processing time to solve. For these reasons, various methods have been devised to improve the effectiveness of CSP solving. One such method is to find additional information about the domain being studied and use this knowledge to reformulate the CSP solver to improve its effectiveness. In particular, when the domain of investigation is described by axioms in first-order logic then it may be possible to derive new theorems from those axioms. Such implied theorems are true for all instances of the domain and can therefore be added to the CSP formulation without loss of generality.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } A constraint satisfaction problem (CSP) consists of a set of variables {x1,x2,...,xn}, a set of domains of values the variables can take and a set of constraints specifying which values the variables can take simultaneously. A solution to a CSP is an assignment of values to each of the variables from their domains such that no constraints are broken. They find widespread use in science and industry and can be extremely complicated, involving a large number of variables and complex constraints. CSP solvers allow users to specify CSPs in a particular syntax, and then search for solutions to the problem, normally using a configurable search approach. Correctly formulating CSPs is a skilled and time-consuming task. Moreover, once formulated, a CSP problem can take a large amount of processing time to solve. For these reasons, various methods have been devised to improve the effectiveness of CSP solving. One such method is to find additional information about the domain being studied and use this knowledge to reformulate the CSP solver to improve its effectiveness. In particular, when the domain of investigation is described by axioms in first-order logic then it may be possible to derive new theorems from those axioms. Such implied theorems are true for all instances of the domain and can therefore be added to the CSP formulation without loss of generality. |
Charnley, John; Colton, Simon; Miguel, Ian Automatic generation of Implied Constraints Inproceedings In: ECAI, pp. 73–77, 2006. @inproceedings{charnley2006automatic, title = {Automatic generation of Implied Constraints}, author = { John Charnley and Simon Colton and Ian Miguel}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/charnley_ecai06.pdf}, year = {2006}, date = {2006-01-01}, booktitle = {ECAI}, volume = {141}, pages = {73--77}, abstract = {A well-known difficulty with solving Constraint Satis- faction Problems (CSPs) is that, while one formulation of a CSP may enable a solver to solve it quickly, a different formulation may take prohibitively long to solve. We demonstrate a system for automati- cally reformulating CSP solver models by combining the capabilities of machine learning and automated theorem proving with CSP sys- tems. Our system is given a basic CSP formulation and outputs a set of reformulations, each of which includes additional constraints. The additional constraints are generated through a machine learn- ing process and are proven to follow from the basic formulation by a theorem prover. Experimenting with benchmark problem classes from finite algebras, we show how the time invested in reformulation is often recovered many times over when searching for solutions to more difficult problems from the problem class.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } A well-known difficulty with solving Constraint Satis- faction Problems (CSPs) is that, while one formulation of a CSP may enable a solver to solve it quickly, a different formulation may take prohibitively long to solve. We demonstrate a system for automati- cally reformulating CSP solver models by combining the capabilities of machine learning and automated theorem proving with CSP sys- tems. Our system is given a basic CSP formulation and outputs a set of reformulations, each of which includes additional constraints. The additional constraints are generated through a machine learn- ing process and are proven to follow from the basic formulation by a theorem prover. Experimenting with benchmark problem classes from finite algebras, we show how the time invested in reformulation is often recovered many times over when searching for solutions to more difficult problems from the problem class. |
Colton, Simon; Pease, Alison The TM System for Repairing Non-Theorems Journal Article In: Electronic Notes in Theoretical Computer Science, 125 (3), pp. 87–101, 2005. @article{colton2005tm, title = {The TM System for Repairing Non-Theorems}, author = { Simon Colton and Alison Pease}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_ijcar04workshop.pdf}, year = {2005}, date = {2005-01-01}, journal = {Electronic Notes in Theoretical Computer Science}, volume = {125}, number = {3}, pages = {87--101}, publisher = {Elsevier}, abstract = {We describe a flexible approach to automated reasoning, where non-theorems can be automatically altered to produce proved results which are related to the origi-nal. This is achieved in the TM system through an interaction of the HR machine learning program, the Otter theorem prover and the Mace model generator. Given a non-theorem, Mace is used to generate examples which support the non-theorem, and examples which falsify it. HR then invents concepts which categorise these examples and TM uses these concepts to modify the original non-theorem into spe-cialised theorems which Otter can prove. The methods employed by TM are inspired by the piecemeal exclusion, strategic withdrawal and counterexample barring meth-ods described in Lakatos's philosophy of mathematics. In addition, TM can also determine which modified theorems are likely to be interesting and which are not. We demonstrate the effectiveness of this approach by modifying non-theorems taken from the TPTP library of first order theorems. We show that, for 98 non-theorems, TM produced meaningful modifications for 81 of them. This work forms part of two larger projects. Firstly, we are working towards a full implementation both of the reasoning and the social interaction notions described by Lakatos. Secondly, we are aiming to show that the combination of reasoning systems such as those used in TM will lead to a new generation of more powerful AI systems. Key words: Automated theorem modification, automated reasoning, model generation, machine learning, automated theory formation, philosophy of mathematics. }, keywords = {}, pubstate = {published}, tppubtype = {article} } We describe a flexible approach to automated reasoning, where non-theorems can be automatically altered to produce proved results which are related to the origi-nal. This is achieved in the TM system through an interaction of the HR machine learning program, the Otter theorem prover and the Mace model generator. Given a non-theorem, Mace is used to generate examples which support the non-theorem, and examples which falsify it. HR then invents concepts which categorise these examples and TM uses these concepts to modify the original non-theorem into spe-cialised theorems which Otter can prove. The methods employed by TM are inspired by the piecemeal exclusion, strategic withdrawal and counterexample barring meth-ods described in Lakatos's philosophy of mathematics. In addition, TM can also determine which modified theorems are likely to be interesting and which are not. We demonstrate the effectiveness of this approach by modifying non-theorems taken from the TPTP library of first order theorems. We show that, for 98 non-theorems, TM produced meaningful modifications for 81 of them. This work forms part of two larger projects. Firstly, we are working towards a full implementation both of the reasoning and the social interaction notions described by Lakatos. Secondly, we are aiming to show that the combination of reasoning systems such as those used in TM will lead to a new generation of more powerful AI systems. Key words: Automated theorem modification, automated reasoning, model generation, machine learning, automated theory formation, philosophy of mathematics. |
Colton, Simon; Hoermann, Ferdinand; Sutcliffe, Geoff; Pease, Alison Machine Learning Case Splits for Theorem Proving Inproceedings In: Proceedings of the Automated Reasoning Workshop, Edinburgh, 2005. @inproceedings{colton2005machine, title = {Machine Learning Case Splits for Theorem Proving}, author = { Simon Colton and Ferdinand Hoermann and Geoff Sutcliffe and Alison Pease}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_arw05.pdf}, year = {2005}, date = {2005-01-01}, booktitle = {Proceedings of the Automated Reasoning Workshop, Edinburgh}, abstract = {We believe that in order to build more powerful AI systems, it will be necessary to combine techniques from machine learn-ing, automated deduction, constraint solving, computer al-gebra, planning and other domains. In particular, as argued by philosophers such as Lakatos [5], mathematical discovery processes rely on a plethora of reasoning techniques, includ-ing deduction, induction, abduction, symbolic manipulation, etc. To demonstrate that the whole can be more than the sum of the parts when combining systems, we have performed a number of case studies in automated mathematics. These demonstrate that, with respect to stand-alone systems, com-bined reasoning systems can: (a) be more flexible in their application [4] (b) undertake new tasks [2] and (c) perform standard tasks better [3]. }, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We believe that in order to build more powerful AI systems, it will be necessary to combine techniques from machine learn-ing, automated deduction, constraint solving, computer al-gebra, planning and other domains. In particular, as argued by philosophers such as Lakatos [5], mathematical discovery processes rely on a plethora of reasoning techniques, includ-ing deduction, induction, abduction, symbolic manipulation, etc. To demonstrate that the whole can be more than the sum of the parts when combining systems, we have performed a number of case studies in automated mathematics. These demonstrate that, with respect to stand-alone systems, com-bined reasoning systems can: (a) be more flexible in their application [4] (b) undertake new tasks [2] and (c) perform standard tasks better [3]. |
Pease, Alison; Colton, Simon Automatic Conjecture Modification Book Chapter In: Proceedings of the 11th Workshop On Automated Reasoning: Bridging The Gap Between Theory And Practice, 2004. @inbook{Pease2004, title = {Automatic Conjecture Modification}, author = {Alison Pease and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/pease_arw04.pdf}, year = {2004}, date = {2004-01-01}, booktitle = {Proceedings of the 11th Workshop On Automated Reasoning: Bridging The Gap Between Theory And Practice}, abstract = {One of the original goals of writing theorem provers was to provide tools which mathematicians could use to aid their research, yet this goal remains unsatisfied to a large extent. We believe that one of the reasons for this failure is that so far automated theorem provers have failed to incorporate the flexibility which humans take for granted, and which is inherent in intelligent activity. To begin to address this, we have implemented a theorem modification system, called TM. This is able to take in a conjecture, try to prove it, and if unsuccessful (either because the conjecture is too hard to prove or because it is false), produce modified versions of the conjecture which it can prove. As a simple, yet illustrative, example, given the non-theorem that all groups are Abelian, TM states that it cannot prove the original result, but it has discovered that all self-inverse groups are Abelian. TM is a combined reasoning system, which uses inductive, deductive and model-based reasoning to achieve the goal of modifying theorems. }, keywords = {}, pubstate = {published}, tppubtype = {inbook} } One of the original goals of writing theorem provers was to provide tools which mathematicians could use to aid their research, yet this goal remains unsatisfied to a large extent. We believe that one of the reasons for this failure is that so far automated theorem provers have failed to incorporate the flexibility which humans take for granted, and which is inherent in intelligent activity. To begin to address this, we have implemented a theorem modification system, called TM. This is able to take in a conjecture, try to prove it, and if unsuccessful (either because the conjecture is too hard to prove or because it is false), produce modified versions of the conjecture which it can prove. As a simple, yet illustrative, example, given the non-theorem that all groups are Abelian, TM states that it cannot prove the original result, but it has discovered that all self-inverse groups are Abelian. TM is a combined reasoning system, which uses inductive, deductive and model-based reasoning to achieve the goal of modifying theorems. |
Colton, Simon; Pease, Alison Lakatos-style automated theorem modification Inproceedings In: ECAI, pp. 977, 2004. @inproceedings{colton2004lakatos, title = {Lakatos-style automated theorem modification}, author = { Simon Colton and Alison Pease}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_ecai04poster.pdf}, year = {2004}, date = {2004-01-01}, booktitle = {ECAI}, volume = {16}, pages = {977}, abstract = {We describe a flexible approach to automated reasoning, where non-theorems can be automatically altered to produce proved results which are related to the original. This is achieved through an interaction of the HR machine learning system, the Otter theorem prover and the Mace model generator, and uses methods inspired by Lakatos’s philosophy of mathematics. We demonstrate the effec- tiveness of this approach by modifying non-theorems taken from the TPTP library of first order theorems.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We describe a flexible approach to automated reasoning, where non-theorems can be automatically altered to produce proved results which are related to the original. This is achieved through an interaction of the HR machine learning system, the Otter theorem prover and the Mace model generator, and uses methods inspired by Lakatos’s philosophy of mathematics. We demonstrate the effec- tiveness of this approach by modifying non-theorems taken from the TPTP library of first order theorems. |
Sutcliffe, Geoff; Gao, Yi; Colton, Simon A Grand Challenge of Theorem Discovery Inproceedings In: Proceedings of the Workshop on Challenges and Novel Applications for Automated Reasoning, 19th International Conference on Automated Reasoning, pp. 1–11, 2003. @inproceedings{sutcliffe2003grand, title = {A Grand Challenge of Theorem Discovery}, author = { Geoff Sutcliffe and Yi Gao and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/sutcliffe_cade03.pdf}, year = {2003}, date = {2003-01-01}, booktitle = {Proceedings of the Workshop on Challenges and Novel Applications for Automated Reasoning, 19th International Conference on Automated Reasoning}, pages = {1--11}, abstract = {A primary mode of operation of ATP systems is to supply the system with axioms and a conjecture, and to then ask the system to produce a proof (or at least an assurance that there is a proof) that the conjecture is a theorem of the axioms. This paper challenges ATP to a new mode of operation, by which interesting theorems are generated from a set of axioms. The challenge requires solutions to both theoretical and computational issues. }, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } A primary mode of operation of ATP systems is to supply the system with axioms and a conjecture, and to then ask the system to produce a proof (or at least an assurance that there is a proof) that the conjecture is a theorem of the axioms. This paper challenges ATP to a new mode of operation, by which interesting theorems are generated from a set of axioms. The challenge requires solutions to both theoretical and computational issues. |
Zimmer, Jürgen; Franke, Andreas; Colton, Simon; Sutcliffe, Geoff Integrating HR and tptp2x into MathWeb to Compare Automated Theorem Provers Inproceedings In: In Proceedings of the CADE'02 Workshop on Problems and Problem sets, Citeseer 2002. @inproceedings{Zimmer2002, title = {Integrating HR and tptp2x into MathWeb to Compare Automated Theorem Provers}, author = { Jürgen Zimmer and Andreas Franke and Simon Colton and Geoff Sutcliffe}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/zimmer_paps02.pdf}, year = {2002}, date = {2002-01-01}, booktitle = {In Proceedings of the CADE'02 Workshop on Problems and Problem sets}, organization = {Citeseer}, abstract = {The assessment and comparison of automated theorem proving sys-tems (ATPs) is important for the advancement of the field. At present, the de facto assessment method is to test provers on the TPTP library of nearly 6000 theorems. We describe here a project which aims to com-plement the TPTP service by automatically generating theorems of suf-ficient difficulty to provide a significant test for first order provers. This has been achieved by integrating the HR automated theory formation program into the MathWeb Software Bus. HR generates first order con-jectures in TPTP format and passes them to a concurrent ATP service in MathWeb. MathWeb then uses the tptp2X utility to translate the conjectures into the input format of a set of provers. In this way, var-ious ATP systems can be compared on their performance over sets of thousands of theorems they have not been previously exposed to. Our purpose here is to describe the integration of various new programs into the MathWeb architecture, rather than to present a full analysis of the performance of theorem provers. However, to demonstrate the potential of the combination of the systems, we describe some preliminary results from experiments in group theory. }, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } The assessment and comparison of automated theorem proving sys-tems (ATPs) is important for the advancement of the field. At present, the de facto assessment method is to test provers on the TPTP library of nearly 6000 theorems. We describe here a project which aims to com-plement the TPTP service by automatically generating theorems of suf-ficient difficulty to provide a significant test for first order provers. This has been achieved by integrating the HR automated theory formation program into the MathWeb Software Bus. HR generates first order con-jectures in TPTP format and passes them to a concurrent ATP service in MathWeb. MathWeb then uses the tptp2X utility to translate the conjectures into the input format of a set of provers. In this way, var-ious ATP systems can be compared on their performance over sets of thousands of theorems they have not been previously exposed to. Our purpose here is to describe the integration of various new programs into the MathWeb architecture, rather than to present a full analysis of the performance of theorem provers. However, to demonstrate the potential of the combination of the systems, we describe some preliminary results from experiments in group theory. |
Colton, Simon; Sutcliffe, Geoff Automatic Generation of Benchmark Problems for Automated Theorem Proving Systems. Inproceedings In: AMAI, 2002. @inproceedings{Colton2002, title = {Automatic Generation of Benchmark Problems for Automated Theorem Proving Systems.}, author = { Simon Colton and Geoff Sutcliffe}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_aim02_2.pdf}, year = {2002}, date = {2002-01-01}, booktitle = {AMAI}, abstract = {Automated Theorem Proving (ATP) researchers who always use the same problems for testing their systems, run the risk of producing systems that can solve only those problems, and are weak on new problems or applications. Furthermore, as the state-of-the-art in ATP progresses, existing test problems become too easy, and testing on them provides little useful information. It is thus important to regularly find new and harder problems for testing ATP systems. HR is a program that performs automated theory formation in mathematical domains, such as group theory, quasigroup theory, and ring theory. Given the axioms of the domain, HR invents concepts, finds examples of them using a model generator, and makes conjectures empirically about the concepts. HR has been used to discover new group theory theorems of sufficient difficulty to be included in the TPTP - the standard library of test problems for first order ATP systems. As HR produces tens of thousands of distinct theorems, there has also been an opportunity to determine some characteristics that can be used to identify hard problems. }, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Automated Theorem Proving (ATP) researchers who always use the same problems for testing their systems, run the risk of producing systems that can solve only those problems, and are weak on new problems or applications. Furthermore, as the state-of-the-art in ATP progresses, existing test problems become too easy, and testing on them provides little useful information. It is thus important to regularly find new and harder problems for testing ATP systems. HR is a program that performs automated theory formation in mathematical domains, such as group theory, quasigroup theory, and ring theory. Given the axioms of the domain, HR invents concepts, finds examples of them using a model generator, and makes conjectures empirically about the concepts. HR has been used to discover new group theory theorems of sufficient difficulty to be included in the TPTP - the standard library of test problems for first order ATP systems. As HR produces tens of thousands of distinct theorems, there has also been an opportunity to determine some characteristics that can be used to identify hard problems. |
Colton, Simon Automated Theorem Discovery: Future Direction for Theorem Provers Miscellaneous 2001. @misc{Colton2001, title = {Automated Theorem Discovery: Future Direction for Theorem Provers}, author = {Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_ijcar01.pdf}, year = {2001}, date = {2001-01-01}, abstract = {One obvious and important aspect of automated theorem proving is that the users know in advance which theorem they wish to prove. A possible future direction for theorem provers is to enable users to discover theorems which they were not necessarily aware of. We sur-vey previous attempts at this and give a new demonstration of theorem generation using our HR program [10] in the domain of 'anti-associative' algebras. We also suggest three applications where this functionality may prove useful, and discuss how this would add value to theorem provers. }, keywords = {}, pubstate = {published}, tppubtype = {misc} } One obvious and important aspect of automated theorem proving is that the users know in advance which theorem they wish to prove. A possible future direction for theorem provers is to enable users to discover theorems which they were not necessarily aware of. We sur-vey previous attempts at this and give a new demonstration of theorem generation using our HR program [10] in the domain of 'anti-associative' algebras. We also suggest three applications where this functionality may prove useful, and discuss how this would add value to theorem provers. |
Colton, Simon; Miguel, Ian Constraint Generation via Automated Theory Formation Inproceedings In: International Conference on Principles and Practice of Constraint Programming, pp. 575–579, Springer 2001. @inproceedings{Colton2001, title = {Constraint Generation via Automated Theory Formation}, author = { Simon Colton and Ian Miguel}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_cp01.pdf}, year = {2001}, date = {2001-01-01}, booktitle = {International Conference on Principles and Practice of Constraint Programming}, pages = {575--579}, organization = {Springer}, abstract = {Adding constraints to a basic CSP model can significantly reduce search, e.g. for Golomb rulers [6]. The generation process is usually performed by hand, although some recent work has focused on automatically generating symmetry breaking constraints [4] and (less so) on generating implied constraints [5]. We describe an approach to generating implied, symmetry breaking and specialisa-tion constraints and apply this technique to quasigroup construction [10]. Given a problem class parameterised by size, we use a basic model to solve small instances with the Choco constraint programming language [7]. We then give these solutions to the HR automated theory formation program [1] which detects implied constraints (proved to follow from the specifications) and in-duced constraints (true of a subset of solutions). Interpreting HR's results to reformulate the model can lead to a reduction in search on larger instances. It is often more efficient to run HR, interpret the results and solve the CSP, than to solve the problem with the basic model alone. }, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Adding constraints to a basic CSP model can significantly reduce search, e.g. for Golomb rulers [6]. The generation process is usually performed by hand, although some recent work has focused on automatically generating symmetry breaking constraints [4] and (less so) on generating implied constraints [5]. We describe an approach to generating implied, symmetry breaking and specialisa-tion constraints and apply this technique to quasigroup construction [10]. Given a problem class parameterised by size, we use a basic model to solve small instances with the Choco constraint programming language [7]. We then give these solutions to the HR automated theory formation program [1] which detects implied constraints (proved to follow from the specifications) and in-duced constraints (true of a subset of solutions). Interpreting HR's results to reformulate the model can lead to a reduction in search on larger instances. It is often more efficient to run HR, interpret the results and solve the CSP, than to solve the problem with the basic model alone. |
Colton, Simon Theory Formation Applied to Learning, Discovery and Problem Solving Inproceedings In: Proceedings of Machine Intelligence 17, 2000. @inproceedings{Colton2000, title = {Theory Formation Applied to Learning, Discovery and Problem Solving}, author = {Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/colton_mi00.pdf}, year = {2000}, date = {2000-01-01}, booktitle = {Proceedings of Machine Intelligence 17}, abstract = {We discuss the HR program [1] which is designed to perform automated theory formation in domains of pure mathematics. We overview the recent application of theory formation to discovery, learning and problem solving tasks. We compare how theory formation is used for these tasks and discuss how to compare HR to the machine learning program Progol [9]. }, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We discuss the HR program [1] which is designed to perform automated theory formation in domains of pure mathematics. We overview the recent application of theory formation to discovery, learning and problem solving tasks. We compare how theory formation is used for these tasks and discuss how to compare HR to the machine learning program Progol [9]. |
Automating Graphic Design and Visual Arts Processes
While the HR system provided a good platform for the study of how to automate mathematical and scientific creative processes, in order to further study computational creativity, we have also undertaken a number of projects aimed at automating processes in the creative industries. In particular, we have built The Painting Fool as a software artist, which we intend will be taken seriously as a creative artist in its own right, one day. In order to facilitate the creative construction of scenes, we have pushed evolutionary and constraint solving techniques to the limit. We have also looked into various evolutionary art projects, and we have introduced a new browsing paradigm called Objet Trouve Computing, where the software drives the process as much as the user, but also learns the user’s preferences along the way. The following papers describe some of our projects in this area:
Colton, Simon; Halskov, Jakob; Ventura, Dan; Gouldstone, Ian; Cook, Michael; Ferrer, Blanca P'erez The Painting Fool Sees! New Projects with the Automated Painter Inproceedings In: Proceedings of the 6th International Conference on Computational Creativity, 2015. @inproceedings{Colton2015ICCC, title = {The Painting Fool Sees! New Projects with the Automated Painter}, author = {Simon Colton and Jakob Halskov and Dan Ventura and Ian Gouldstone and Michael Cook and Blanca P'erez Ferrer}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/colton_iccc2015.pdf}, year = {2015}, date = {2015-10-01}, booktitle = {Proceedings of the 6th International Conference on Computational Creativity}, abstract = {We report the most recent advances in The Painting Fool project, where we have integrated machine vision capabilities from the DARCI system into the automated painter, to enhance its abilities before, during and after the painting process. This has enabled new art projects, including a commission from an Artificial Intelligence company, and we report on this collaboration, which is one of the first instances in Computational Creativity research where creative software has been commissioned directly. The new projects have advanced The Painting Fool as an independent artist able to produce more diverse styles which break away from simulating natural media. The projects have also raised a philosophical question about whether software artists need to see in the same way as people, which we discuss briefly.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We report the most recent advances in The Painting Fool project, where we have integrated machine vision capabilities from the DARCI system into the automated painter, to enhance its abilities before, during and after the painting process. This has enabled new art projects, including a commission from an Artificial Intelligence company, and we report on this collaboration, which is one of the first instances in Computational Creativity research where creative software has been commissioned directly. The new projects have advanced The Painting Fool as an independent artist able to produce more diverse styles which break away from simulating natural media. The projects have also raised a philosophical question about whether software artists need to see in the same way as people, which we discuss briefly. |
Colton, Simon; Ventura, Dan You Can't Know my Mind: A Festival of Computational Creativity Inproceedings In: Late Breaking Proceedings of the Fifth International Conference on Computational Creativity, 2014. @inproceedings{colton2014you, title = {You Can't Know my Mind: A Festival of Computational Creativity}, author = { Simon Colton and Dan Ventura}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/09/colton_iccc2014lbp.pdf}, year = {2014}, date = {2014-01-01}, booktitle = {Late Breaking Proceedings of the Fifth International Conference on Computational Creativity}, journal = {ICCC}, abstract = {We report on a week-long celebration of Computational Cre- ativity research and practice in a gallery in Paris, France. The festival was called You Can’t Know my Mind, and was in- tended to introduce to the public the idea that researchers such as ourselves are writing software to be surprisingly un- predictable and creative in nature. The festival included a tra- ditional art exhibition with a vernissage, a live music evening, a poetry night coupled with a food tasting, and a week long demonstration of mood-driven portraiture from The Painting Fool software. Each of the events – which are described here for the first time – involved an element of creative respon- sibility taken on by various software systems. The success of the festival was demonstrated in terms of attendance and feedback, pieces written by journalists, and follow up events which have taken place in 2013 and 2014.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We report on a week-long celebration of Computational Cre- ativity research and practice in a gallery in Paris, France. The festival was called You Can’t Know my Mind, and was in- tended to introduce to the public the idea that researchers such as ourselves are writing software to be surprisingly un- predictable and creative in nature. The festival included a tra- ditional art exhibition with a vernissage, a live music evening, a poetry night coupled with a food tasting, and a week long demonstration of mood-driven portraiture from The Painting Fool software. Each of the events – which are described here for the first time – involved an element of creative respon- sibility taken on by various software systems. The success of the festival was demonstrated in terms of attendance and feedback, pieces written by journalists, and follow up events which have taken place in 2013 and 2014. |
Colton, Simon; Ferrer, Blanca P'erez No Photos Harmed/Growing Paths from Seed: An Exhibition Inproceedings In: Proceedings of the Symposium on Non-Photorealistic Animation and Rendering, pp. 1–10, Eurographics Association 2012. @inproceedings{colton2012no, title = {No Photos Harmed/Growing Paths from Seed: An Exhibition}, author = { Simon Colton and Blanca P'erez Ferrer}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/09/colton_npar12.pdf}, year = {2012}, date = {2012-01-01}, booktitle = {Proceedings of the Symposium on Non-Photorealistic Animation and Rendering}, pages = {1--10}, organization = {Eurographics Association}, abstract = {We report on an exhibition centered around a dialogue between a Computational Creativity researcher presenting artwork generated by a computer program and a classically trained artist taking in- spiration from the computational processes. The main purpose of the exhibition was to place software-generated art (where the pro- gram takes on some aesthetic and generative responsibilities, rather than acting as a mere tool) in both an art-production context and an art-historical context, by exploring the themes of creative re- sponsibility and the loss of aura surrounding a work of art. A sec- ondary purpose was to highlight the fact that computer generated art can be representational without relying on digital photographs as inputs. We describe certain technical hurdles we overcame in the production of the exhibition and the feedback we gained, in ad- dition to elaborating on how the event and the project as a whole fits into an art-historical context. We conclude with brief details of another exhibition involving art generated by the same software system, where the notion of progression was explored; by describ- ing a planned exhibition, where autonomy and independence in the system will be highlighted; and by providing a partial roadmap for progress towards autonomously creative software in the visual arts.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We report on an exhibition centered around a dialogue between a Computational Creativity researcher presenting artwork generated by a computer program and a classically trained artist taking in- spiration from the computational processes. The main purpose of the exhibition was to place software-generated art (where the pro- gram takes on some aesthetic and generative responsibilities, rather than acting as a mere tool) in both an art-production context and an art-historical context, by exploring the themes of creative re- sponsibility and the loss of aura surrounding a work of art. A sec- ondary purpose was to highlight the fact that computer generated art can be representational without relying on digital photographs as inputs. We describe certain technical hurdles we overcame in the production of the exhibition and the feedback we gained, in ad- dition to elaborating on how the event and the project as a whole fits into an art-historical context. We conclude with brief details of another exhibition involving art generated by the same software system, where the notion of progression was explored; by describ- ing a planned exhibition, where autonomy and independence in the system will be highlighted; and by providing a partial roadmap for progress towards autonomously creative software in the visual arts. |
Colton, Simon Evolving a Library of Artistic Scene Descriptors Inproceedings In: International Conference on Evolutionary and Biologically Inspired Music and Art, pp. 35–47, Springer 2012. @inproceedings{colton2012evolving, title = {Evolving a Library of Artistic Scene Descriptors}, author = { Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/colton_evomusart12.pdf}, year = {2012}, date = {2012-01-01}, booktitle = {International Conference on Evolutionary and Biologically Inspired Music and Art}, pages = {35--47}, organization = {Springer}, abstract = {We describe the building of a library of 10,000 distinct ab- stract art images, and how these can be interpreted as describing the placement of objects in a scene for generative painting projects. Build- ing the library to contain only markedly distinct images necessitated a machine learning approach, whereby two decision trees were derived to predict visual similarity in pairs of images. The first tree uses genotypical information to predict before image generation whether two images will be too similar. The second tree uses phenotypical information, namely how pairs of images differ when segmented using various distance thresh- olds. Taken together, the trees are highly effective at quickly predicting when two images are similar, and we used this in an evolutionary search where non-unique individuals are pruned, to build up the library. We show how the pruning approach can be used alongside a fitness function to increase the yield of images with certain properties, such as low/high colour variety, symmetry and contrast.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We describe the building of a library of 10,000 distinct ab- stract art images, and how these can be interpreted as describing the placement of objects in a scene for generative painting projects. Build- ing the library to contain only markedly distinct images necessitated a machine learning approach, whereby two decision trees were derived to predict visual similarity in pairs of images. The first tree uses genotypical information to predict before image generation whether two images will be too similar. The second tree uses phenotypical information, namely how pairs of images differ when segmented using various distance thresh- olds. Taken together, the trees are highly effective at quickly predicting when two images are similar, and we used this in an evolutionary search where non-unique individuals are pruned, to build up the library. We show how the pruning approach can be used alongside a fitness function to increase the yield of images with certain properties, such as low/high colour variety, symmetry and contrast. |
Colton, Simon The Painting Fool: Stories from Building an Automated Painter Incollection In: Computers and creativity, pp. 3–38, Springer, 2012. @incollection{colton2012painting, title = {The Painting Fool: Stories from Building an Automated Painter}, author = { Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/09/colton_tpfchapter12.pdf}, year = {2012}, date = {2012-01-01}, booktitle = {Computers and creativity}, pages = {3--38}, publisher = {Springer}, abstract = {The Painting Fool is software that we hope will one day be taken seri- ously a creative artist in its own right. This aim is being pursued as an Artificial Intelligence project, with the hope that the technical difficulties overcome along the way will lead to new and improved generic AI techniques. It is also being pursued as a sociological project, where the effect of software which might be deemed as creative is tested in the art world and the wider public. In this chapter, we sum- marise our progress so far in The Painting Fool project. To do this, we first compare and contrast The Painting Fool with software of a similar nature arising from AI and graphics projects. We follow this with a discussion of the guiding principles from Computational Creativity research that we adhere to in building the software. We then describe five projects with The Painting Fool where our aim has been to produce increasingly interesting and culturally valuable pieces of art. We end by discussing the issues raised in building an automated painter, and describe further work and future prospects for the project. By studying both the technical difficul- ties and sociological issues involved in engineering software for creative purposes, we hope to help usher in a new era where computers routinely act as our creative collaborators, as well as independent and creative artists, musicians, writers, design- ers, engineers and scientists, and contribute in meaningful and interesting ways to human culture.}, keywords = {}, pubstate = {published}, tppubtype = {incollection} } The Painting Fool is software that we hope will one day be taken seri- ously a creative artist in its own right. This aim is being pursued as an Artificial Intelligence project, with the hope that the technical difficulties overcome along the way will lead to new and improved generic AI techniques. It is also being pursued as a sociological project, where the effect of software which might be deemed as creative is tested in the art world and the wider public. In this chapter, we sum- marise our progress so far in The Painting Fool project. To do this, we first compare and contrast The Painting Fool with software of a similar nature arising from AI and graphics projects. We follow this with a discussion of the guiding principles from Computational Creativity research that we adhere to in building the software. We then describe five projects with The Painting Fool where our aim has been to produce increasingly interesting and culturally valuable pieces of art. We end by discussing the issues raised in building an automated painter, and describe further work and future prospects for the project. By studying both the technical difficul- ties and sociological issues involved in engineering software for creative purposes, we hope to help usher in a new era where computers routinely act as our creative collaborators, as well as independent and creative artists, musicians, writers, design- ers, engineers and scientists, and contribute in meaningful and interesting ways to human culture. |
Colton, Simon The Painting Fool in New Dimensions Inproceedings In: Proceedings of the 2nd International Conference on Computational Creativity, 2011. @inproceedings{ColtonICCC10PaintingFoolb, title = {The Painting Fool in New Dimensions}, author = {Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/colton_sat_iccc11.pdf}, year = {2011}, date = {2011-10-01}, booktitle = {Proceedings of the 2nd International Conference on Computational Creativity}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } |
Cook, Michael; Colton, Simon Automated Collage Generation – With More Intent Inproceedings In: Proceedings of the Second International Conference on Computational Creativity, 2011. @inproceedings{Cook2011ICCC, title = {Automated Collage Generation – With More Intent}, author = {Michael Cook and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/cook_iccc11.pdf}, year = {2011}, date = {2011-10-01}, booktitle = {Proceedings of the Second International Conference on Computational Creativity}, abstract = {The majority of software has no meta-level perception of what it is doing, or what it intends to achieve. With- out such higher cognitive functions, we might be dis- inclined to bestow creativity onto such software. We generalise previous work on collage generation, which attempted to blur the line between the intentionality of the programmer and that of the software in the visual arts. Firstly, we embed the collage generation process into a computational creativity collective, which con- tains processes and mashups of processes, designed so that the output of one generative system becomes the input of another. Secondly, we analyse the previous approach to collage generation to determine where in- tentionality arose, leading to experimentation where we test whether augmented keyword searches can enable the software to exert more intentional control.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } The majority of software has no meta-level perception of what it is doing, or what it intends to achieve. With- out such higher cognitive functions, we might be dis- inclined to bestow creativity onto such software. We generalise previous work on collage generation, which attempted to blur the line between the intentionality of the programmer and that of the software in the visual arts. Firstly, we embed the collage generation process into a computational creativity collective, which con- tains processes and mashups of processes, designed so that the output of one generative system becomes the input of another. Secondly, we analyse the previous approach to collage generation to determine where in- tentionality arose, leading to experimentation where we test whether augmented keyword searches can enable the software to exert more intentional control. |
Colton, Simon; Cook, Michael; Raad, Azalea Ludic Considerations of Tablet-Based Evo-Art Inproceedings In: European Conference on the Applications of Evolutionary Computation, pp. 223–233, Springer 2011. @inproceedings{colton2011ludic, title = {Ludic Considerations of Tablet-Based Evo-Art}, author = { Simon Colton and Michael Cook and Azalea Raad}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/colton2011ludic.pdf}, year = {2011}, date = {2011-01-01}, booktitle = {European Conference on the Applications of Evolutionary Computation}, pages = {223--233}, organization = {Springer}, abstract = {With the introduction of the iPad and similar devices, there is a unique opportunity to build tablet-based evolutionary art software for general consumption, and we describe here the i-ELVIRA iPad ap- plication for such purposes. To increase the ludic enjoyment users have with i-ELVIRA, we designed a GUI which gives the user a higher level of control and more efficient feedback than usual for desktop evo-art software. This relies on the efficient delivery of crossover and mutation images which bear an appropriate amount of resemblance to their par- ent(s). This requirement in turn led to technical difficulties which we resolved via the implementation and experimentation described here.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } With the introduction of the iPad and similar devices, there is a unique opportunity to build tablet-based evolutionary art software for general consumption, and we describe here the i-ELVIRA iPad ap- plication for such purposes. To increase the ludic enjoyment users have with i-ELVIRA, we designed a GUI which gives the user a higher level of control and more efficient feedback than usual for desktop evo-art software. This relies on the efficient delivery of crossover and mutation images which bear an appropriate amount of resemblance to their par- ent(s). This requirement in turn led to technical difficulties which we resolved via the implementation and experimentation described here. |
Colton, Simon; Gow, Jeremy; Torres, Pedro; Cairns, Paul Experiments in Objet Trouvé Browsing Inproceedings In: Proceedings of the 1st Int. Joint Conference on Computational Creativity, 2010. @inproceedings{ColtonICCC10Objet, title = {Experiments in Objet Trouvé Browsing}, author = {Simon Colton and Jeremy Gow and Pedro Torres and Paul Cairns}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/colton_cc10.pdf}, year = {2010}, date = {2010-10-01}, booktitle = {Proceedings of the 1st Int. Joint Conference on Computational Creativity}, journal = {Proceedings of the 1st Int. Joint Conference on Computational Creativity}, abstract = {We report on two experiments to study the use of a graphic design tool for generating and selecting image lters, in which the aesthetic preferences that the user expresses whilst browsing ltered images drives the lter generation process. In the first experiment, we found evidence for the idea that intelligent employment of the user's preferences when generating flters can improve the overall quality of the designs produced, as assessed by the users themselves. The results also suggest some user behaviours related to the delity of the image lters, i.e., how much they alter the image they are applied to. A second experiment tested whether evolutionary techniques which manage delity would be preferred by users. Our results did not support this hypothesis, which opens up interesting questions about how user preferences can be intelligently employed in browsing-based design tools.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We report on two experiments to study the use of a graphic design tool for generating and selecting image lters, in which the aesthetic preferences that the user expresses whilst browsing ltered images drives the lter generation process. In the first experiment, we found evidence for the idea that intelligent employment of the user's preferences when generating flters can improve the overall quality of the designs produced, as assessed by the users themselves. The results also suggest some user behaviours related to the delity of the image lters, i.e., how much they alter the image they are applied to. A second experiment tested whether evolutionary techniques which manage delity would be preferred by users. Our results did not support this hypothesis, which opens up interesting questions about how user preferences can be intelligently employed in browsing-based design tools. |
Colton, Simon The Painting Fool Teaching Interface Incollection In: Proceedings of the 1st International Conference on Computational Creativity, 2010. @incollection{ColtonICCC10PaintingFool, title = {The Painting Fool Teaching Interface}, author = {Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/colton_ccshowandtell10.pdf}, year = {2010}, date = {2010-10-01}, booktitle = {Proceedings of the 1st International Conference on Computational Creativity}, keywords = {}, pubstate = {published}, tppubtype = {incollection} } |
Colton, Simon Stroke Matching for Paint Dances Inproceedings In: Proceedings of the Sixth international Conference on Computational Aesthetics in Graphics, Visualization and Imaging, Eurographics Association, 2010. @inproceedings{Colton2010StrokeMatching, title = {Stroke Matching for Paint Dances}, author = {Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/colton_computationalaesthetics10.pdf}, year = {2010}, date = {2010-10-01}, booktitle = {Proceedings of the Sixth international Conference on Computational Aesthetics in Graphics, Visualization and Imaging}, publisher = {Eurographics Association}, abstract = {We have implemented a non-photorealistic rendering system which simulates the placement of paint/pencil/pastel strokes to produce representational artworks from digital images. The system is able to record an image of each paint stroke independent of the overall picture, in addition to some details about each stroke. Working with sets of paint strokes from paintings of different images, we investigate how to determine which stroke from one picture most closely resembles a given stroke from another picture. This enables the paint strokes from one picture to be used to paint a different painting. This further enables the animation of one picture morphing into another, as the paint strokes move and rotate into new positions and orientations. Using a K-means clustering approach, we can extract a set of representative strokes from a series of paintings/drawings, and animate the same set of strokes moving around a picture in order to represent different scenes at different times. We call such animations “paint dances”.We apply this technique to sets of portraits and we present the resulting paint dances in an artistic context as video art. We describe here the various methods we experimented with in order to determine an optimal stroke matching and extraction approach.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We have implemented a non-photorealistic rendering system which simulates the placement of paint/pencil/pastel strokes to produce representational artworks from digital images. The system is able to record an image of each paint stroke independent of the overall picture, in addition to some details about each stroke. Working with sets of paint strokes from paintings of different images, we investigate how to determine which stroke from one picture most closely resembles a given stroke from another picture. This enables the paint strokes from one picture to be used to paint a different painting. This further enables the animation of one picture morphing into another, as the paint strokes move and rotate into new positions and orientations. Using a K-means clustering approach, we can extract a set of representative strokes from a series of paintings/drawings, and animate the same set of strokes moving around a picture in order to represent different scenes at different times. We call such animations “paint dances”.We apply this technique to sets of portraits and we present the resulting paint dances in an artistic context as video art. We describe here the various methods we experimented with in order to determine an optimal stroke matching and extraction approach. |
Krzeczkowska, Anna; El-Hage, Jad; Colton, Simon; Clark, Stephen Automated Collage Generation - With Intent Inproceedings In: Proceedings of the 1st International Conference on Computational Creativity, 2010. @inproceedings{Krzeczkowska2010, title = {Automated Collage Generation - With Intent}, author = {Anna Krzeczkowska and Jad El-Hage and Simon Colton and Stephen Clark}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/krzeczkowska_cc10.pdf}, year = {2010}, date = {2010-10-01}, booktitle = {Proceedings of the 1st International Conference on Computational Creativity}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } |
Colton, Simon; Browne, Cameron Evolving Simple Art-based Games Inproceedings In: Workshops on Applications of Evolutionary Computation, 2009. @inproceedings{Colton2009EvoGames, title = {Evolving Simple Art-based Games}, author = {Simon Colton and Cameron Browne}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/colton_evogames09.pdf}, year = {2009}, date = {2009-10-01}, booktitle = {Workshops on Applications of Evolutionary Computation}, abstract = {Evolutionary art has a long and distinguished history, and genetic programming is one of only a handful of AI techniques which is used in graphic design and the visual arts. A recent trend in so-called `new media' art is to design online pieces which are dynamic and have an element of interaction and sometimes simple game-playing aspects. This de nes the challenge addressed here: to automatically evolve dynamic, interactive art pieces with game elements. We do this by extending the Avera user-driven evolutionary art system to produce programs which generate spirograph-style images by repeatedly placing, scaling, rotating and colouring geometric objects such as squares and circles. Such images are produced in an inherently causal way which provides the dynamic element to the pieces.We further extend the system to produce programs which react to mouse clicks, and to evolve sequential patterns of clicks for the user to uncover. We wrap the programs in a simple front end which provides the user with feedback on how close they are to uncovering the pattern, adding a lightweight game-playing element to the pieces. The evolved interactive artworks are a preliminary step in the creation of more sophisticated multimedia pieces.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Evolutionary art has a long and distinguished history, and genetic programming is one of only a handful of AI techniques which is used in graphic design and the visual arts. A recent trend in so-called `new media' art is to design online pieces which are dynamic and have an element of interaction and sometimes simple game-playing aspects. This de nes the challenge addressed here: to automatically evolve dynamic, interactive art pieces with game elements. We do this by extending the Avera user-driven evolutionary art system to produce programs which generate spirograph-style images by repeatedly placing, scaling, rotating and colouring geometric objects such as squares and circles. Such images are produced in an inherently causal way which provides the dynamic element to the pieces.We further extend the system to produce programs which react to mouse clicks, and to evolve sequential patterns of clicks for the user to uncover. We wrap the programs in a simple front end which provides the user with feedback on how close they are to uncovering the pattern, adding a lightweight game-playing element to the pieces. The evolved interactive artworks are a preliminary step in the creation of more sophisticated multimedia pieces. |
Colton, Simon; Torres, Pedro Evolving Approximate Image Filters Inproceedings In: 7th European Workshop on Evolutionary and Biologically Inspired Music, Sound, Art and Design , 2009. @inproceedings{Colton2009ImageFilters, title = {Evolving Approximate Image Filters}, author = {Simon Colton and Pedro Torres}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/colton_evomusart09.pdf}, year = {2009}, date = {2009-10-01}, booktitle = {7th European Workshop on Evolutionary and Biologically Inspired Music, Sound, Art and Design }, abstract = {Image filtering involves taking a digital image and producing a new image from it. In software packages such as Adobe's Photoshop, image lters are used to produce artistic versions of original images. Such software usually includes hundreds of di erent image ltering algorithms, each with many ne-tuneable parameters. While this freedom of exploration may be liberating to artists and designers, it can be daunting for less experienced users. Photoshop provides image lter browsing technology, but does not yet enable the construction of a lter which produces a reasonable approximation of a given ltered image from a given original image. We investigate here whether it is possible to automatically evolve an image lter to approximate a target lter, given only an original image and a ltered version of the original. We describe a tree based representation for lters, the tness functions and search techniques we employed, and we present the results of experimentation with various search setups. We demonstrate the feasibility of evolving image lters and suggest new ways to improve the process.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Image filtering involves taking a digital image and producing a new image from it. In software packages such as Adobe's Photoshop, image lters are used to produce artistic versions of original images. Such software usually includes hundreds of di erent image ltering algorithms, each with many ne-tuneable parameters. While this freedom of exploration may be liberating to artists and designers, it can be daunting for less experienced users. Photoshop provides image lter browsing technology, but does not yet enable the construction of a lter which produces a reasonable approximation of a given ltered image from a given original image. We investigate here whether it is possible to automatically evolve an image lter to approximate a target lter, given only an original image and a ltered version of the original. We describe a tree based representation for lters, the tness functions and search techniques we employed, and we present the results of experimentation with various search setups. We demonstrate the feasibility of evolving image lters and suggest new ways to improve the process. |
Colton, Simon Amelie’s Progress Gallery / Imaginations #1 Booklet 2008. @booklet{Colton2008Amelie, title = {Amelie’s Progress Gallery / Imaginations #1}, author = {Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/colton_cae08.pdf}, year = {2008}, date = {2008-10-01}, booktitle = {Computational Aesthetics}, month = {10}, keywords = {}, pubstate = {published}, tppubtype = {booklet} } |
Colton, Simon Experiments in Constraint-Based Automated Scene Generation Inproceedings In: Proceedings of the 5th international Joint Workshop on Computational Creativity, 2008. @inproceedings{Colton2008CC, title = {Experiments in Constraint-Based Automated Scene Generation}, author = {Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/colton_cc08.pdf}, year = {2008}, date = {2008-10-01}, booktitle = {Proceedings of the 5th international Joint Workshop on Computational Creativity}, abstract = {We investigate the question of automatic scene construction for visual arts applications. We have implemented a system which can automatically infer a user’s intentions from a partially formed scene, express the inferences as constraints, and then use these to complete the scene. We provide some initial experimental results with the system in order to compare two approaches to constraint-based scene construction. This leads on to a discussion about handing over increasingly meta-level responsibility when building computationally creative systems.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We investigate the question of automatic scene construction for visual arts applications. We have implemented a system which can automatically infer a user’s intentions from a partially formed scene, express the inferences as constraints, and then use these to complete the scene. We provide some initial experimental results with the system in order to compare two approaches to constraint-based scene construction. This leads on to a discussion about handing over increasingly meta-level responsibility when building computationally creative systems. |
Torres, Pedro; Colton, Simon; Rüger, Stefan Experiments in Example-Based Image Filter Retrieval Inproceedings In: Proceedings of the Cross-Media Workshop, 2008. @inproceedings{Torres2008CrossMedia, title = {Experiments in Example-Based Image Filter Retrieval}, author = {Pedro Torres and Simon Colton and Stefan Rüger}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/torres_crossmedia08.pdf}, year = {2008}, date = {2008-10-01}, booktitle = {Proceedings of the Cross-Media Workshop}, abstract = {We present a novel image filter generation method and an image filter retrieval algorithm and analyse their properties. Based on an original image and a filtered version of the original, the retrieval al- gorithm can find, to a high probability, which filter was applied to the original from a large pre-defined list of filters, without having to apply all filters to the original image, which is usually a time consuming task when the number of filters is large. This is achieved by pre-computing image annotations for a set of filtered images obtained by applying the pre-defined filters to a database of 50 images. Using standard image- based annotation techniques, we show that the filter retrieval can be achieved by taking the closest images to the original from the database and analysing those known images instead. The retrieval algorithm has a set of parameters and we present results of experiments with these values to maximise the probability of retrieving the correct filter.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We present a novel image filter generation method and an image filter retrieval algorithm and analyse their properties. Based on an original image and a filtered version of the original, the retrieval al- gorithm can find, to a high probability, which filter was applied to the original from a large pre-defined list of filters, without having to apply all filters to the original image, which is usually a time consuming task when the number of filters is large. This is achieved by pre-computing image annotations for a set of filtered images obtained by applying the pre-defined filters to a database of 50 images. Using standard image- based annotation techniques, we show that the filter retrieval can be achieved by taking the closest images to the original from the database and analysing those known images instead. The retrieval algorithm has a set of parameters and we present results of experiments with these values to maximise the probability of retrieving the correct filter. |
Colton, Simon; Valstar, Michel F; Pantic, Maja Emotionally Aware Automated Portrait Painting Inproceedings In: Proceedings of the 3rd international conference on Digital Interactive Media in Entertainment and Arts, 2008. @inproceedings{Colton2008Dimea, title = {Emotionally Aware Automated Portrait Painting}, author = {Simon Colton and Michel F. Valstar and Maja Pantic}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/colton_dimea08.pdf}, year = {2008}, date = {2008-10-01}, booktitle = {Proceedings of the 3rd international conference on Digital Interactive Media in Entertainment and Arts}, abstract = {We combine a machine vision system that recognises emotions and a non-photorealistic rendering (NPR) system to automatically produce portraits which heighten the emotion of the sitter. To do this, the vision system analyses a short video clip of a person express- ing an emotion, then tracks the movement of facial features and uses this tracking data to analyse which emotion was expressed and what the temporal dynamics of the expression were. The im- age where the emotion is expressed strongest, the location of the facial features in that image and a keyword describing the emotion detected are passed to the NPR software. This keyword is used to choose appropriate (simulated) art materials, colour palettes, abstraction methods and painting styles, so that the rendered image may heighten the emotion being expressed. We describe the vision and rendering systems and their combination, and provide exam- ples of portraits produced in this emotionally aware fashion.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We combine a machine vision system that recognises emotions and a non-photorealistic rendering (NPR) system to automatically produce portraits which heighten the emotion of the sitter. To do this, the vision system analyses a short video clip of a person express- ing an emotion, then tracks the movement of facial features and uses this tracking data to analyse which emotion was expressed and what the temporal dynamics of the expression were. The im- age where the emotion is expressed strongest, the location of the facial features in that image and a keyword describing the emotion detected are passed to the NPR software. This keyword is used to choose appropriate (simulated) art materials, colour palettes, abstraction methods and painting styles, so that the rendered image may heighten the emotion being expressed. We describe the vision and rendering systems and their combination, and provide exam- ples of portraits produced in this emotionally aware fashion. |
Hull, Marc; Colton, Simon Towards a General Framework for Program Generation in Creative Domains Inproceedings In: Proceedings of the 4th International Joint Workshop on Computational Creativity, 2007. @inproceedings{HullCC2007, title = {Towards a General Framework for Program Generation in Creative Domains}, author = {Marc Hull and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/hull_cc07.pdf}, year = {2007}, date = {2007-10-01}, booktitle = {Proceedings of the 4th International Joint Workshop on Computational Creativity}, abstract = {Choosing an efficient artificial intelligence approach for producing artefacts for a particular creative domain can be a difficult task. Seemingly minor changes to the solution representation and learning parameters can have an unpredictably large impact on the success of the process. A standard approach is to try various different setups in order to investigate their effects and refine the technique over time. Our aim is to produce a pluggable framework for exploring different representations and learning techniques for creative artefact generation. Here we describe our initial work towards this goal, including how problems are specified to our system in a format that is concise but still able to cover a wide range of domains. We also tackle the general problem of constrained solution generation by bringing information from the constraints into the generation and variation process and we discuss some of the advantages and disadvantages of doing this. Finally, we present initial results of applying our system to the domain of algorithmic art generation, where we have used the framework to code up and test three different representations for producing artwork.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Choosing an efficient artificial intelligence approach for producing artefacts for a particular creative domain can be a difficult task. Seemingly minor changes to the solution representation and learning parameters can have an unpredictably large impact on the success of the process. A standard approach is to try various different setups in order to investigate their effects and refine the technique over time. Our aim is to produce a pluggable framework for exploring different representations and learning techniques for creative artefact generation. Here we describe our initial work towards this goal, including how problems are specified to our system in a format that is concise but still able to cover a wide range of domains. We also tackle the general problem of constrained solution generation by bringing information from the constraints into the generation and variation process and we discuss some of the advantages and disadvantages of doing this. Finally, we present initial results of applying our system to the domain of algorithmic art generation, where we have used the framework to code up and test three different representations for producing artwork. |
Issues in Automated Game Design
We have been working with video games companies towards the long term goal of dynamically adapting games, which tailor their content and gameplay to individual players, by learning about them and predicting how their experience will change as the game changes. We have concentrated on evaluating and predicting player experience from their gameplay data, in addition to working on content generation projects and the use of Monte-Carlo Tree Search methods. Through the ANGELINA system, we have also studied how entire games can be generated through a co-evolution procedure, which has brought up a number of higher-level issues such as player verbs, subjectivity, software as part of a creative community and automated code generation.
Cook, Michael; Colton, Simon; Gow, Jeremy The ANGELINA Videogame Design System, Part I Journal Article In: IEEE Transactions on Computational Intelligence and AI in Games, 9 (2), pp. 192-203, 2017, ISSN: 1943-0698. @article{Cook2016TCIAIGb, title = {The ANGELINA Videogame Design System, Part I}, author = {Michael Cook and Simon Colton and Jeremy Gow}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/11/COM-Cook2016a.pdf}, doi = {10.1109/TCIAIG.2016.2520256}, issn = {1943-0698}, year = {2017}, date = {2017-06-01}, journal = {IEEE Transactions on Computational Intelligence and AI in Games}, volume = {9}, number = {2}, pages = {192-203}, abstract = {Automatically generating content for videogames has long been a staple of game development and the focus of much successful research. Such forays into content generation usually concern themselves with producing a specific game component, such as a level design. This has proven a rich and challenging area of research, but in focusing on creating separate parts of a larger game, we miss out on the most challenging and interesting aspects of game development. By expanding our scope to the automated design of entire games, we can investigate the relationship between the different creative tasks undertaken in game development, tackle the higher-level creative challenges of game design, and ultimately build systems capable of much greater novelty, surprise and quality in their output. This paper, the first in a series of two, describes two case studies in automating game design, proposing cooperative coevo- lution as a useful technique to use within systems that automate this process. We show how this technique allows essentially separate content generators to produce content that complements each other. We also describe systems that have used this to design games with subtle emergent effects. After introducing the technique and its technical basis in this paper, in the second paper in the series we discuss higher level issues in automated game design, such as potential overlap with computational creativity and the issue of evaluation.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Automatically generating content for videogames has long been a staple of game development and the focus of much successful research. Such forays into content generation usually concern themselves with producing a specific game component, such as a level design. This has proven a rich and challenging area of research, but in focusing on creating separate parts of a larger game, we miss out on the most challenging and interesting aspects of game development. By expanding our scope to the automated design of entire games, we can investigate the relationship between the different creative tasks undertaken in game development, tackle the higher-level creative challenges of game design, and ultimately build systems capable of much greater novelty, surprise and quality in their output. This paper, the first in a series of two, describes two case studies in automating game design, proposing cooperative coevo- lution as a useful technique to use within systems that automate this process. We show how this technique allows essentially separate content generators to produce content that complements each other. We also describe systems that have used this to design games with subtle emergent effects. After introducing the technique and its technical basis in this paper, in the second paper in the series we discuss higher level issues in automated game design, such as potential overlap with computational creativity and the issue of evaluation. |
Cook, Michael; Colton, Simon; Gow, Jeremy The ANGELINA Videogame Design System, Part II Journal Article Forthcoming In: IEEE Transactions on Computational Intelligence and AI in Games, Forthcoming. @article{Cook2016TCIAGa, title = {The ANGELINA Videogame Design System, Part II}, author = {Michael Cook and Simon Colton and Jeremy Gow}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/11/COM-Cook2016b.pdf}, year = {2016}, date = {2016-11-01}, journal = {IEEE Transactions on Computational Intelligence and AI in Games}, abstract = {Procedural content generation is generally viewed as a means to an end – a tool employed by designers to overcome technical problems or achieve a particular design goal. When we move from generating single parts of games to automating the entirety of their design, however, we find ourselves facing a far wider and more interesting set of problems than mere generation. When the designer of a game is a piece of software, we face questions about what it means to be a designer, about Computational Creativity, and about how to assess the growth of these automated game designers and the value of their output. Answering these questions can lead to new ideas in how to generate content procedurally, and produce systems that can further the cutting edge of game design. This paper describes work done to take an automated game designer and advance it towards being a member of a creative community. We outline extensions made to the system to give it more autonomy and creative independence, in order to strengthen claims that the software is acting creatively. We describe and reflect upon the software’s participation in the games community, including entering two game development contests, and show the opportunities and difficulties of such engagement. We consider methods for evaluating automated game designers as creative entities, and underline the need for automated game design to be a major frontier in future games research.}, keywords = {}, pubstate = {forthcoming}, tppubtype = {article} } Procedural content generation is generally viewed as a means to an end – a tool employed by designers to overcome technical problems or achieve a particular design goal. When we move from generating single parts of games to automating the entirety of their design, however, we find ourselves facing a far wider and more interesting set of problems than mere generation. When the designer of a game is a piece of software, we face questions about what it means to be a designer, about Computational Creativity, and about how to assess the growth of these automated game designers and the value of their output. Answering these questions can lead to new ideas in how to generate content procedurally, and produce systems that can further the cutting edge of game design. This paper describes work done to take an automated game designer and advance it towards being a member of a creative community. We outline extensions made to the system to give it more autonomy and creative independence, in order to strengthen claims that the software is acting creatively. We describe and reflect upon the software’s participation in the games community, including entering two game development contests, and show the opportunities and difficulties of such engagement. We consider methods for evaluating automated game designers as creative entities, and underline the need for automated game design to be a major frontier in future games research. |
Cook, Michael; Colton, Simon; Gow, Jeremy Automating Game Design in Three Dimensions Inproceedings In: Proceedings of the AISB symposium on AI and Games, 2014. @inproceedings{Cook2014AISB, title = {Automating Game Design in Three Dimensions}, author = {Michael Cook and Simon Colton and Jeremy Gow}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/11/cook_aisb14a.pdf}, year = {2014}, date = {2014-11-01}, booktitle = {Proceedings of the AISB symposium on AI and Games}, abstract = {We describe ANGELINA-5, a new iteration of the AN- GELINA framework for investigating and building software which automates the process of videogame design. ANGELINA-5 is the first automated game design tool that produces 3D games. We outline here the system’s structure, the challenges inherent in building an auto- mated game designer in a modern game engine, and we discuss the future research directions for the project.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We describe ANGELINA-5, a new iteration of the AN- GELINA framework for investigating and building software which automates the process of videogame design. ANGELINA-5 is the first automated game design tool that produces 3D games. We outline here the system’s structure, the challenges inherent in building an auto- mated game designer in a modern game engine, and we discuss the future research directions for the project. |
Browne, Cameron; Colton, Simon; Cook, Michael; Gow, Jeremy; Baumgarten, Robin Toward the Adaptive Generation of Bespoke Game Content Book Chapter In: IEEE Handbook of Digital Games , pp. 15–61, John Wiley & Sons, Inc., 2014. @inbook{browne2014toward, title = {Toward the Adaptive Generation of Bespoke Game Content}, author = { Cameron Browne and Simon Colton and Michael Cook and Jeremy Gow and Robin Baumgarten}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/browne_ieeechapter14-2.pdf}, year = {2014}, date = {2014-01-01}, journal = {Handbook of Digital Games}, volume = {IEEE Handbook of Digital Games}, pages = {15--61}, publisher = {John Wiley & Sons, Inc.}, abstract = {In this chapter, we explore methods for automatically generating game content — and games themselves — adapted to individual players, in order to improve their playing experience or achieve a desired effect. This goes beyond notions of mere replayability, and involves modelling player needs to maximise their enjoyment, in- volvement and interest in the game being played. We identify three main aspects of this process: Generation of new content and rule sets; Measurement of this content and the player; Adaptation of the game to change player experience. This process forms a feedback loop of constant refinement, as games are continually improved while being played. Framed within this methodology, we present an overview of our recent and ongoing research in this area. This is illustrated by a number of case studies that demonstrate these ideas in action over a variety of game types, includ- ing: 3D action games, arcade games, platformers, board games, puzzles and open world games. We draw together some of the lessons learned from these projects to comment on the difficulties, the benefits and the potential for personalised gaming via adaptive game design.}, keywords = {}, pubstate = {published}, tppubtype = {inbook} } In this chapter, we explore methods for automatically generating game content — and games themselves — adapted to individual players, in order to improve their playing experience or achieve a desired effect. This goes beyond notions of mere replayability, and involves modelling player needs to maximise their enjoyment, in- volvement and interest in the game being played. We identify three main aspects of this process: Generation of new content and rule sets; Measurement of this content and the player; Adaptation of the game to change player experience. This process forms a feedback loop of constant refinement, as games are continually improved while being played. Framed within this methodology, we present an overview of our recent and ongoing research in this area. This is illustrated by a number of case studies that demonstrate these ideas in action over a variety of game types, includ- ing: 3D action games, arcade games, platformers, board games, puzzles and open world games. We draw together some of the lessons learned from these projects to comment on the difficulties, the benefits and the potential for personalised gaming via adaptive game design. |
Cook, Michael; Colton, Simon Ludus Ex Machina: Building a 3D Game Designer that Competes Alongside Humans Inproceedings In: Proceedings of the 5th international conference on computational creativity, 2014. @inproceedings{cook2014ludus, title = {Ludus Ex Machina: Building a 3D Game Designer that Competes Alongside Humans}, author = { Michael Cook and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/cook_iccc2014.pdf}, year = {2014}, date = {2014-01-01}, booktitle = {Proceedings of the 5th international conference on computational creativity}, volume = {380}, abstract = {We describe ANGELINA-5, software capable of creat- ing simple three-dimensional games autonomously. To the best of our knowledge, this is the first system which creates complete games in 3D. We summarise the his- tory of the ANGELINA project so far, describe the ar- chitecture of the latest version, and give details of its participation in Ludum Dare, a game design competi- tion. This is the first time that a piece of software has en- tered a videogame design contest for human designers, and represents a step forward for automated videogame design and computational creativity.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We describe ANGELINA-5, software capable of creat- ing simple three-dimensional games autonomously. To the best of our knowledge, this is the first system which creates complete games in 3D. We summarise the his- tory of the ANGELINA project so far, describe the ar- chitecture of the latest version, and give details of its participation in Ludum Dare, a game design competi- tion. This is the first time that a piece of software has en- tered a videogame design contest for human designers, and represents a step forward for automated videogame design and computational creativity. |
Llano, Maria Teresa; Cook, Michael; Guckelsberger, Christian; Colton, Simon; Hepworth, Rose Towards the Automatic Generation of Fictional Ideas for Games Inproceedings In: Experimental AI in Games (EXAG’14), a workshop collocated with the tenth annual AAAI conference on artificial intelligence and interactive digital entertainment (AIIDE’14). AAAI Publications, 2014. @inproceedings{llano2014towards, title = {Towards the Automatic Generation of Fictional Ideas for Games}, author = { Maria Teresa Llano and Michael Cook and Christian Guckelsberger and Simon Colton and Rose Hepworth}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/09/llano_exag14.pdf}, year = {2014}, date = {2014-01-01}, booktitle = {Experimental AI in Games (EXAG’14), a workshop collocated with the tenth annual AAAI conference on artificial intelligence and interactive digital entertainment (AIIDE’14). AAAI Publications}, abstract = {The invention of fictional ideas is often a central pro- cess in the creative production of artefacts such as po- ems, music, paintings and games. Currently, fictional ideation is being studied by the Computational Creativ- ity community within the WHIM European project. The aim of WHIM is to develop the What-If Machine, a soft- ware system capable of inventing, evaluating and pre- senting fictional ideas with cultural value. In this pa- per we explore the potential applications of the What-If Machine in the context of games. Specifically, we pro- pose ways in which the What-If Machine can be used as an assistant for the design of games, by providing ideas about characters, the environment, etc., as well as a creative system during gameplay, through interesting interactions with the player.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } The invention of fictional ideas is often a central pro- cess in the creative production of artefacts such as po- ems, music, paintings and games. Currently, fictional ideation is being studied by the Computational Creativ- ity community within the WHIM European project. The aim of WHIM is to develop the What-If Machine, a soft- ware system capable of inventing, evaluating and pre- senting fictional ideas with cultural value. In this pa- per we explore the potential applications of the What-If Machine in the context of games. Specifically, we pro- pose ways in which the What-If Machine can be used as an assistant for the design of games, by providing ideas about characters, the environment, etc., as well as a creative system during gameplay, through interesting interactions with the player. |
Cook, Michael; Colton, Simon A Rogue Dream: Automatically Generating Meaningful Content for Games Inproceedings In: Proceedings of the AIIDE Workshop on Experimental AI and Games, 2014. @inproceedings{cook2014rogue, title = {A Rogue Dream: Automatically Generating Meaningful Content for Games}, author = { Michael Cook and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/09/cook_exag14.pdf}, year = {2014}, date = {2014-01-01}, booktitle = {Proceedings of the AIIDE Workshop on Experimental AI and Games}, abstract = {Procedural content generation is often seen simply as a means to generate ‘stuff ’, elaborating on or rearrang- ing abstract data types that describe levels or modular pieces of gameplay. Generating content which is situated in an understanding of the real-world is a much harder task; it requires access to large amounts of knowledge, and a good technique for parsing and using that knowledge. In this paper we describe A Rogue Dream, a game prototype which can generate new visual content and change its design based on an input word from the player at the start of the game. We describe the game and the tools it makes use of to do this, and use the game to discuss ways in which such techniques might enable unique kinds of gameplay or new directions for intelligent design tools.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Procedural content generation is often seen simply as a means to generate ‘stuff ’, elaborating on or rearrang- ing abstract data types that describe levels or modular pieces of gameplay. Generating content which is situated in an understanding of the real-world is a much harder task; it requires access to large amounts of knowledge, and a good technique for parsing and using that knowledge. In this paper we describe A Rogue Dream, a game prototype which can generate new visual content and change its design based on an input word from the player at the start of the game. We describe the game and the tools it makes use of to do this, and use the game to discuss ways in which such techniques might enable unique kinds of gameplay or new directions for intelligent design tools. |
Colton, Simon Countdown Numbers Game: Solved, Analysed, Extended Inproceedings In: Proceedings of the AISB symposium on AI and Games, 2014. @inproceedings{colton2014countdown, title = {Countdown Numbers Game: Solved, Analysed, Extended}, author = { Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/colton_aisb14a.pdf}, year = {2014}, date = {2014-01-01}, booktitle = {Proceedings of the AISB symposium on AI and Games}, abstract = {The Countdown Numbers Game is a popular arithmeti- cal puzzle which has been played as a two-player game on French and British television weekly for decades. We have solved this game in the sense that the optimal solution for the nearly 12 million puzzle instances has been generated and recorded. We describe here how we have achieved this using the HR3 Automated Theory Formation system. This has allowed us to analyse the space of puzzles; sug- gest gamesmanship tactics and game design improvements to the online/handheld versions of the game; and begin to investigate the potential for automatic invention of such games.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } The Countdown Numbers Game is a popular arithmeti- cal puzzle which has been played as a two-player game on French and British television weekly for decades. We have solved this game in the sense that the optimal solution for the nearly 12 million puzzle instances has been generated and recorded. We describe here how we have achieved this using the HR3 Automated Theory Formation system. This has allowed us to analyse the space of puzzles; sug- gest gamesmanship tactics and game design improvements to the online/handheld versions of the game; and begin to investigate the potential for automatic invention of such games. |
Cook, Michael; Colton, Simon A Puzzling Present: Code Modification for Game Mechanic Design Inproceedings In: Demo session Proceedings of the 4th International Conference on Computational Creativity, 2013. @inproceedings{Cook2013ICCC, title = {A Puzzling Present: Code Modification for Game Mechanic Design}, author = {Michael Cook and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/11/cook_icccdemo13.pdf}, year = {2013}, date = {2013-11-01}, booktitle = {Demo session Proceedings of the 4th International Conference on Computational Creativity}, abstract = {A Puzzling Present is an Android and Desktop game re- leased in December 2012. The game mechanics (that is, the player’s abilities) as well as the level designs were generated using Mechanic Miner, a procedural content generator that is capable of exploring, modifying and executing codebases to create game content. It is the first game developed using direct code modification as a means of procedural mechanic generation.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } A Puzzling Present is an Android and Desktop game re- leased in December 2012. The game mechanics (that is, the player’s abilities) as well as the level designs were generated using Mechanic Miner, a procedural content generator that is capable of exploring, modifying and executing codebases to create game content. It is the first game developed using direct code modification as a means of procedural mechanic generation. |
Cook, Michael; Colton, Simon From Mechanics to Meaning and Back Again: Exploring Techniques for the Contextualisation of Code Inproceedings In: Procs. of the AIIDE Workshop on Artificial Intelligence and Game Aesthetics, 2013. @inproceedings{cook2013mechanics, title = {From Mechanics to Meaning and Back Again: Exploring Techniques for the Contextualisation of Code}, author = { Michael Cook and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/cook_aiga13.pdf}, year = {2013}, date = {2013-01-01}, booktitle = {Procs. of the AIIDE Workshop on Artificial Intelligence and Game Aesthetics}, abstract = {Code generation is a promising new area for the automatic production of mechanics and systems in games. Generated code alone is not sufficient for inclusion in a rich, fully-designed game, however - it lacks context to bind the functionality of code to the metaphorical setting of the game. In this paper we explore potential solutions to this problem, both in terms of creative systems which co-operate with human content, and the possibility for contextual meaning in autonomous, human-free creative systems as well. }, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Code generation is a promising new area for the automatic production of mechanics and systems in games. Generated code alone is not sufficient for inclusion in a rich, fully-designed game, however - it lacks context to bind the functionality of code to the metaphorical setting of the game. In this paper we explore potential solutions to this problem, both in terms of creative systems which co-operate with human content, and the possibility for contextual meaning in autonomous, human-free creative systems as well. |
Cook, Michael; Colton, Simon; Gow, Jeremy Nobody’s a Critic: On the Evaluation of Creative Code Generators--A Case Study in Video Game Design Inproceedings In: Proceedings of the 4th International Conference on Computational Creativity, pp. 123–130, 2013. @inproceedings{cook2013nobody, title = {Nobody’s a Critic: On the Evaluation of Creative Code Generators--A Case Study in Video Game Design}, author = { Michael Cook and Simon Colton and Jeremy Gow}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/cook_iccc13.pdf}, year = {2013}, date = {2013-01-01}, booktitle = {Proceedings of the 4th International Conference on Computational Creativity}, pages = {123--130}, abstract = {Application domains for Computational Creativity projects range from musical composition to recipe design, but despite all of these systems having computational methods in common, we are aware of no projects to date that focus on program code as the created artefact. We present the Mechanic Miner tool for inventing new concepts for videogame interaction which works by inspecting, modifying and executing code. We describe the system in detail and report on an evaluation based on a large survey of people playing games using content it produced. We use this to raise issues regarding the assessment of code as a created artefact and to discuss future directions for Computational Creativity research. }, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Application domains for Computational Creativity projects range from musical composition to recipe design, but despite all of these systems having computational methods in common, we are aware of no projects to date that focus on program code as the created artefact. We present the Mechanic Miner tool for inventing new concepts for videogame interaction which works by inspecting, modifying and executing code. We describe the system in detail and report on an evaluation based on a large survey of people playing games using content it produced. We use this to raise issues regarding the assessment of code as a created artefact and to discuss future directions for Computational Creativity research. |
Cook, Michael; Colton, Simon; Raad, Azalea; Gow, Jeremy Mechanic Miner: Reflection-Driven Game Mechanic Discovery and Level Design Inproceedings In: European Conference on the Applications of Evolutionary Computation, pp. 284–293, Springer 2013. @inproceedings{cook2013mechanic, title = {Mechanic Miner: Reflection-Driven Game Mechanic Discovery and Level Design}, author = { Michael Cook and Simon Colton and Azalea Raad and Jeremy Gow}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/cook_evogames13.pdf}, year = {2013}, date = {2013-01-01}, booktitle = {European Conference on the Applications of Evolutionary Computation}, pages = {284--293}, organization = {Springer}, abstract = {We introduce Mechanic Miner, an evolutionary system for discovering simple two-state game mechanics for puzzle platform games. We demonstrate how a reflection-driven generation technique can use a simulation of gameplay to select good mechanics, and how the simulationdriven process can be inverted to produce challenging levels specific to a generated mechanic. We give examples of levels and mechanics generated by the system, summarise a small pilot study conducted with example levels and mechanics, and point to further applications of the technique, including applications to automated game design. }, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We introduce Mechanic Miner, an evolutionary system for discovering simple two-state game mechanics for puzzle platform games. We demonstrate how a reflection-driven generation technique can use a simulation of gameplay to select good mechanics, and how the simulationdriven process can be inverted to produce challenging levels specific to a generated mechanic. We give examples of levels and mechanics generated by the system, summarise a small pilot study conducted with example levels and mechanics, and point to further applications of the technique, including applications to automated game design. |
Cook, Michael; Colton, Simon; Pease, Alison Aesthetic Considerations for Automated Platformer Design Inproceedings In: Proceedings of the 8th AAAI Conference on Artificial Intelligence and Interactive Digital Entertainment, 2012. @inproceedings{Cook2012AIIDE, title = {Aesthetic Considerations for Automated Platformer Design}, author = {Michael Cook and Simon Colton and Alison Pease}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/11/cook_aiide12.pdf}, year = {2012}, date = {2012-11-01}, booktitle = {Proceedings of the 8th AAAI Conference on Artificial Intelligence and Interactive Digital Entertainment}, abstract = {We describe ANGELINA3, a system that can automati- cally develop games along a defined theme, by select- ing appropriate multimedia content from a variety of sources and incorporating it into a game’s design. We discuss these capabilities in the context of the FACE model for assessing progress in the building of cre- ative systems, and discuss how ANGELINA3 can be improved through further work.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We describe ANGELINA3, a system that can automati- cally develop games along a defined theme, by select- ing appropriate multimedia content from a variety of sources and incorporating it into a game’s design. We discuss these capabilities in the context of the FACE model for assessing progress in the building of cre- ative systems, and discuss how ANGELINA3 can be improved through further work. |
Browne, Cameron; Colton, Simon Computational Creativity in a Closed Game System Inproceedings In: 2012 IEEE Conference on Computational Intelligence and Games (CIG), pp. 296–303, IEEE 2012. @inproceedings{browne2012computational, title = {Computational Creativity in a Closed Game System}, author = { Cameron Browne and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/browne_cig12.pdfhttp://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/browne_cig12-1.pdf}, year = {2012}, date = {2012-01-01}, booktitle = {2012 IEEE Conference on Computational Intelligence and Games (CIG)}, pages = {296--303}, organization = {IEEE}, abstract = {This paper describes the early stages of an experiment investigating the role of the computer as a creative collaborator in the game design process. We introduce the Shibumi set, a closed game system so simple that its rule space can be completely defined, yet deep enough to allow interesting games to emerge. Constraining the search space to such a closed system has computational benefits, but had unexpected effects on the creative process of designers during a related game design contest. These effects yield some insight into the creative process of experienced game designers, in particular, the way they search for rule sets to realise desired behaviours, and suggest a simple unified model of the game design process. We suggest ways in which these insights may be incorporated into future work, to produce software that might not only search for new games more effectively and assist the designer as a creative collaborator, but to automate the game design process in ways that might be perceived as more creative.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } This paper describes the early stages of an experiment investigating the role of the computer as a creative collaborator in the game design process. We introduce the Shibumi set, a closed game system so simple that its rule space can be completely defined, yet deep enough to allow interesting games to emerge. Constraining the search space to such a closed system has computational benefits, but had unexpected effects on the creative process of designers during a related game design contest. These effects yield some insight into the creative process of experienced game designers, in particular, the way they search for rule sets to realise desired behaviours, and suggest a simple unified model of the game design process. We suggest ways in which these insights may be incorporated into future work, to produce software that might not only search for new games more effectively and assist the designer as a creative collaborator, but to automate the game design process in ways that might be perceived as more creative. |
Cook, Michael; Colton, Simon; Gow, Jeremy Initial Results From Co-Operative Co-Evolution for Automated Platformer Design Inproceedings In: European Conference on the Applications of Evolutionary Computation, pp. 194–203, Springer 2012. @inproceedings{cook2012initial, title = {Initial Results From Co-Operative Co-Evolution for Automated Platformer Design}, author = { Michael Cook and Simon Colton and Jeremy Gow}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/cook_evogames12.pdf}, year = {2012}, date = {2012-01-01}, booktitle = {European Conference on the Applications of Evolutionary Computation}, pages = {194--203}, organization = {Springer}, abstract = {We present initial results from ACCME,A Co-operative Co-evolutionary Metroidvania Engine, which uses co-operative co-evolution to automatically evolve simple platform games. We describe the system in detail and justify the use of co-operative co-evolution. We then address two fundamental questions about the use of this method in automated game design, both in terms of its ability to maximise fitness functions, and whether our choice of fitness function produces scores which correlate with player preference in the resulting games.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We present initial results from ACCME,A Co-operative Co-evolutionary Metroidvania Engine, which uses co-operative co-evolution to automatically evolve simple platform games. We describe the system in detail and justify the use of co-operative co-evolution. We then address two fundamental questions about the use of this method in automated game design, both in terms of its ability to maximise fitness functions, and whether our choice of fitness function produces scores which correlate with player preference in the resulting games. |
Cook, Michael; Colton, Simon ANGELINA-Coevolution in Automated Game Design Inproceedings In: Proceedings of the 1st International Conference on Computational Creativity, pp. 228, 2012. @inproceedings{cook2012angelina, title = {ANGELINA-Coevolution in Automated Game Design}, author = { Michael Cook and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/cook_iccc12.pdf}, year = {2012}, date = {2012-01-01}, booktitle = {Proceedings of the 1st International Conference on Computational Creativity}, pages = {228}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } |
Browne, Cameron B; Powley, Edward; Whitehouse, Daniel; Lucas, Simon M; Cowling, Peter; Rohlfshagen, Philipp; Tavener, Stephen; Perez, Diego; Samothrakis, Spyridon; Colton, Simon A Survey of Monte Carlo Tree Search Methods Journal Article In: IEEE Transactions on Computational Intelligence and AI in Games, 4 (1), pp. 1–43, 2012. @article{browne2012survey, title = {A Survey of Monte Carlo Tree Search Methods}, author = { Cameron B Browne and Edward Powley and Daniel Whitehouse and Simon M Lucas and Peter Cowling and Philipp Rohlfshagen and Stephen Tavener and Diego Perez and Spyridon Samothrakis and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/browne_tciaig12_1.pdf}, year = {2012}, date = {2012-01-01}, journal = {IEEE Transactions on Computational Intelligence and AI in Games}, volume = {4}, number = {1}, pages = {1--43}, abstract = {Monte Carlo Tree Search (MCTS) is a recently proposed search method that combines the precision of tree search with the generality of random sampling. It has received considerable interest due to its spectacular success in the difficult problem of computer Go, but has also proved beneficial in a range of other domains. This paper is a survey of the literature to date, intended to provide a snapshot of the state of the art after the first five years of MCTS research. We outline the core algorithm’s derivation, impart some structure on the many variations and enhancements that have been proposed, and summarise the results from the key game and non-game domains to which MCTS methods have been applied. A number of open research questions indicate that the field is ripe for future work.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Monte Carlo Tree Search (MCTS) is a recently proposed search method that combines the precision of tree search with the generality of random sampling. It has received considerable interest due to its spectacular success in the difficult problem of computer Go, but has also proved beneficial in a range of other domains. This paper is a survey of the literature to date, intended to provide a snapshot of the state of the art after the first five years of MCTS research. We outline the core algorithm’s derivation, impart some structure on the many variations and enhancements that have been proposed, and summarise the results from the key game and non-game domains to which MCTS methods have been applied. A number of open research questions indicate that the field is ripe for future work. |
Gow, Jeremy; Baumgarten, Robin; Cairns, Paul A; Colton, Simon; Miller, Paul Unsupervised Modeling of Player Style With LDA Journal Article In: IEEE Trans. Comput. Intellig. and AI in Games, 4 (3), pp. 152–166, 2012. @article{DBLP:journals/tciaig/GowBCCM12, title = {Unsupervised Modeling of Player Style With LDA}, author = {Jeremy Gow and Robin Baumgarten and Paul A. Cairns and Simon Colton and Paul Miller}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/03/gow_tciaig12.pdf}, doi = {10.1109/TCIAIG.2012.2213600}, year = {2012}, date = {2012-01-01}, journal = {IEEE Trans. Comput. Intellig. and AI in Games}, volume = {4}, number = {3}, pages = {152--166}, abstract = {Computational analysis of player style has signifi- cant potential for video game design: it can provide insights into player behaviour, as well as the means to dynamically adapt a game to each individual’s style of play. To realise this potential, computational methods need to go beyond considerations of challenge and ability and account for aesthetic aspects of player style. We describe here a semi-automatic unsupervised learning approach to modelling player style using multi-class Linear Discriminant Analysis (LDA). We argue that this approach is widely applicable for modelling player style in a wide range of games, including commercial applications, and illustrate it with two case studies: the first for a novel arcade game called Snakeotron, the second for Rogue Trooper, a modern commercial third-person shooter video game.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Computational analysis of player style has signifi- cant potential for video game design: it can provide insights into player behaviour, as well as the means to dynamically adapt a game to each individual’s style of play. To realise this potential, computational methods need to go beyond considerations of challenge and ability and account for aesthetic aspects of player style. We describe here a semi-automatic unsupervised learning approach to modelling player style using multi-class Linear Discriminant Analysis (LDA). We argue that this approach is widely applicable for modelling player style in a wide range of games, including commercial applications, and illustrate it with two case studies: the first for a novel arcade game called Snakeotron, the second for Rogue Trooper, a modern commercial third-person shooter video game. |
Gow, Jeremy; Colton, Simon; Cairns, Paul A; Miller, Paul Mining Rules from Player Experience and Activity Data Inproceedings In: Proceedings of the Eighth AAAI Conference on Artificial Intelligence and Interactive Digital Entertainment, AIIDE-12, Stanford, California, October 8-12, 2012, 2012. @inproceedings{DBLP:conf/aiide/GowCCM12, title = {Mining Rules from Player Experience and Activity Data}, author = {Jeremy Gow and Simon Colton and Paul A. Cairns and Paul Miller}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/03/gow_aiide12.pdf}, year = {2012}, date = {2012-01-01}, booktitle = {Proceedings of the Eighth AAAI Conference on Artificial Intelligence and Interactive Digital Entertainment, AIIDE-12, Stanford, California, October 8-12, 2012}, crossref = {DBLP:conf/aiide/2012}, abstract = {Feedback on player experience and behaviour can be invaluable to game designers, but there is need for specialised knowledge discovery tools to deal with high volume playtest data. We describe a study with a commercial third-person shooter, in which integrated player activity and experience data was captured and mined for design-relevant knowledge. We demonstrate that association rule learning and rule templates can be used to extract meaningful rules relating player activity and experience during combat. We found that the number, type and quality of rules varies between experiences, and is affected by feature distributions. Further work is required on rule selection and evaluation.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Feedback on player experience and behaviour can be invaluable to game designers, but there is need for specialised knowledge discovery tools to deal with high volume playtest data. We describe a study with a commercial third-person shooter, in which integrated player activity and experience data was captured and mined for design-relevant knowledge. We demonstrate that association rule learning and rule templates can be used to extract meaningful rules relating player activity and experience during combat. We found that the number, type and quality of rules varies between experiences, and is affected by feature distributions. Further work is required on rule selection and evaluation. |
Cook, Michael; Colton, Simon Multi-Faceted Evolution of Simple Arcade Games Inproceedings In: Proceedings IEEE Conference on Computational Intelligence and Games, pp. 289–296, 2011. @inproceedings{cook2011multi, title = {Multi-Faceted Evolution of Simple Arcade Games}, author = { Michael Cook and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/cook_cig11-2.pdf}, year = {2011}, date = {2011-01-01}, booktitle = {Proceedings IEEE Conference on Computational Intelligence and Games}, pages = {289--296}, abstract = {We present a system for generating complete game designs by evolving rulesets, character layouts and terrain maps in an orchestrated way. In contrast to existing approaches to generate such game components in isolation, our ANGELINA system develops game components in unison with an appreciation for their interrelatedness. We describe this multi-faceted evolutionary approach, and give some results from a first round of experimentation. }, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We present a system for generating complete game designs by evolving rulesets, character layouts and terrain maps in an orchestrated way. In contrast to existing approaches to generate such game components in isolation, our ANGELINA system develops game components in unison with an appreciation for their interrelatedness. We describe this multi-faceted evolutionary approach, and give some results from a first round of experimentation. |
Baumgarten, Robin; Colton, Simon; Morris, Mark Combining AI Methods for Learning Bots in a Real-Time Strategy Game Journal Article In: International Journal of Computer Games Technology, 2009. @article{Baumgarten2009Combining, title = {Combining AI Methods for Learning Bots in a Real-Time Strategy Game}, author = {Robin Baumgarten and Simon Colton and Mark Morris}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/baumgarten_ijcgt09.pdf}, year = {2009}, date = {2009-10-01}, journal = {International Journal of Computer Games Technology}, abstract = {We describe an approach for simulating human game-play in strategy games using a variety of AI techniques, including simulated annealing, decision tree learning, and case-based reasoning. We have implemented an AI-bot that uses these techniques to form a novel approach for planning fleet movements and attacks in DEFCON, a nuclear war simulation strategy game released in 2006 by Introversion Software Ltd. The AI-bot retrieves plans from a case-base of recorded games, then uses these to generate a new plan using a method based on decision tree learning. In addition, we have implemented more sophisticated control over low-level actions that enable the AI-bot to synchronize bombing runs, and used a simulated annealing approach for assigning bombing targets to planes and opponent cities to missiles.We describe how our AI-bot operates, and the experimentation we have performed in order to determine an optimal configuration for it. With this configuration, our AI-bot beats Introversion’s finite state machine automated player in 76.7% of 150 matches played.We briefly introduce the notion of ability versus enjoyability and discuss initial results of a survey we conducted with human players.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We describe an approach for simulating human game-play in strategy games using a variety of AI techniques, including simulated annealing, decision tree learning, and case-based reasoning. We have implemented an AI-bot that uses these techniques to form a novel approach for planning fleet movements and attacks in DEFCON, a nuclear war simulation strategy game released in 2006 by Introversion Software Ltd. The AI-bot retrieves plans from a case-base of recorded games, then uses these to generate a new plan using a method based on decision tree learning. In addition, we have implemented more sophisticated control over low-level actions that enable the AI-bot to synchronize bombing runs, and used a simulated annealing approach for assigning bombing targets to planes and opponent cities to missiles.We describe how our AI-bot operates, and the experimentation we have performed in order to determine an optimal configuration for it. With this configuration, our AI-bot beats Introversion’s finite state machine automated player in 76.7% of 150 matches played.We briefly introduce the notion of ability versus enjoyability and discuss initial results of a survey we conducted with human players. |
Colton, Simon; Browne, Cameron Evolving Simple Art-based Games Inproceedings In: Workshops on Applications of Evolutionary Computation, 2009. @inproceedings{Colton2009EvoGames, title = {Evolving Simple Art-based Games}, author = {Simon Colton and Cameron Browne}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/colton_evogames09.pdf}, year = {2009}, date = {2009-10-01}, booktitle = {Workshops on Applications of Evolutionary Computation}, abstract = {Evolutionary art has a long and distinguished history, and genetic programming is one of only a handful of AI techniques which is used in graphic design and the visual arts. A recent trend in so-called `new media' art is to design online pieces which are dynamic and have an element of interaction and sometimes simple game-playing aspects. This de nes the challenge addressed here: to automatically evolve dynamic, interactive art pieces with game elements. We do this by extending the Avera user-driven evolutionary art system to produce programs which generate spirograph-style images by repeatedly placing, scaling, rotating and colouring geometric objects such as squares and circles. Such images are produced in an inherently causal way which provides the dynamic element to the pieces.We further extend the system to produce programs which react to mouse clicks, and to evolve sequential patterns of clicks for the user to uncover. We wrap the programs in a simple front end which provides the user with feedback on how close they are to uncovering the pattern, adding a lightweight game-playing element to the pieces. The evolved interactive artworks are a preliminary step in the creation of more sophisticated multimedia pieces.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Evolutionary art has a long and distinguished history, and genetic programming is one of only a handful of AI techniques which is used in graphic design and the visual arts. A recent trend in so-called `new media' art is to design online pieces which are dynamic and have an element of interaction and sometimes simple game-playing aspects. This de nes the challenge addressed here: to automatically evolve dynamic, interactive art pieces with game elements. We do this by extending the Avera user-driven evolutionary art system to produce programs which generate spirograph-style images by repeatedly placing, scaling, rotating and colouring geometric objects such as squares and circles. Such images are produced in an inherently causal way which provides the dynamic element to the pieces.We further extend the system to produce programs which react to mouse clicks, and to evolve sequential patterns of clicks for the user to uncover. We wrap the programs in a simple front end which provides the user with feedback on how close they are to uncovering the pattern, adding a lightweight game-playing element to the pieces. The evolved interactive artworks are a preliminary step in the creation of more sophisticated multimedia pieces. |
Baumgarten, Robin; Colton, Simon Case-based Player Simulation for the Commercial Strategy Game DEFCON Inproceedings In: Proceedings of CGames, 2007. @inproceedings{Baumgarten2007, title = {Case-based Player Simulation for the Commercial Strategy Game DEFCON}, author = {Robin Baumgarten and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/11/baumgarten_cgames07.pdf}, year = {2007}, date = {2007-11-01}, booktitle = {Proceedings of CGames}, abstract = {DEFCON is a nuclear war simulation strategy game released in 2006 by Introversion Software Ltd. We describe an approach to simulating human game-play using a variety of AI techniques, including simulated annealing, decision tree learning and case-based reasoning. We have implemented an AI-bot that uses a novel approach to planning fleet movements and attacks. This retrieves plans from a case base of previous games, then merges these using a method based on decision tree learning. In addition, we have implemented more sophisticated control over low-level actions such as firing missiles and guiding planes. In particular, we have written routines to enable the AI-bot to synchronise bombing runs, and enabled a simulated annealing approach to assigning bombing targets to planes and opponent cities to missiles. We describe how our AI-bot operates, and the experimentation we have performed in order to determine an optimal configuration for it. With this configuration, our AI- bot beat Introversion’s finite state machine automated player in 76.7% of 150 matches played.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } DEFCON is a nuclear war simulation strategy game released in 2006 by Introversion Software Ltd. We describe an approach to simulating human game-play using a variety of AI techniques, including simulated annealing, decision tree learning and case-based reasoning. We have implemented an AI-bot that uses a novel approach to planning fleet movements and attacks. This retrieves plans from a case base of previous games, then merges these using a method based on decision tree learning. In addition, we have implemented more sophisticated control over low-level actions such as firing missiles and guiding planes. In particular, we have written routines to enable the AI-bot to synchronise bombing runs, and enabled a simulated annealing approach to assigning bombing targets to planes and opponent cities to missiles. We describe how our AI-bot operates, and the experimentation we have performed in order to determine an optimal configuration for it. With this configuration, our AI- bot beat Introversion’s finite state machine automated player in 76.7% of 150 matches played. |
Automating Tasks in Creative Language
Our newest application domain is creative language, where we are have looked at poetry generation as part of The Painting Fool project, and we are part of a team building The What-If Machine for fictional ideation. One of our main contributions is to push the idea of software accounting for its actions via generating texts which acts as commentaries on what it has done, why, and what it has produced.
Llano, Maria Teresa; Colton, Simon; Hepworth, Rose; Gow, Jeremy Automated Fictional Ideation via Knowledge Base Manipulation Journal Article In: Cognitive Computation, 8 (2), pp. 153-174, 2016. @article{Llano2011usingb, title = {Automated Fictional Ideation via Knowledge Base Manipulation}, author = {Maria Teresa Llano and Simon Colton and Rose Hepworth and Jeremy Gow}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/llano_jcc2015.pdf}, year = {2016}, date = {2016-10-01}, journal = {Cognitive Computation}, volume = {8}, number = {2}, pages = {153-174}, abstract = {The invention of fictional ideas (ideation) is often a central process in the creative production of arte- facts such as poems, music and paintings, but has barely been studied in the computational creativity community. We present here a general approach to automated fictional ideation that works by manipulating facts specified in knowledge bases. More specifically, we specify a number of constructions which, by altering and combining facts from a knowledge base, result in the generation of fictions. Moreover, we present an instantiation of these construc- tions through the use of ConceptNet, a database of common sense knowledge. In order to evaluate the success of these constructions, we present a curation analysis that calculates the proportion of ideas which pass a typicality judgement. We further evaluate the output of this approach through a crowd-sourcing experiment in which participants were asked to rank ideas. We found a positive correlation between the participant’s rankings and a chaining inference technique that automatically assesses the value of the fic- tions generated through our approach. We believe that these results show that this approach constitutes a firm basis for automated fictional ideation with evaluative capacity.}, keywords = {}, pubstate = {published}, tppubtype = {article} } The invention of fictional ideas (ideation) is often a central process in the creative production of arte- facts such as poems, music and paintings, but has barely been studied in the computational creativity community. We present here a general approach to automated fictional ideation that works by manipulating facts specified in knowledge bases. More specifically, we specify a number of constructions which, by altering and combining facts from a knowledge base, result in the generation of fictions. Moreover, we present an instantiation of these construc- tions through the use of ConceptNet, a database of common sense knowledge. In order to evaluate the success of these constructions, we present a curation analysis that calculates the proportion of ideas which pass a typicality judgement. We further evaluate the output of this approach through a crowd-sourcing experiment in which participants were asked to rank ideas. We found a positive correlation between the participant’s rankings and a chaining inference technique that automatically assesses the value of the fic- tions generated through our approach. We believe that these results show that this approach constitutes a firm basis for automated fictional ideation with evaluative capacity. |
Corneli, Joseph; Jordanous, Anna; Shepperd, Rosie; Llano, Maria Teresa; Misztal, Joanna; Colton, Simon; Guckelsberger, Christian Computational Poetry Workshop: Making Sense of Work in Progress Inproceedings In: Proc. 6th Int. Conf. Computational Creativity, 2015. @inproceedings{Corneli2015, title = {Computational Poetry Workshop: Making Sense of Work in Progress}, author = {Joseph Corneli and Anna Jordanous and Rosie Shepperd and Maria Teresa Llano and Joanna Misztal and Simon Colton and Christian Guckelsberger}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/03/corneli_iccc15_poetry-1.pdf}, year = {2015}, date = {2015-01-01}, booktitle = {Proc. 6th Int. Conf. Computational Creativity}, abstract = {Creativity cannot exist in a vacuum; it develops through feedback, learning, reflection and social interaction with others. However, this perspective has been relat- ively under-investigated in computational creativity re- search, which typically examines systems that operate individually. We develop a thought experiment showing how structured dialogues can help develop the creative aspects of computer poetry. Centrally in this approach, we ask questions of a poem, inviting it to tell us in what way it may be considered a “creative making.”}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Creativity cannot exist in a vacuum; it develops through feedback, learning, reflection and social interaction with others. However, this perspective has been relat- ively under-investigated in computational creativity re- search, which typically examines systems that operate individually. We develop a thought experiment showing how structured dialogues can help develop the creative aspects of computer poetry. Centrally in this approach, we ask questions of a poem, inviting it to tell us in what way it may be considered a “creative making.” |
Llano, Maria Teresa; Hepworth, Rose; Colton, Simon; Gow, Jeremy; Charnley, John; Lavrač, Nada; Žnidaršič, Martin; Perovšek, Matic; Granroth-Wilding, Mark; Clark, Stephen Baseline Methods For Automated Fictional Ideation Inproceedings In: Proceedings of the 5th international conference on computational creativity, 2014. @inproceedings{llano2014baseline, title = {Baseline Methods For Automated Fictional Ideation}, author = { Maria Teresa Llano and Rose Hepworth and Simon Colton and Jeremy Gow and John Charnley and Nada Lavrač and Martin Žnidaršič and Matic Perovšek and Mark Granroth-Wilding and Stephen Clark}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/09/llano_iccc2014.pdf}, year = {2014}, date = {2014-01-01}, booktitle = {Proceedings of the 5th international conference on computational creativity}, abstract = {The invention of fictional ideas (ideation) is often a central process in the creative production of artefacts such as po- ems, music and paintings, but has barely been studied in the Computational Creativity community. We present here three baseline approaches for automated fictional ideation, using methods which invert and alter facts from the ConceptNet and ReVerb databases, and perform bisociative discovery. For each method, we present a curation analysis, by calculating the proportion of ideas which pass a typicality evaluation. We further evaluate one ideation approach through a crowd- sourcing experiment in which participants were asked to rank ideas. The results from this study, and the baseline meth- ods and methodologies presented here, constitute a firm basis on which to build more sophisticated models for automated ideation with evaluative capacity.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } The invention of fictional ideas (ideation) is often a central process in the creative production of artefacts such as po- ems, music and paintings, but has barely been studied in the Computational Creativity community. We present here three baseline approaches for automated fictional ideation, using methods which invert and alter facts from the ConceptNet and ReVerb databases, and perform bisociative discovery. For each method, we present a curation analysis, by calculating the proportion of ideas which pass a typicality evaluation. We further evaluate one ideation approach through a crowd- sourcing experiment in which participants were asked to rank ideas. The results from this study, and the baseline meth- ods and methodologies presented here, constitute a firm basis on which to build more sophisticated models for automated ideation with evaluative capacity. |
Llano, Maria Teresa; Hepworth, Rose; Colton, Simon; Charnley, John; Gow, Jeremy Automating Fictional Ideation Using ConceptNet Inproceedings In: Proceedings of the AISB14 symposium on computational creativity, 2014. @inproceedings{llano2014automating, title = {Automating Fictional Ideation Using ConceptNet}, author = {Maria Teresa Llano and Rose Hepworth and Simon Colton and John Charnley and Jeremy Gow}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/09/llano_aisb14.pdf}, year = {2014}, date = {2014-01-01}, booktitle = {Proceedings of the AISB14 symposium on computational creativity}, abstract = {The invention of fictional ideas (ideation) is often a cen- tral process in producing artefacts such as poems, music and paint- ings in a creative way. Automated fictional ideation should, there- fore, be of much interest in the study of Computational Creativity, but only a few approaches have been explored. We describe here the preliminary results of a new method for automated generation and evaluation of fictional ideas which uses ConceptNet, a semantic net- work. We evaluate the results obtained through a small study that involves participants scoring ideas via an online survey. We believe this approach constitutes a firm basis on which a more sophisticated model for automated creative ideation can be built.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } The invention of fictional ideas (ideation) is often a cen- tral process in producing artefacts such as poems, music and paint- ings in a creative way. Automated fictional ideation should, there- fore, be of much interest in the study of Computational Creativity, but only a few approaches have been explored. We describe here the preliminary results of a new method for automated generation and evaluation of fictional ideas which uses ConceptNet, a semantic net- work. We evaluate the results obtained through a small study that involves participants scoring ideas via an online survey. We believe this approach constitutes a firm basis on which a more sophisticated model for automated creative ideation can be built. |
Charnley, John; Colton, Simon; Llano, Maria Teresa The FloWr Framework: Automated Flowchart Construction, Optimisation and Alteration for Creative Systems Inproceedings In: Proceedings of the 5th international conference on computational creativity, 2014. @inproceedings{charnley2014flowr, title = {The FloWr Framework: Automated Flowchart Construction, Optimisation and Alteration for Creative Systems}, author = { John Charnley and Simon Colton and Maria Teresa Llano}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/08/charnley_iccc2014.pdf}, year = {2014}, date = {2014-01-01}, booktitle = {Proceedings of the 5th international conference on computational creativity}, volume = {9}, abstract = {We describe the FloWr framework for implementing creative systems as scripts over processes and manipulated visually as flowcharts. FloWr has been specifically developed to be able to automatically optimise, alter and ultimately generate novel flowcharts, thus innovating at process level. We describe the fundamental architecture of the framework and provide ex- amples of creative systems which have been implemented in FloWr. Via some preliminary experimentation, we demon- strate how FloWr can optimise a given system for efficiency and yield, alter input parameters to increase unexpectedness, and build novel generative systems automatically.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We describe the FloWr framework for implementing creative systems as scripts over processes and manipulated visually as flowcharts. FloWr has been specifically developed to be able to automatically optimise, alter and ultimately generate novel flowcharts, thus innovating at process level. We describe the fundamental architecture of the framework and provide ex- amples of creative systems which have been implemented in FloWr. Via some preliminary experimentation, we demon- strate how FloWr can optimise a given system for efficiency and yield, alter input parameters to increase unexpectedness, and build novel generative systems automatically. |
Perovšek, Matic; Cestnik, Bojan; Urbančič, Tanja; Colton, Simon; Lavrač, Nada Towards Narrative Ideation via Cross-Context Link Discovery Using Banded Matrices Incollection In: Proceedings of the Twelfth International Symposium on Intelligent Data Analysis, 2013. @incollection{Perovsek2013, title = {Towards Narrative Ideation via Cross-Context Link Discovery Using Banded Matrices}, author = {Matic Perovšek and Bojan Cestnik and Tanja Urbančič and Simon Colton and Nada Lavrač}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/03/perovsek_ida13.pdf}, year = {2013}, date = {2013-11-01}, booktitle = {Proceedings of the Twelfth International Symposium on Intelligent Data Analysis}, abstract = {Knowledge discovery and computational creativity have until lately been investigated by two separate research communities. However, research in bisociative, cross-context knowledge discovery has recently started addressing creative tasks, including creative literature mining. This paper contributes to this effort by investigating an approach to cross-context link discovery based on banded matrices, aimed at identifying meaningful bridging terms (b-terms) at the intersection of two different domains. The proposed approach was applied to a simplified computational creativity task of narrative ideation from pairs of short sentences. As input, we took sentences from two different contexts: what-if sentences retrieved from Twitter, and morals from Aesop’s fables, respectively. The approach resulted in a list of linked pairs of sentences from these two do- mains, illustrating the potential of the proposed approach to cross-context narrative ideation.}, keywords = {}, pubstate = {published}, tppubtype = {incollection} } Knowledge discovery and computational creativity have until lately been investigated by two separate research communities. However, research in bisociative, cross-context knowledge discovery has recently started addressing creative tasks, including creative literature mining. This paper contributes to this effort by investigating an approach to cross-context link discovery based on banded matrices, aimed at identifying meaningful bridging terms (b-terms) at the intersection of two different domains. The proposed approach was applied to a simplified computational creativity task of narrative ideation from pairs of short sentences. As input, we took sentences from two different contexts: what-if sentences retrieved from Twitter, and morals from Aesop’s fables, respectively. The approach resulted in a list of linked pairs of sentences from these two do- mains, illustrating the potential of the proposed approach to cross-context narrative ideation. |
Colton, Simon; Charnley, John Towards a Flowcharting System for Automated Process Invention Inproceedings In: Demo session Proceedings of the 4th International Conference on Computational Creativity, 2013. @inproceedings{Colton2013ICCC, title = {Towards a Flowcharting System for Automated Process Invention}, author = {Simon Colton and John Charnley}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/11/colton_icccdemo13.pdf}, year = {2013}, date = {2013-11-01}, booktitle = {Demo session Proceedings of the 4th International Conference on Computational Creativity}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } |
Colton, Simon On Shape Poems and the Shape of Poems: A Computational Creativity Perspective Inproceedings In: Proceedings of the Second Interdisciplinary Workshop The Shape of Things, Rio de Janeiro, Brazil, April 3-4, 2013, pp. 23–28, 2013. @inproceedings{Colton2013, title = {On Shape Poems and the Shape of Poems: A Computational Creativity Perspective}, author = {Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/colton_shapes13.pdf}, year = {2013}, date = {2013-01-01}, booktitle = {Proceedings of the Second Interdisciplinary Workshop The Shape of Things, Rio de Janeiro, Brazil, April 3-4, 2013}, pages = {23--28}, crossref = {DBLP:conf/shapes/2013}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } |
Colton, Simon; Goodwin, Jacob; Veale, Tony Full-FACE Poetry Generation Inproceedings In: Proceedings of the Third International Conference on Computational Creativity, pp. 95–102, 2012. @inproceedings{colton2012full, title = {Full-FACE Poetry Generation}, author = { Simon Colton and Jacob Goodwin and Tony Veale}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/09/colton_iccc12.pdf}, year = {2012}, date = {2012-01-01}, booktitle = {Proceedings of the Third International Conference on Computational Creativity}, pages = {95--102}, abstract = {We describe a corpus-based poetry generation system which uses templates to construct poems according to given con- straints on rhyme, meter, stress, sentiment, word frequency and word similarity. Moreover, the software constructs a mood for the day by analysing newspaper articles; uses this to determine both an article to base a poem on and a tem- plate for the poem; creates an aesthetic based on relevance to the article, lyricism, sentiment and flamboyancy; searches for an instantiation of the template which maximises the aes- thetic; and provides a commentary for the whole process to add value to the creative act. We describe the processes be- hind this approach, present some experimental results which helped in fine tuning, and provide some illustrative poems and commentaries. We argue that this is the first poetry system which generates examples, forms concepts, invents aesthetics and frames its work, and so can be assessed favourably with respect to the FACE model for comparing creative systems.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We describe a corpus-based poetry generation system which uses templates to construct poems according to given con- straints on rhyme, meter, stress, sentiment, word frequency and word similarity. Moreover, the software constructs a mood for the day by analysing newspaper articles; uses this to determine both an article to base a poem on and a tem- plate for the poem; creates an aesthetic based on relevance to the article, lyricism, sentiment and flamboyancy; searches for an instantiation of the template which maximises the aes- thetic; and provides a commentary for the whole process to add value to the creative act. We describe the processes be- hind this approach, present some experimental results which helped in fine tuning, and provide some illustrative poems and commentaries. We argue that this is the first poetry system which generates examples, forms concepts, invents aesthetics and frames its work, and so can be assessed favourably with respect to the FACE model for comparing creative systems. |
Addressing Questions of Computational Creativity
A number of researchers are taking a longer view, and addressing broader questions in computing, such as the notion of whether a computer can exhibit creative behaviour. Only in recent years has AI software reached a level of complexity and ability that this question can be addressed in a concrete rather than a purely theoretical way. This is a field we have been involved in via research, organisation and participation in various workshops and conferences, since 1999. Given that the HR system undertakes some of the more creative tasks in pure mathematics (such as inventing concepts and making conjectures), we have used HR (and other systems) to look at various notions connected to computational creativity. In more recent work, we have addressed the issues raised by The Painting Fool project, to further our understanding of computational creativity in an artistic rather than a scientific domain. The following papers describe some of our projects in this area:
Cook, Michael; Colton, Simon Generating Code For Expressing Simple Preferences: Moving On From Hardcoding And Randomness Inproceedings In: Proceedings of the Sixth International Conference on Computational Creativity, pp. 8, 2015. @inproceedings{cook2015generating, title = {Generating Code For Expressing Simple Preferences: Moving On From Hardcoding And Randomness}, author = { Michael Cook and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/cook_iccc2015.pdf}, year = {2015}, date = {2015-01-01}, booktitle = {Proceedings of the Sixth International Conference on Computational Creativity}, pages = {8}, abstract = {Software expressing intent and justifying creative decisions are important considerations when building systems in the context of Computational Creativity. However, getting software to express subjective opinions like simple preferences is difficult without mimicking existing people’s opinions or using random choice. In this paper, we propose an alternative way of enabling software to make meaningful decisions in smallscale subjective scenarios, such as choosing a favourite colour. Our system uses a combination of metrics as a fitness function for evolving short pieces of code that choose between artefacts. These ‘preference functions’ can make choices between simple items that are neither random nor based on an already existing opinion, and additionally have a sense of consistency. We describe the system, offer some example results from the work and suggest how this might lead to further developments in generative subjectivity in the future.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Software expressing intent and justifying creative decisions are important considerations when building systems in the context of Computational Creativity. However, getting software to express subjective opinions like simple preferences is difficult without mimicking existing people’s opinions or using random choice. In this paper, we propose an alternative way of enabling software to make meaningful decisions in smallscale subjective scenarios, such as choosing a favourite colour. Our system uses a combination of metrics as a fitness function for evolving short pieces of code that choose between artefacts. These ‘preference functions’ can make choices between simple items that are neither random nor based on an already existing opinion, and additionally have a sense of consistency. We describe the system, offer some example results from the work and suggest how this might lead to further developments in generative subjectivity in the future. |
Colton, Simon; Pease, Alison; Corneli, Joseph; Cook, Michael; Hepworth, Rose; Ventura, Dan Stakeholder Groups in Computational Creativity Research and Practice Incollection In: Computational Creativity Research: Towards Creative Machines, pp. 3–36, Springer, 2015. @incollection{colton2015stakeholder, title = {Stakeholder Groups in Computational Creativity Research and Practice}, author = { Simon Colton and Alison Pease and Joseph Corneli and Michael Cook and Rose Hepworth and Dan Ventura}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/colton_ccchapter15.pdf}, year = {2015}, date = {2015-01-01}, booktitle = {Computational Creativity Research: Towards Creative Machines}, pages = {3--36}, publisher = {Springer}, abstract = {The notion that software could be independently and usefully creative is becoming more commonplace in scientific, cultural, business and public circles. It is not fanciful to imagine creative software embedded in society in the short to medium term, acting as collaborators and autonomous creative agents for much societal benefit. Technologically, there is still some way to go to enable Artificial Intelligence methods to create artefacts and ideas of value, and to get software to do so in interesting and engaging ways. There are also a number of sociological hurdles to overcome in getting society to accept software as being truly creative, and we concentrate on those here. We discuss the various communities that can be considered stakeholders in the perception of computers being creative or not. In particular, we look in detail at three sets of stakeholders, namely the general public, Computational Creativity researchers and fellow creatives.We put forward various philosophical points which we argue will shape the way in which society accepts creative software. We make various claims along the way about how people perceive software as being creative or not, which we believe should be addressed with scientific experimentation, and we call on the Computational Creativity research community to do just that.}, keywords = {}, pubstate = {published}, tppubtype = {incollection} } The notion that software could be independently and usefully creative is becoming more commonplace in scientific, cultural, business and public circles. It is not fanciful to imagine creative software embedded in society in the short to medium term, acting as collaborators and autonomous creative agents for much societal benefit. Technologically, there is still some way to go to enable Artificial Intelligence methods to create artefacts and ideas of value, and to get software to do so in interesting and engaging ways. There are also a number of sociological hurdles to overcome in getting society to accept software as being truly creative, and we concentrate on those here. We discuss the various communities that can be considered stakeholders in the perception of computers being creative or not. In particular, we look in detail at three sets of stakeholders, namely the general public, Computational Creativity researchers and fellow creatives.We put forward various philosophical points which we argue will shape the way in which society accepts creative software. We make various claims along the way about how people perceive software as being creative or not, which we believe should be addressed with scientific experimentation, and we call on the Computational Creativity research community to do just that. |
Colton, Simon; Cook, Michael; Hepworth, Rose; Pease, Alison On Acid Drops and Teardrops: Observer Issues in Computational Creativity Inproceedings In: Proceedings of the 7th AISB Symposium on Computing and Philosophy, 2014. @inproceedings{colton2014acid, title = {On Acid Drops and Teardrops: Observer Issues in Computational Creativity}, author = { Simon Colton and Michael Cook and Rose Hepworth and Alison Pease}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/colton_aisb14c.pdf}, year = {2014}, date = {2014-01-01}, booktitle = {Proceedings of the 7th AISB Symposium on Computing and Philosophy}, abstract = {We argue that the notion of creativity in a person or software is a secondary and essentially contested concept. Hence, in Computational Creativity research – where we aim to build software taken seriously as independently creative – understanding the roles people take as process observer and product consumer is paramount. Depending on the domain, there can be a natural bias against software created artefacts, and Computational Creativity researchers have exacerbated this situation through Turing-style comparison tests. Framing this as a modified Chinese Room experiment, we propose two remedies to the situation. These involve software accounting for its decisions, actions and products, and taking the radical step of thinking of computer generated artefacts as fundamentally different to their human-produced counterparts. We use two case studies, where people interact with an automated painter and with computer-generated videogames, to highlight the observer issues we raise, and to demonstrate partial implementations of our remedies.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We argue that the notion of creativity in a person or software is a secondary and essentially contested concept. Hence, in Computational Creativity research – where we aim to build software taken seriously as independently creative – understanding the roles people take as process observer and product consumer is paramount. Depending on the domain, there can be a natural bias against software created artefacts, and Computational Creativity researchers have exacerbated this situation through Turing-style comparison tests. Framing this as a modified Chinese Room experiment, we propose two remedies to the situation. These involve software accounting for its decisions, actions and products, and taking the radical step of thinking of computer generated artefacts as fundamentally different to their human-produced counterparts. We use two case studies, where people interact with an automated painter and with computer-generated videogames, to highlight the observer issues we raise, and to demonstrate partial implementations of our remedies. |
Colton, Simon; Pease, Alison; Corneli, Joseph; Cook, Michael; Llano, Maria Teresa Assessing Progress in Building Autonomously Creative Systems Inproceedings In: Proceedings of the Fifth International Conference on Computational Creativity, pp. 137–145, 2014. @inproceedings{colton2014assessing, title = {Assessing Progress in Building Autonomously Creative Systems}, author = { Simon Colton and Alison Pease and Joseph Corneli and Michael Cook and Maria Teresa Llano}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/colton_iccc2014.pdf}, year = {2014}, date = {2014-01-01}, booktitle = {Proceedings of the Fifth International Conference on Computational Creativity}, pages = {137--145}, abstract = {Determining conclusively whether a new version of software creatively exceeds a previous version or a third party system is dicult, yet very important for scientific approaches in Computational Creativity research. We argue that software product and process need to be assessed simultaneously in assessing progress, and we introduce a diagrammatic formalism which exposes various timelines of creative acts in the construction and execution of successive versions of artefactgenerating software. The formalism enables estimations of progress or regress from system to system by comparing their diagrams and assessing changes in quality, quantity and variety of creative acts undertaken; audience perception of behaviours; and the quality of artefacts produced. We present a case study in the building of evolutionary art systems, and we use the formalism to highlight various issues in measuring progress in the building of creative systems.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Determining conclusively whether a new version of software creatively exceeds a previous version or a third party system is dicult, yet very important for scientific approaches in Computational Creativity research. We argue that software product and process need to be assessed simultaneously in assessing progress, and we introduce a diagrammatic formalism which exposes various timelines of creative acts in the construction and execution of successive versions of artefactgenerating software. The formalism enables estimations of progress or regress from system to system by comparing their diagrams and assessing changes in quality, quantity and variety of creative acts undertaken; audience perception of behaviours; and the quality of artefacts produced. We present a case study in the building of evolutionary art systems, and we use the formalism to highlight various issues in measuring progress in the building of creative systems. |
Pease, Alison; Colton, Simon; Ramezani, Ramin; Charnley, John; Reed, Kate A Discussion on Serendipity in Creative Systems Inproceedings In: Proceedings of the Fourth International Conference on Computational Creativity, pp. 64–71, 2013. @inproceedings{pease2013discussion, title = {A Discussion on Serendipity in Creative Systems}, author = { Alison Pease and Simon Colton and Ramin Ramezani and John Charnley and Kate Reed}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/pease_iccc13.pdf}, year = {2013}, date = {2013-01-01}, booktitle = {Proceedings of the Fourth International Conference on Computational Creativity}, pages = {64--71}, abstract = {We investigate serendipity, or happy, accidental discoveries, in CC, and propose computational concepts related to serendipity. These include a focus-shift, a breakdown of serendipitous discovery into prepared mind, serendipity trigger, bridge and result and three dimensions of serendipity: chance, sagacity and value. We propose a definition and standards for computational serendipity and evaluate three creative systems with respect to our standards. We argue that this is an important notion in creativity and, if carefully developed and used with caution, could result in a valuable new discovery technique in CC.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We investigate serendipity, or happy, accidental discoveries, in CC, and propose computational concepts related to serendipity. These include a focus-shift, a breakdown of serendipitous discovery into prepared mind, serendipity trigger, bridge and result and three dimensions of serendipity: chance, sagacity and value. We propose a definition and standards for computational serendipity and evaluate three creative systems with respect to our standards. We argue that this is an important notion in creativity and, if carefully developed and used with caution, could result in a valuable new discovery technique in CC. |
Pease, Alison; Colton, Simon; Charnley, John The Turing Test and Computational Creativity Inproceedings In: Contributed talks proceedings of the Turing Centenary Conference, 2012. @inproceedings{Pease2012Turing, title = {The Turing Test and Computational Creativity}, author = {Alison Pease and Simon Colton and John Charnley}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/11/pease_tc12.pdf}, year = {2012}, date = {2012-11-01}, booktitle = {Contributed talks proceedings of the Turing Centenary Conference}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } |
Charnley, John; Pease, Alison; Colton, Simon On the Notion of Framing in Computational Creativity Inproceedings In: Proceedings of the Third International Conference on Computational Creativity, pp. 77–81, 2012. @inproceedings{charnley2012notion, title = {On the Notion of Framing in Computational Creativity}, author = { John Charnley and Alison Pease and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/charnley_iccc12.pdf}, year = {2012}, date = {2012-01-01}, booktitle = {Proceedings of the Third International Conference on Computational Creativity}, pages = {77--81}, abstract = {In most domains, artefacts and the creativity that went into their production is judged within a context; where a context may include background information on how the creator feels about their work, what they think it expresses, how it fits in with other work done within their community, their mood before, during and after creation, and so on. We identify areas of framing information, such as motivation, intention, or the processes involved in creating a work, and consider how these areas might be applicable to the context of Computational Creativity. We suggest examples of how such framing information may be derived in existing creative systems and propose a novel dually-creative approach to framing, whereby an automated story generation system is employed, in tandem with the artefact generator, to produce suitable framing information. We outline how this method might be developed and some longer term goals.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } In most domains, artefacts and the creativity that went into their production is judged within a context; where a context may include background information on how the creator feels about their work, what they think it expresses, how it fits in with other work done within their community, their mood before, during and after creation, and so on. We identify areas of framing information, such as motivation, intention, or the processes involved in creating a work, and consider how these areas might be applicable to the context of Computational Creativity. We suggest examples of how such framing information may be derived in existing creative systems and propose a novel dually-creative approach to framing, whereby an automated story generation system is employed, in tandem with the artefact generator, to produce suitable framing information. We outline how this method might be developed and some longer term goals. |
Colton, Simon; Wiggins, Geraint A Computational Creativity: The Final Frontier? Inproceedings In: ECAI, pp. 21–26, 2012. @inproceedings{colton2012computational, title = {Computational Creativity: The Final Frontier?}, author = {Simon Colton and Geraint A Wiggins}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/colton_ecai12.pdf}, year = {2012}, date = {2012-01-01}, booktitle = {ECAI}, volume = {12}, pages = {21--26}, abstract = {Notions relating to computational systems exhibiting creative behaviours have been explored since the very early days of computer science, and the field of Computational Creativity research has formed in the last dozen years to scientifically explore the potential of such systems. We describe this field via a working definition; a brief history of seminal work; an exploration of the main issues, technologies and ideas; and a look towards future directions. As a society, we are jealous of our creativity: creative people and their contributions to cultural progression are highly valued. Moreover, creative behaviour in people draws on a full set of intelligent abilities, so simulating such behaviour represents a serious technical challenge for Artificial Intelligence research. As such, we believe it is fair to characterise Computational Creativity as a frontier for AI research beyond all others—maybe, even, the final frontier.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Notions relating to computational systems exhibiting creative behaviours have been explored since the very early days of computer science, and the field of Computational Creativity research has formed in the last dozen years to scientifically explore the potential of such systems. We describe this field via a working definition; a brief history of seminal work; an exploration of the main issues, technologies and ideas; and a look towards future directions. As a society, we are jealous of our creativity: creative people and their contributions to cultural progression are highly valued. Moreover, creative behaviour in people draws on a full set of intelligent abilities, so simulating such behaviour represents a serious technical challenge for Artificial Intelligence research. As such, we believe it is fair to characterise Computational Creativity as a frontier for AI research beyond all others—maybe, even, the final frontier. |
Pease, Alison; Charnley, John; Colton, Simon Using Grounded Theory to Suggest Types of Framing Information for Computational Creativity Book Chapter In: Proceedings of the Workshop "Computational Creativity, Concept Invention, and General Intelligence", pp. 7–13, University of Osnabrück, Institute of Cognitive Science, 2012. @inbook{pease2012using, title = {Using Grounded Theory to Suggest Types of Framing Information for Computational Creativity}, author = { Alison Pease and John Charnley and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/pease_c3g12.pdf}, year = {2012}, date = {2012-01-01}, booktitle = {Proceedings of the Workshop "Computational Creativity, Concept Invention, and General Intelligence"}, pages = {7--13}, publisher = {University of Osnabrück, Institute of Cognitive Science}, series = {PICS Publications of the Institute of Cognitive Science}, abstract = {In most domains, artefacts and the creativity that went into their production is judged within a context; where a context may include background information on how the creator feels about their work, what they think it expresses, how it fits in with other work done within their community, and so on. In some cases, such framing information may involve obfuscation in order to add mystery to the work or its creator, which can add to our perception of creativity.We describe a novel method for the analysis of human creativity, using grounded theory.We demonstrate the importance of grounded theory via an ethnographic study of interviews by John Tusa with contemporary artists. By exploring the type of context and background that the artists share, we have developed theories which highlight the importance of areas of framing information, such as motivation, intention, or the processes involved in creating a work. We extend this to consider the role of mystery and obfuscation in framing, by considering what artists do not say versus what is explicitly revealed.}, keywords = {}, pubstate = {published}, tppubtype = {inbook} } In most domains, artefacts and the creativity that went into their production is judged within a context; where a context may include background information on how the creator feels about their work, what they think it expresses, how it fits in with other work done within their community, and so on. In some cases, such framing information may involve obfuscation in order to add mystery to the work or its creator, which can add to our perception of creativity.We describe a novel method for the analysis of human creativity, using grounded theory.We demonstrate the importance of grounded theory via an ethnographic study of interviews by John Tusa with contemporary artists. By exploring the type of context and background that the artists share, we have developed theories which highlight the importance of areas of framing information, such as motivation, intention, or the processes involved in creating a work. We extend this to consider the role of mystery and obfuscation in framing, by considering what artists do not say versus what is explicitly revealed. |
Pease, Alison; Colton, Simon On Impact and Evaluation in Computational Creativity: A Discussion of the Turing Test and an Alternative Proposal Inproceedings In: Proceedings of the AISB symposium on AI and Philosophy, 2011. @inproceedings{pease2011impact, title = {On Impact and Evaluation in Computational Creativity: A Discussion of the Turing Test and an Alternative Proposal}, author = { Alison Pease and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/pease_aisb11.pdf}, year = {2011}, date = {2011-01-01}, booktitle = {Proceedings of the AISB symposium on AI and Philosophy}, abstract = {Computational Creativity is the AI subfield in which we study how to build computational models of creative thought in science and the arts. From an engineering perspective, it is desirable to have concrete measures for assessing the progress made from one version of a program to another, or for comparing and contrasting different software systems for the same creative task. We describe the Turing Test and versions of it which have been used in order to measure progress in Computational Creativity. We show that the versions proposed thus far lack the important aspect of interaction, without which much of the power of the Turing Test is lost. We argue that the Turing Test is largely inappropriate for the purposes of evaluation in Computational Creativity, since it attempts to homogenize creativity into a single (human) style, does not take into account the importance of background and contextual information for a creative act, encourages superficial, uninteresting advances in front-ends, and rewards creativity which adheres to a certain style over that which creates something which is genuinely novel. We further argue that although there may be some place for Turing-style tests for Computational Creativity at some point in the future, it is currently untenable to apply any defensible version of the Turing Test. As an alternative to Turing-style tests, we introduce two descriptive models for evaluating creative software, the FACE model which describes creative acts performed by software in terms of tuples of generative acts, and the IDEA model which describes how such creative acts can have an impact upon an ideal audience, given ideal information about background knowledge and the software development process. While these models require further study and elaboration, we believe that they can be usefully applied to current systems as well as guiding further development of creative systems.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Computational Creativity is the AI subfield in which we study how to build computational models of creative thought in science and the arts. From an engineering perspective, it is desirable to have concrete measures for assessing the progress made from one version of a program to another, or for comparing and contrasting different software systems for the same creative task. We describe the Turing Test and versions of it which have been used in order to measure progress in Computational Creativity. We show that the versions proposed thus far lack the important aspect of interaction, without which much of the power of the Turing Test is lost. We argue that the Turing Test is largely inappropriate for the purposes of evaluation in Computational Creativity, since it attempts to homogenize creativity into a single (human) style, does not take into account the importance of background and contextual information for a creative act, encourages superficial, uninteresting advances in front-ends, and rewards creativity which adheres to a certain style over that which creates something which is genuinely novel. We further argue that although there may be some place for Turing-style tests for Computational Creativity at some point in the future, it is currently untenable to apply any defensible version of the Turing Test. As an alternative to Turing-style tests, we introduce two descriptive models for evaluating creative software, the FACE model which describes creative acts performed by software in terms of tuples of generative acts, and the IDEA model which describes how such creative acts can have an impact upon an ideal audience, given ideal information about background knowledge and the software development process. While these models require further study and elaboration, we believe that they can be usefully applied to current systems as well as guiding further development of creative systems. |
Pease, Alison; Colton, Simon Computational Creativity Theory: Inspirations Behind the FACE and the IDEA Models Inproceedings In: Proceedings of the Second International Conference on Computational Creativity, 2011. @inproceedings{pease2011computational, title = {Computational Creativity Theory: Inspirations Behind the FACE and the IDEA Models}, author = { Alison Pease and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/pease_iccc11.pdf}, year = {2011}, date = {2011-01-01}, booktitle = {Proceedings of the Second International Conference on Computational Creativity}, abstract = {We introduce two descriptive models for evaluating creative software; the FACE model, which describes creative acts performed by software in terms of tuples of generative acts, and the IDEA model, which describes how such creative acts can have an impact upon an audience. We show how these models have been inspired both by ideas in the psychology of creativity and by an analysis of acts of human creativity.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We introduce two descriptive models for evaluating creative software; the FACE model, which describes creative acts performed by software in terms of tuples of generative acts, and the IDEA model, which describes how such creative acts can have an impact upon an audience. We show how these models have been inspired both by ideas in the psychology of creativity and by an analysis of acts of human creativity. |
Colton, Simon; Pease, Alison; Charnley, John Computational Creativity Theory: The FACE and IDEA Descriptive Models Inproceedings In: Proceedings of the Second International Conference on Computational Creativity, pp. 90–95, 2011. @inproceedings{colton2011computational, title = {Computational Creativity Theory: The FACE and IDEA Descriptive Models}, author = { Simon Colton and Alison Pease and John Charnley}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/colton_iccc11.pdf}, year = {2011}, date = {2011-01-01}, booktitle = {Proceedings of the Second International Conference on Computational Creativity}, pages = {90--95}, abstract = {We introduce computational creativity theory (CCT) as an analogue in computational creativity research to computational learning theory in machine learning. In its current draft, CCT comprises the FACE descriptive model of creative acts as tuples of generative acts, and the IDEA descriptive model of the impact such creative acts may have. To introduce these, we simplify various assumptions about software development, background material given to software, how creative acts are performed by computer, and how audiences consume the results. We use the two descriptive models to perform two comparisons studies, firstly for mathematical discovery software, and secondly for visual art generating programs. We conclude by discussing possible additions, improvements and refinements to CCT.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We introduce computational creativity theory (CCT) as an analogue in computational creativity research to computational learning theory in machine learning. In its current draft, CCT comprises the FACE descriptive model of creative acts as tuples of generative acts, and the IDEA descriptive model of the impact such creative acts may have. To introduce these, we simplify various assumptions about software development, background material given to software, how creative acts are performed by computer, and how audiences consume the results. We use the two descriptive models to perform two comparisons studies, firstly for mathematical discovery software, and secondly for visual art generating programs. We conclude by discussing possible additions, improvements and refinements to CCT. |
Colton, Simon; de Mantaras, Ram'on L'opez; Stock, Oliviero Computational Creativity: Coming of Age Journal Article In: 2009. @article{colton2009computational, title = {Computational Creativity: Coming of Age}, author = { Simon Colton and Ram'on L'opez de Mantaras and Oliviero Stock}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/colton_aimag09_editorial.pdf}, year = {2009}, date = {2009-01-01}, booktitle = {AI Magazine}, publisher = {AAAI Press}, abstract = {This editorial provides an introduction to current AI research on computationally created artifacts as well as to the papers and topics covered by this special issue on computational creativity.}, keywords = {}, pubstate = {published}, tppubtype = {article} } This editorial provides an introduction to current AI research on computationally created artifacts as well as to the papers and topics covered by this special issue on computational creativity. |
Pease, Alison; Smaill, Alan; Colton, Simon; Lee, John Bridging the Gap Between Argumentation Theory and the Philosophy of Mathematics Journal Article In: Foundations of Science, 14 (1-2), pp. 111–135, 2009. @article{pease2009bridging, title = {Bridging the Gap Between Argumentation Theory and the Philosophy of Mathematics}, author = { Alison Pease and Alan Smaill and Simon Colton and John Lee}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/pease_fos09.pdf}, year = {2009}, date = {2009-01-01}, journal = {Foundations of Science}, volume = {14}, number = {1-2}, pages = {111--135}, publisher = {Springer}, abstract = {We argue that there are mutually beneficial connections to be made between ideas in argumentation theory and the philosophy of mathematics, and that these connections can be suggested via the process of producing computational models of theories in these domains.We discuss Lakatos’s work (1976) in which he championed the informal nature of mathematics, and our computational representation of his theory. In particular, we outline our representation of Cauchy’s proof of Euler’s conjecture, which uses work by Haggith on argumentation structures, and identify connections between these structures and Lakatos’s methods.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We argue that there are mutually beneficial connections to be made between ideas in argumentation theory and the philosophy of mathematics, and that these connections can be suggested via the process of producing computational models of theories in these domains.We discuss Lakatos’s work (1976) in which he championed the informal nature of mathematics, and our computational representation of his theory. In particular, we outline our representation of Cauchy’s proof of Euler’s conjecture, which uses work by Haggith on argumentation structures, and identify connections between these structures and Lakatos’s methods. |
Colton, Simon Seven Catchy Phrases for Computational Creativity Research Inproceedings In: Dagstuhl Seminar Proceedings, Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik 2009. @inproceedings{colton2009seven, title = {Seven Catchy Phrases for Computational Creativity Research}, author = { Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/colton_dagstuhl09.pdf}, year = {2009}, date = {2009-01-01}, booktitle = {Dagstuhl Seminar Proceedings}, organization = {Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik}, abstract = {I understand that simulating creative processes by computer can enhance our understanding of creativity in humans. I also understand that there is more need than ever for software to help people to be more efficient in creative jobs. And I know that computational creativity research can be of great value in both these areas. However, Iʼm really only interested in the intellectual challenge of enabling nuts and bolts machines - bits and bytes computers - to create artefacts of real cultural value to society. Such behaviour used to be thought of as divinely inspired, no less than a gift from the Gods. This is why it is a worthy challenge for me to bet my career against. Building a truly computationally creative machine is as much a societal as a technical challenge, and it will need computational creativity researchers to come together in consensus about certain aspects of their field. To this end, I have written here seven phrases around which we could rally (or about which we could debate - which may also be healthy). I present the ideas from which the phrases emerged with little argumentation, in the tradition of a position paper. They are drawn from twelve years of immersion in the field of computational creativity during which Iʼve written an automated mathematician (HR) and an automated painter (The Painting Fool), and they have created artefacts which I believe are of real value to society.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } I understand that simulating creative processes by computer can enhance our understanding of creativity in humans. I also understand that there is more need than ever for software to help people to be more efficient in creative jobs. And I know that computational creativity research can be of great value in both these areas. However, Iʼm really only interested in the intellectual challenge of enabling nuts and bolts machines - bits and bytes computers - to create artefacts of real cultural value to society. Such behaviour used to be thought of as divinely inspired, no less than a gift from the Gods. This is why it is a worthy challenge for me to bet my career against. Building a truly computationally creative machine is as much a societal as a technical challenge, and it will need computational creativity researchers to come together in consensus about certain aspects of their field. To this end, I have written here seven phrases around which we could rally (or about which we could debate - which may also be healthy). I present the ideas from which the phrases emerged with little argumentation, in the tradition of a position paper. They are drawn from twelve years of immersion in the field of computational creativity during which Iʼve written an automated mathematician (HR) and an automated painter (The Painting Fool), and they have created artefacts which I believe are of real value to society. |
Colton, Simon Creativity Versus the Perception of Creativity in Computational Systems Inproceedings In: AAAI Spring Symposium: Creative Intelligent Systems, pp. 14–20, 2008. @inproceedings{colton2008creativity, title = {Creativity Versus the Perception of Creativity in Computational Systems}, author = { Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/colton_aaai08symp.pdf}, year = {2008}, date = {2008-01-01}, booktitle = {AAAI Spring Symposium: Creative Intelligent Systems}, pages = {14--20}, abstract = {We add to the discussion of how to assess the creativity of programs which generate artefacts such as poems, theorems, paintings, melodies, etc. To do so, we first review some existing frameworks for assessing artefact generation programs. Then, drawing on our experience of building both a mathematical discovery system and an automated painter, we argue that it is not appropriate to base the assessment of a system on its output alone, and that the way it produces artefacts also needs to be taken into account. We suggest a simple framework within which the behaviour of a program can be categorised and described which may add to the perception of creativity in the system.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We add to the discussion of how to assess the creativity of programs which generate artefacts such as poems, theorems, paintings, melodies, etc. To do so, we first review some existing frameworks for assessing artefact generation programs. Then, drawing on our experience of building both a mathematical discovery system and an automated painter, we argue that it is not appropriate to base the assessment of a system on its output alone, and that the way it produces artefacts also needs to be taken into account. We suggest a simple framework within which the behaviour of a program can be categorised and described which may add to the perception of creativity in the system. |
Colton, Simon Creative Logic Programming Inproceedings In: Proceedings of the 3rd. IJCAI Workshop on Creative Systems, pp. 77, 2003. @inproceedings{colton2003creative, title = {Creative Logic Programming}, author = { Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/colton_ijcai03_creativity.pdf}, year = {2003}, date = {2003-01-01}, booktitle = {Proceedings of the 3rd. IJCAI Workshop on Creative Systems}, pages = {77}, abstract = {The standard machine learning paradigm is to find something that users know they are looking for, with the discovered artefact defined in terms of given background knowledge. We propose to extend this to automating the task of finding novel and interesting information – also based on the background knowledge – that the users do not knowthey are looking for. We sketch various methods for introducing knowledge to a knowledge base which are inspired by notions from the study of creativity. We attempt to determine situations where it is possible to project certain words from the creativity literature onto an agent (human, machine or otherwise), as it undertakes the task of adding information to a knowledge base. This study has enabled us to suggest a road-map for the development of creative logic programming systems, which extends inductive logic programming approaches to discovery tasks.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } The standard machine learning paradigm is to find something that users know they are looking for, with the discovered artefact defined in terms of given background knowledge. We propose to extend this to automating the task of finding novel and interesting information – also based on the background knowledge – that the users do not knowthey are looking for. We sketch various methods for introducing knowledge to a knowledge base which are inspired by notions from the study of creativity. We attempt to determine situations where it is possible to project certain words from the creativity literature onto an agent (human, machine or otherwise), as it undertakes the task of adding information to a knowledge base. This study has enabled us to suggest a road-map for the development of creative logic programming systems, which extends inductive logic programming approaches to discovery tasks. |
Pease, Alison; Colton, Simon; Smaill, Alan; Lee, John Lakatos and Machine Creativity Inproceedings In: Second Workshop on Creative Systems, Approaches to Creativity in Artificial Intelligence and Cognitive Science at the European Conference on Artificial Intelligence (ECAI 2002), 2002. @inproceedings{pease2002lakatos, title = {Lakatos and Machine Creativity}, author = { Alison Pease and Simon Colton and Alan Smaill and John Lee}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/pease_ecai02workshop.pdf}, year = {2002}, date = {2002-01-01}, booktitle = {Second Workshop on Creative Systems, Approaches to Creativity in Artificial Intelligence and Cognitive Science at the European Conference on Artificial Intelligence (ECAI 2002)}, abstract = {We argue that Lakatos’ work on the history and philosophy of mathematics is of key relevance to machine creativity as it suggests ways in which to explore and transform concept spaces, rerepresent knowledge and change evaluation criteria. We describe approaches to implementing methods which Lakatos identifies, including our own approach, which extends Colton’s HR and has enabled us to automatically generate mathematical conjectures, concepts and examples which were previously impossible in HR - including Goldbach’s conjecture. The methods are of general importance as they can be applied to many domains - we describe their theoretical application to game plans, two-dimensional geometry, moral philosophy, philosophy of mind, political argument and meta-level reasoning.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We argue that Lakatos’ work on the history and philosophy of mathematics is of key relevance to machine creativity as it suggests ways in which to explore and transform concept spaces, rerepresent knowledge and change evaluation criteria. We describe approaches to implementing methods which Lakatos identifies, including our own approach, which extends Colton’s HR and has enabled us to automatically generate mathematical conjectures, concepts and examples which were previously impossible in HR - including Goldbach’s conjecture. The methods are of general importance as they can be applied to many domains - we describe their theoretical application to game plans, two-dimensional geometry, moral philosophy, philosophy of mind, political argument and meta-level reasoning. |
Colton, Simon; Pease, Alison; Ritchie, Graeme The Effect of Input Knowledge on Creativity Inproceedings In: Proceedings of the ICCBR'01 Workshop on Creative Systems, 2001. @inproceedings{colton2001effect, title = {The Effect of Input Knowledge on Creativity}, author = { Simon Colton and Alison Pease and Graeme Ritchie}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/colton_iccbr01.pdf}, year = {2001}, date = {2001-01-01}, booktitle = {Proceedings of the ICCBR'01 Workshop on Creative Systems}, abstract = {Recently, many programs have been written to perform tasks which are usually regarded as requiring creativity in humans. We can derive some commonalities between these programs in order to build further creative programs. Key to this is the derivation of certain measures which assess how creative a program is. Starting from recent proposals by Ritchie, we define possible measures which describe the extent to which a program produces novel output. We discuss how this relates to the creativity of the program.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Recently, many programs have been written to perform tasks which are usually regarded as requiring creativity in humans. We can derive some commonalities between these programs in order to build further creative programs. Key to this is the derivation of certain measures which assess how creative a program is. Starting from recent proposals by Ritchie, we define possible measures which describe the extent to which a program produces novel output. We discuss how this relates to the creativity of the program. |
Pease, Alison; Winterstein, Daniel; Colton, Simon Evaluating Machine Creativity Inproceedings In: Workshop on Creative Systems, 4th International Conference on Case Based Reasoning, pp. 129–137, 2001. @inproceedings{pease2001evaluating, title = {Evaluating Machine Creativity}, author = { Alison Pease and Daniel Winterstein and Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/pease_iccbr01.pdf}, year = {2001}, date = {2001-01-01}, booktitle = {Workshop on Creative Systems, 4th International Conference on Case Based Reasoning}, pages = {129--137}, abstract = {We consider relevant aspects of evaluating creativity to be input, output and the process by which the output is achieved. These issues may be further divided, and we highlight associated justifications and controversies. Appropriate methods of measuring these aspects are suggested and discussed.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We consider relevant aspects of evaluating creativity to be input, output and the process by which the output is achieved. These issues may be further divided, and we highlight associated justifications and controversies. Appropriate methods of measuring these aspects are suggested and discussed. |
Colton, Simon; Steel, Graham Artificial Intelligence and Scientific Creativity Journal Article In: Artificial Intelligence and the Study of Behaviour Quarterly, 102 , 1999. @article{colton1999artificial, title = {Artificial Intelligence and Scientific Creativity}, author = { Simon Colton and Graham Steel}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/colton_aisbq99.pdf}, year = {1999}, date = {1999-01-01}, journal = {Artificial Intelligence and the Study of Behaviour Quarterly}, volume = {102}, keywords = {}, pubstate = {published}, tppubtype = {article} } |
Uncategorised Publications
AAAI Addressing Questions of Computational Creativity AISB Applications of ATF and Combined Reasoning to Other Domains Applications to Discovery Tasks in Pure Mathematics ARW Automating Graphic Design and Visual Arts Processes Automating Tasks in Creative Language CADE CADGame Calculemus CreativeEvolution DEFCON ECAI Empowerment EvoMusArt Featured Games ICCC IJCAI ILP Improvement of AI Techniques Intrinsic Motivation Issues in Automated Game Design Issues in Automated Game Design MKM More Sophisticated Mathematical Theory Formation Models SelectedGow The Combination of Reasoning Systems The Development of Automated Theory Formation
Colton, Simon Automated Theory Formation in Pure Mathematics PhD Thesis 2001. @phdthesis{colton2001d, title = {Automated Theory Formation in Pure Mathematics}, author = {Simon Colton}, url = {http://ccg.doc.gold.ac.uk/wp-content/uploads/2016/10/colton_phd01.pdf}, year = {2001}, date = {2001-01-01}, publisher = {Springer}, institution = {University of Edinburgh}, keywords = {Thesis}, pubstate = {published}, tppubtype = {phdthesis} } |
Colton, Simon Involving Computers with Mathematics, Minimum Distances of Quadratic Residue Codes Masters Thesis 1996. @mastersthesis{colton96, title = {Involving Computers with Mathematics, Minimum Distances of Quadratic Residue Codes}, author = {Simon Colton}, url = {http://ccg.doc.gold.ac.uk/papers/colton_msc96.pdf}, year = {1996}, date = {1996-01-01}, institution = {University of Liverpool}, keywords = {Thesis}, pubstate = {published}, tppubtype = {mastersthesis} } |
Research Collaborators
I’ve been very fortunate to work with a number of very good researchers, including the following co-authors (in surname alphabetical order):
- Eduardo Alonso
- Robin Baumgarten
- Cameron Browne
- Alan Bundy
- Paul Cairns
- Emilios Cambouropoulos
- Flaminia Cavallo
- Bojan Cestnik
- John Charnley
- Stephen Clark
- James Clewitt
- Michael Cook
- Joe Corneli
- Peter Cowling
- Stephen Cresswell
- Louise Dennis
- Lydon Drake
- Jad El-Hage
- Colin Farquhar
- Andreas Franke
- Alan Frisch
- Pablo Gervas
- Yi Gao
- Mark Granroth-Wilding
- Jacob Goodwin
- Ian Gouldstone
- Jeremy Gow
- Gudmund Grov
- Christian Guckelsberger
- Marcus Guhe
- Jakob Halskov
- Rose Hepworth
- Ferdinand Hoermann
- Andrew Howlett
- Marc Hull
- Sophie Huczynska
- Andrew Ireland
- Ning Jiang
- Anna Krzeczkowska
- Kai-Uwe Kuhnberger
- Daniel Kudenko
- Oliver Kutz
- Nada Lavrac
- John Lee
- Andrew Lim
- Chong-U Lim
- Maria Teresa Llano
- Ramon Lopez de Mantaras
- Simon Lucas
- Derek Magee
- Andrew Martin
- Roy McCasland
- Andreas Meier
- Ian Miguel
- Paul Miller
- Joanna Misztal
- Luc Moreau
- Mark Morris
- Stephen Muggleton
- Maria Nika
- Ramon Otero
- Maja Pantic
- Diego Perez
- Blanca Perez-Ferrer
- Matic Perovsek
- Edward Powley
- Azalea Raad
- Ramin Ramezani
- Daniel Ramirez-Cano
- Kate Reed
- Graeme Ritchie
- Philipp Rohlfshagen
- Stefan Rueger
- Spyridon Samothrakis
- Paulo Santos
- Marco Schorlemmer
- Michael Schroeder
- Murray Shanahan
- Rosie Shepperd
- Alan Smaill
- Volker Sorge
- Kostas Stathis
- Graham Steel
- Oliviero Stock
- Geoff Sutcliffe
- Stephen Tavener
- Pedro Torres
- Tanja Urbancic
- Michel Valstar
- Tony Veale
- Dan Ventura
- Toby Walsh
- Daniel Wagner
- Daniel Whitehouse
- Geraint Wiggins
- Dan Winterstein
- Georgios Yannakakis
- Jurgen Zimmer
- Martin Znidarsic