For my full publication record, please see my CV


1. The Development of Automated Theory Formation
2. More Sophisticated Mathematical Theory Formation Models
3. The Combination of Reasoning Systems
4. Applications to Discovery Tasks in Pure Mathematics
5. Applications of ATF and Combined Reasoning to Other Domains
6. Improvement of AI Techniques
7. Automating Graphic Design and Visual Arts Processes
8. Issues in Automated Game Design
9. Automating Tasks in Creative Language
10. Addressing Questions of Computational Creativity

Research Collaborators


I am an Artificial Intelligence (AI) researcher. I aim to stretch the boundaries of the intelligent tasks that computers can undertake successfully. I am particularly interested in questions of computational creativity, where the aim is to enable software to take on creative responsibility in scientific and artistic projects. I lead the computational creativity group, and much of the research described here has been undertaken in conjunction with group members, in addition to colleagues from various Universities and companies in the UK and around the world. For details of research undertaken in the computational creativity group, please visit the webpages here:

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.

1. 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.

2. 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:

3. 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:

4. 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:

5. 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:

6. 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:

7. 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:

8. 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.

9. 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.

10. 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:

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