Distinguished Dissertations

By: Simon Colton

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Hardcover | 9 August 2002

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404 Pages

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In recent years, Artificial Intelligence researchers have largely focused their efforts on solving specific problems, with less emphasis on 'the big picture' - automating large scale tasks which require human-level intelligence to undertake. The subject of this book, automated theory formation in mathematics, is such a large scale task. Automated theory formation requires the invention of new concepts, the calculating of examples, the making of conjectures and the proving of theorems. This book, representing four years of PhD work by Dr. Simon Colton demonstrates how theory formation can be automated. Building on over 20 years of research into constructing an automated mathematician carried out in Professor Alan Bundy's mathematical reasoning group in Edinburgh, Dr. Colton has implemented the HR system as a solution to the problem of forming theories by computer. HR uses various pieces of mathematical software, including automated theorem provers, model generators and databases, to build a theory from the bare minimum of information - the axioms of a domain. The main application of this work has been mathematical discovery, and HR has had many successes. In particular, it has invented 20 new types of number of sufficient interest to be accepted into the Encyclopaedia of Integer Sequences, a repository of over 60,000 sequences contributed by many (human) mathematicians.

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Non-Fiction Computing & I.T.Computer Science Artificial Intelligence Expert Systems & Knowledge-Based Systems Mathematics Mathematical Foundation Mathematical Logic Databases Data Capture & Analysis Gardening Mathematical Theory of Computation

Applied Mathematics

Preface
Acknowledgements
Introduction	p. 1
Literature Survey	p. 9
Mathematical Theories	p. 29
Design Considerations	p. 45
Background Knowledge	p. 59
Inventing Concepts	p. 69
Making Conjectures	p. 101
Settling Conjectures	p. 121
Assessing Concepts	p. 141
Assessing Conjectures	p. 165
An Evaluation of HR's Theories	p. 181
The Application of HR to Discovery Tasks	p. 225
Related Work	p. 247
Further Work	p. 281
Conclusions	p. 295
User Manual for HR1.11	p. 303
App. B: Example Sessions	p. 319
Number Theory Results	p. 343
Glossary	p. 359
Bibliography	p. 365
Index	p. 375
Table of Contents provided by Blackwell. All Rights Reserved.

Distinguished Dissertations

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