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Automated Theory Formation in Pure Mathematics

  • Book
  • © 2002

Overview

Authors:
  1. Simon Colton

    1. University of Edinburgh, Edinburgh, UK

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  • Demonstrates how theory formation

Part of the book series: Distinguished Dissertations (DISTDISS)

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Table of contents (15 chapters)

  1. Front Matter

    Pages iii-xvi
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  2. Introduction

    • Simon Colton
    Pages 1-8

  3. Literature Survey

    • Simon Colton
    Pages 9-28

  4. Mathematical Theories

    • Simon Colton
    Pages 29-43

  5. Design Considerations

    • Simon Colton
    Pages 45-58

  6. Background Knowledge

    • Simon Colton
    Pages 59-67

  7. Inventing Concepts

    • Simon Colton
    Pages 69-100

  8. Making Conjectures

    • Simon Colton
    Pages 101-120

  9. Settling Conjectures

    • Simon Colton
    Pages 121-140

  10. Assessing Concepts

    • Simon Colton
    Pages 141-163

  11. Assessing Conjectures

    • Simon Colton
    Pages 165-179

  12. An Evaluation of HR’s Theories

    • Simon Colton
    Pages 181-223

  13. The Application of HR to Discovery Tasks

    • Simon Colton
    Pages 225-245

  14. Related Work

    • Simon Colton
    Pages 247-279

  15. Further Work

    • Simon Colton
    Pages 281-293

  16. Conclusions

    • Simon Colton
    Pages 295-301

  17. Back Matter

    Pages 303-380
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Keywords

About this book

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.

Authors and Affiliations

  • University of Edinburgh, Edinburgh, UK

    Simon Colton

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