http://www.springer.com/computer/ai/book/978-1-85233-609-7
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. Content Level » Research Keywords » Artificial Intelligence - Automated Theory - Computational Creativity - Machine Learning - Pure Mathematics Related subjects » Artificial Intelligence - Theoretical Computer Science TABLE OF CONTENTS Introduction.- Literature Survey.- Mathematical Theories.- Design Considerations.- Background Knowledge.- Inventing Concepts.- Making Conjectures.- Settling Conjectures.- Assessing Concepts.- Assessing Conjectures.- An Evaluation of HR's Theories.- The Application of HR to Discovery Tasks.- Related Work.- Further Work.- Conclusions.- Appendix A: User Manual for HR 1.11.- Appendix B: Example Sessions.- Appendix C: Number Theory Results. -- You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
