Scheme-based Theorem Discovery and Concept Invention: Rewriting theory-exploration - Softcover

Montaño Rivas, Omar

Softcover

ISBN 10: 3659886203 ISBN 13: 9783659886201

Publisher: LAP LAMBERT Academic Publishing, 2016

Synopsis

This book describes an approach to automatically invent/explore new mathematical theories, with the goal of producing results comparable to those produced by humans, as represented, for example, in the libraries of proof assistants. The approach described is based on schemes, which are formulae in higher-order logic. It shows that it is possible to automate the instantiation process of schemes to generate conjectures and definitions. It also shows how the new definitions and the lemmata discovered during the exploration of a theory can be used, not only to help with the proof obligations during the exploration, but also to reduce redundancies inherent in most theory-formation systems. It describes how to exploit associative-commutative (AC) operators using ordered rewriting to avoid AC variations of the same instantiation. All ideas contained in this book are implemented in an automated tool, called IsaScheme, which employs Knuth-Bendix completion and recent automatic inductive proof methods. This systematic and comprehensive introduction to the scheme-based theory exploration will be welcome by researchers and graduate students alike.

About this title

About the Author

Omar Montaño Rivas is a Professor of Automated Reasoning at the Universidad Politécnica de San Luis Potosí. His research interests focus on the exploration of mathematical theories and the automation of mathematical reasoning with applications to formal methods. He is the author of a number of publications and has held several research grants.

Edition details

• Publisher: LAP LAMBERT Academic Publishing
• Publication date: 2016
• Language: English
• ISBN 10: 3659886203
• ISBN 13: 9783659886201
• Binding: Paperback
• Number of pages: 152