Employing Theory Formation to Guide Proof Planning

The invention of suitable concepts to characterise mathematical structures is one of the most challenging tasks for both human mathematicians and automated theorem provers alike. We present an approach where automatic concept formation is used to guide nonisomorphism proofs in the residue class domain. The main idea behind the proof is to automatically identify discriminants for two given structures to show that they are not isomorphic. Suitable discriminants are generated by a theory formation system; the overall proof is constructed by a proof planner with the additional support of traditional automated theorem provers and a computer algebra system.

[1]  A. Meier,et al.  Exploring properties of residue classes , 2001 .

[2]  David A. Redfern,et al.  The Maple Handbook: Maple V Release 3 , 1995 .

[3]  Alan Bundy,et al.  The Use of Classification in Automated Mathematical Concept Formation , 1997 .

[4]  Erica Melis,et al.  Proof planning with multiple strategies , 2000, Artif. Intell..

[5]  Volker Sorge,et al.  Classifying Isomorphic Residue Classes , 2001, EUROCAST.

[6]  Alan Bundy,et al.  The Use of Explicit Plans to Guide Inductive Proofs , 1988, CADE.

[7]  Luís Moniz Pereira,et al.  Proceedings of the First International Conference on Computational Logic , 2000 .

[8]  Andreas Meier.  System Description: TRAMP: Transformation of Machine-Found Proofs into ND-Proofs at the Assertion Level , 2000, CADE.

[9]  Volker Sorge,et al.  ΩMEGA : Towards a mathematical assistant , 1997 .

[10]  Toby Walsh,et al.  Automatic Identification of Mathematical Concepts , 2000, ICML.

[11]  Volker Sorge,et al.  Omega: Towards a Mathematical Assistant , 1997, CADE.

[12]  Toby Walsh,et al.  On the notion of interestingness in automated mathematical discovery , 2000, Int. J. Hum. Comput. Stud..

[13]  Volker Sorge,et al.  Comparing Approaches to the Exploration of the Domain of Residue Classes , 2002, J. Symb. Comput..

[14]  Simon Colton,et al.  An Application-based Comparison of Automated Theory Formation and Inductive Logic Programming , 2000, Electron. Trans. Artif. Intell..

[15]  MSc PhD Simon Colton BSc.  Automated Theory Formation in Pure Mathematics , 2002, Distinguished Dissertations.

[16]  Hantao Zhang,et al.  SEM: a System for Enumerating Models , 1995, IJCAI.

[17]  Erica Melis,et al.  Knowledge-Based Proof Planning , 1999, Artif. Intell..