Matrix-Based Inductive Theorem Proving

We present an approach to inductive theorem proving that integrates rippling-based rewriting into matrix-based logical proof search. The selection of appropriate connections in a matrix proof is guided by the symmetries between induction hypothesis and induction conclusion while unification is extended by a rippling/reverse-rippling heuristic. Conditional substitutions are generated whenever a uniform substitution is impossible. We illustrate the combined approach by discussing several inductive proofs for the integer square root problem.

[1]  Frank van Harmelen,et al.  Extensions to the Rippling-Out Tactic for Guiding Inductive Proofs , 1990, CADE.

[2]  Amy P. Felty,et al.  The Coq proof assistant user's guide : version 5.6 , 1990 .

[3]  Alan Bundy,et al.  Automated Deduction — CADE-12 , 1994, Lecture Notes in Computer Science.

[4]  Christoph Kreitz,et al.  T-String Unification: Unifying Prefixes in Non-classical Proof Methods , 1996, TABLEAUX.

[5]  William McCune,et al.  Automated Deduction—CADE-14 , 1997, Lecture Notes in Computer Science.

[6]  Christoph Kreitz,et al.  Automating Inductive Specification Proofs , 1999, Fundam. Informaticae.

[7]  Wolfgang Bibel,et al.  A Multi-level Approach to Program Synthesis , 1997, LOPSTR.

[8]  Dieter Hutter,et al.  INKA: The Next Generation , 1996, CADE.

[9]  M. A. McRobbie,et al.  Automated Deduction — Cade-13 , 1996, Lecture Notes in Computer Science.

[10]  Christoph Kreitz,et al.  Connection-based Theorem Proving in Classical and Non-classical Logics , 1999, J. Univers. Comput. Sci..

[11]  Wolfgang Bibel,et al.  On Matrices with Connections , 1981, JACM.

[12]  Jane Thurmann Hesketh,et al.  Using middle-out reasoning to guide inductive theorem proving , 1992 .

[13]  Christoph Kreitz,et al.  Converting Non-Classical Matrix Proofs into Sequent-Style Systems , 1996, CADE.

[14]  Christoph Kreitz,et al.  Guiding Program Development Systems by a Connection Based Proof Strategy , 1995, LOPSTR.

[15]  Susanne Biundo-Stephan.  Automated Synthesis of Recursive Algorithms as a Theorem Proving Tool , 1988, ECAI.

[16]  Rance Cleaveland,et al.  Implementing mathematics with the Nuprl proof development system , 1986 .

[17]  Dieter Hutter,et al.  Synthesis of Induction Orderings for Existence Proofs , 1994, CADE.

[18]  Christoph Kreitz,et al.  A Uniform Proof Procedure for Classical and Non-Classical Logics , 1996, KI.

[19]  Tanel Tammet,et al.  A Resolution Theorem Prover for Intuitonistic Logic , 1996, CADE.

[20]  Christoph Kreitz,et al.  Connection-Based Proof Construction in Linear Logic , 1997, CADE.

[21]  Alan Robinson,et al.  Handbook of automated reasoning , 2001 .

[22]  Alan Bundy,et al.  Logic Program Synthesis via Proof Planning , 1992, LOPSTR.

[23]  Frank van Harmelen,et al.  Rippling: A Heuristic for Guiding Inductive Proofs , 1993, Artif. Intell..

[24]  Christoph Weidenbach,et al.  SPASS: Combining Superposition, Sorts and Splitting , 2000 .

[25]  Lawrence J. Henschen,et al.  What Is Automated Theorem Proving? , 1985, J. Autom. Reason..

[26]  Robert L. Constable,et al.  An Introduction to the PL/CV2 Programming Logic , 1982, Lecture Notes in Computer Science.

[27]  Jens Otten,et al.  A Connection Based Proof Method for Intuitionistic Logic , 1995, TABLEAUX.

[28]  Lincoln A. Wallen,et al.  Automated deduction in nonclassical logics , 1990 .

[29]  Christoph Kreitz,et al.  On Transforming Intuitionistic Matrix Proofs into Standard-Sequent Proofs , 1995, TABLEAUX.