Failure Reasoning in Multiple-Strategy Proof Planning

Monitoring a solution process and applying the right action at the right moment are at the heart of intelligent problem solving by humans. This includes the analysis of failure events and the development of “recommendations” to overcome typical failures.In this article, we present how meta-reasoning on failures is used in multiple-strategy proof planning with the Multi system. Multi allows for a flexible traversal of the search space and a flexible construction of the proof plan guided by mathematically motivated heuristics. Because of the flexible control in Multi failures can be exploited to guide subsequent proof plan manipulations and refinements. The failure reasoning cannot only ease the derivation of a solution proof plan but is required for some problems to find a solution at all.

[1]  Ian Green,et al.  System description : Proof planning in higher-order logic with λ Clam , 1998 .

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

[3]  Edmund H. Durfee,et al.  Incremental Planning to Control a Blackboard-based Problem Solver , 1986, AAAI.

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

[5]  Bevan K. Youse,et al.  Introduction to real analysis , 1972 .

[6]  Erica Melis,et al.  Constraint Solving for Proof Planning , 2004, Journal of Automated Reasoning.

[7]  Alan H. Schoenfeld,et al.  Mathematical Problem Solving , 1985 .

[8]  Alan Bundy.  A Critique of Proof Planning , 2002, Computational Logic: Logic Programming and Beyond.

[9]  Matthew L. Ginsberg,et al.  Dynamic Backtracking , 1993, J. Artif. Intell. Res..

[10]  Victor R. Lesser,et al.  Unifying Data-Directed and Goal-Directed Control: An Example and Experiments , 1982, AAAI.

[11]  Volker Sorge.  Non-Trivial Symbolic Computations in Proof Planning , 2000, FroCoS.

[12]  W. W. Bledsoe,et al.  Challenge problems in elementary calculus , 1990, Journal of Automated Reasoning.

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

[14]  Andrew Ireland,et al.  Productive use of failure in inductive proof , 1996, Journal of Automated Reasoning.

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

[16]  Andrew Ireland,et al.  The Use of Planning Critics in Mechanizing Inductive Proofs , 1992, LPAR.

[17]  Volker Sorge,et al.  Proof Development with OMEGA , 2002, CADE.

[18]  Ian Green,et al.  System Description: Proof Planning in Higher-Order Logic with Lambda-Clam , 1998, CADE.