AI-Techniques in Proof Planning

Proof planning is an application of Artiicial Intelligence (AI)-planning in mathematical domains for theorem proving. The paper presents a knowledge-based proof planning approach that is implemented in the OMEGA proof planner. It evaluates control-rules in order to restrict the otherwise intractable search spaces and combines proof planning with domain-speciic constraint solving. Several AI-techniques contribute to the successful planning of proofs that were beyond the capabilities of theorem provers and proof planners previously.

[1]  Larry M. Hines.  Str+ve ⊆ : the Str+ve-based subset prover , 1990 .

[2]  Alan Bundy,et al.  A Science of Reasoning , 1991, Computational Logic - Essays in Honor of Alan Robinson.

[3]  Erica Melis,et al.  A Model of Analogy-Driven Proof-Plan Construction , 1995, IJCAI.

[4]  John R. Anderson.  Acquisition of Proof Skills in Geometry , 1983 .

[5]  William McCune,et al.  OTTER 1.0 Users' Guide , 1990 .

[6]  Roland H. C. Yap,et al.  The CLP( R ) language and system , 1992, TOPL.

[7]  Robert S. Boyer,et al.  Computer Proofs of Limit Theorems , 1971, IJCAI.

[8]  Richard Fikes,et al.  STRIPS: A New Approach to the Application of Theorem Proving to Problem Solving , 1971, IJCAI.

[9]  Frieder Stolzenburg,et al.  Membership-Constraints and Complexity in Logic Programming with Sets , 1996, FroCoS.

[10]  John R. Anderson,et al.  Abstract Planning and Perceptual Chunks: Elements of Expertise in Geometry , 1990, Cogn. Sci..

[11]  Robin Milner,et al.  Edinburgh lcf: a mechanized logic of computation , 1978 .

[12]  Pascal Van Hentenryck.  Constraint satisfaction in logic programming , 1989, Logic programming.

[13]  Toby Walsh,et al.  Coloured Rippling: An Extension of a Theorem Proving Heuristic , 1994, ECAI.

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

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

[16]  Oren Etzioni,et al.  PRODIGY4.0: The Manual and Tutorial , 1992 .

[17]  Erica Melis,et al.  Progress in Proof Planning:Planning Limit Theorems Automatically , 1999 .

[18]  Wolfgang Bibel,et al.  Let's Plan It Deductively! , 1997, IJCAI.