Computational approaches to analogical reasoning: a comparative analysis
Artificial Intelligence
Explanation-based learning: a survey of programs and perspectives
ACM Computing Surveys (CSUR)
Artificial Intelligence
Handbook of logic in artificial intelligence and logic programming
Patching Proofs for Reuse (Extended Abstract)
ECML '95 Proceedings of the 8th European Conference on Machine Learning
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Analogy in Inductive Theorem Proving
Journal of Automated Reasoning
Semantic Generalizations for Proving and Disproving Conjectures by Analogy
Journal of Automated Reasoning
Flexibly Interleaving Processes
ICCBR '99 Proceedings of the Third International Conference on Case-Based Reasoning and Development
Analogy and abduction in automated deduction
IJCAI'97 Proceedings of the 15th international joint conference on Artifical intelligence - Volume 1
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We investigate the improvement of therom provers by reusing previously computed proofs. A proof of a conjecture is generalized by replacing function symbols with function variables. This yields a schematic proof of a schematic conjecture which is instantiated subsequently for obtaining proofs of new, similar conjectures. Our reuse method requires solving so-called free function variables, i.e. variables which cannot be instantiated by matching the schematic conjecture with a new conjecture. We develop an algorithm for solving free function variables by combining the techniques of symbolic evaluation and second-order matching. Heuristics for controlling the algorithm are presented, and several examples demonstrate their usefulness. We also show how our reuse proposal supports the discovery of useful lemmata.