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Analogy Makes Proofs Feasible
(1999)
- Many mathematical proofs are hard to generate forhumans and even harder for automated theoremprovers. Classical techniques of automated theoremproving involve the application of basic rules, of built-in special procedures, or of tactics. Melis (Melis 1993)introduced a new method for analogical reasoning inautomated theorem proving. In this paper we showhow the derivational analogy replay method is relatedand extended to encompass analogy-driven proof planconstruction. The method is evaluated by showing theproof plan generation of the Pumping Lemma for con-text free languages derived by analogy with the proofplan of the Pumping Lemma for regular languages.This is an impressive evaluation test for the analogicalreasoning method applied to automated theorem prov-ing, as the automated proof of this Pumping Lemmais beyond the capabilities of any of the current auto-mated theorem provers.
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Case-Based Reasoning Applied to Planning
(1999)
- Planning means constructing a course of actions to achieve a specified set of goals when starting from an initial situation. For example, determining a sequence of actions (a plan) for transporting goods from an initial location to some destination is a typical planning problem in the transportation domain. Many planning problems are of practical interest.
