@INPROCEEDINGS{Melis93changeof, author = {Erica Melis}, title = {Change of Representation in Theorem Proving by Analogy}, booktitle = {}, year = {1993} }

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Abstract

Constructing an analogy between a known and already proven theorem (the base case) and another yet to be proven theorem (the target case) often amounts to finding the appropriate representation at which the base and the target are similar. This is a well-known fact in mathematics, and it was corroborated by our empirical study of a mathematical textbook, which showed that a reformulation of the representation of a theorem and its proof is indeed more often than not a necessary prerequisite for an analogical inference. Thus machine supported reformulation becomes an important component of automated analogy-driven theorem proving too. The reformulation component proposed in this paper is embedded into a proof plan methodology based on methods and meta-methods, where the latter are used to change and appropriately adapt the methods. A theorem and its proof are both represented as a method and then reformulated by the set of metamethods presented in this paper. Our approach supports analog...