Abstract

This paper analyzes how mathematicians prove theorems. The analysis is based upon several empirical sources such as reports of mathematicians and mathematical proofs by analogy. In order to combine the strength of traditional automated theorem provers with human-like capabilities, the questions arise: Which problem solving strategies are appropriate? Which representations have to be employed? As a result of our analysis, the following reasoning strategies are recognized: proof planning with partially instantiated methods, structuring of proofs, the transfer of subproofs and of reformulated subproofs. We discuss the representation of a component of these reasoning strategies, as well as its properties. We find some mechanisms needed for theorem proving by analogy, that are not provided by previous approaches to analogy. This leads us to a computational representation of new components and procedures for automated theorem proving systems.

Citations