Theorem Proving by Analogy - A Compelling Example
نویسنده
چکیده
This paper shows how a new approach to theorem proving by analogy is applicable to real maths problems. This approach works at the level of proof-plans and employs reformulation that goes beyond symbol mapping. The Heine-Borel theorem is a widely known result in mathematics. It is usually stated in R 1 and similar versions are also true in R 2 , in topology, and metric spaces. Its analogical transfer was proposed as a challenge example and could not be solved by previous approaches to theorem proving by analogy. We use a proof-plan of the Heine-Borel theorem in R 1 as a guide in automatically producing a proof-plan of the Heine-Borel theorem in R 2 by analogy-driven proof-plan construction.
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