Abstract
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 R1 and similar versions are also true in R2, 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 R1 as a guide in automatically producing a proof-plan of the Heine-Borel theorem in R2 by analogy-driven proof-plan construction.
This work was supported in part by the HC&M grant CHBICT930806 and by a research grant of the Deutsche Forschungsgemeinschaft.
On leave from University Saarbrücken, Germany
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Melis, E. (1995). Theorem proving by analogy — A compelling example. In: Pinto-Ferreira, C., Mamede, N.J. (eds) Progress in Artificial Intelligence. EPIA 1995. Lecture Notes in Computer Science, vol 990. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60428-6_22
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DOI: https://doi.org/10.1007/3-540-60428-6_22
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