Some Aspects of Analogy in Mathematical Reasoning

  • An important research problem is the incorporation of "declarative" knowledge into an automated theorem prover that can be utilized in the search for a proof. An interesting pro-posal in this direction is Alan Bundy's approach of using explicit proof plans that encapsulatethe general form of a proof and is instantiated into a particular proof for the case at hand. Wegive some examples that show how a "declarative" highlevel description of a proof can be usedto find proofs of apparently "similiar" theorems by analogy. This "analogical" information isused to select the appropriate axioms from the database so that the theorem can be proved.This information is also used to adjust some options of a resolution theorem prover. In orderto get a powerful tool it is necessary to develop an epistemologically appropriate language todescribe proofs, for which a large set of examples should be used as a testbed. We presentsome ideas in this direction.

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Metadaten
Author:Manfred Kerber
URN (permanent link):urn:nbn:de:hbz:386-kluedo-3249
Serie (Series number):SEKI Report (89,12)
Document Type:Article
Language of publication:English
Year of Completion:1999
Year of Publication:1999
Publishing Institute:Technische Universität Kaiserslautern
Tag:abstract description; analogy ; proof plans ; theorem proving
Faculties / Organisational entities:Fachbereich Informatik
DDC-Cassification:004 Datenverarbeitung; Informatik

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