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On Explicit Re ection in Theorem Proving and Formal Veri cation

Summary: On Explicit Re ection in Theorem Proving
and Formal Veri cation
Sergei N. Artemov ?
Department of Computer Science
Cornell University,
Ithaca, NY 14853, U.S.A.
Abstract. We show that the stability requirement for a veri cation sys-
tem yields the necessity of some sort of a re ection mechanism. However,
the traditional re ection rule based on the Godel implicit provability
predicate leads to a \re ection tower" of theories which cannot be for-
mally veri ed. We found natural lower and upper bounds on a metathe-
ory capable of establishing stability of a given veri cation system.
The paper introduces an explicit re ection mechanism which can be veri-
ed internally. This circumvents the re ection tower and provides a strict
justi cation for the veri cation process. On the practical side, the paper
gives speci c recommendations concerning the veri cation of inference
rules and building a veri able re ection mechanism for a theorem prov-
ing system.


Source: Artemov, Sergei N. - Faculty of Mechanics and Mathematics, Moscow State University


Collections: Computer Technologies and Information Sciences