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Workshop on Realizability Preliminary Version Uniform provability realization of

Summary: Workshop on Realizability Preliminary Version
Uniform provability realization of
intuitionistic logic, modality and -terms
Sergei N. Artemov 1;2
Department of Computer Science and
Department of Mathematics
Cornell University
Ithaca, NY 14853, U.S.A.
The intended meaning of intuitionistic logic is explained by the Brouwer-Heyting-
Kolmogorov (BHK) provability semantics which informally de nes intuitionistic
truth as provability and speci es the intuitionistic connectives via operations on
proofs. The problem of nding an adequate formalization of the provability seman-
tics and establishing the completeness of the intuitionistic logic Int was rst raised
by Godel in 1933. This question turned out to be a part of the more general prob-
lem of the intended realization for Godel's modal logic of provability S4 which was
open since 1933. In this tutorial talk we present a provability realization of Int and
S4 that solves both of these problems. We describe the logic of explicit provability
(LP) with the atoms \t is a proof of F" and establish that every theorem of S4 ad-


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


Collections: Computer Technologies and Information Sciences