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The single-conclusion proof logic and inference rules specification

Vladimir N. Krupski

Annals of Pure and Applied Logic 113 (1-3):181-206 (2001)

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(1 other version)Data storage interpretation of labeled modal logic.Sergei Artëmov & Vladimir Krupski - 1996 - Annals of Pure and Applied Logic 78 (1-3):57-71.details We introduce reference structures — a basic mathematical model of a data organization capable of storing and utilizing information about its addresses. A propositional labeled modal language is used as a specification and programming language for reference structures; the satisfiability algorithm for modal language gives a method of building and optimizing reference structures satisfying a given formula. Corresponding labeled modal logics are presented, supplied with cut free axiomatizations, completeness and decidability theorems are proved. Initialization of typed variables in some programming (...) Download Export citation Bookmark 2 citations
Explicit provability and constructive semantics.Sergei N. Artemov - 2001 - Bulletin of Symbolic Logic 7 (1):1-36.details In 1933 Godel introduced a calculus of provability (also known as modal logic S4) and left open the question of its exact intended semantics. In this paper we give a solution to this problem. We find the logic LP of propositions and proofs and show that Godel's provability calculus is nothing but the forgetful projection of LP. This also achieves Godel's objective of defining intuitionistic propositional logic Int via classical proofs and provides a Brouwer-Heyting-Kolmogorov style provability semantics for Int which (...) Download Export citation Bookmark 115 citations
Logic of proofs.Sergei Artëmov - 1994 - Annals of Pure and Applied Logic 67 (1-3):29-59.details In this paper individual proofs are integrated into provability logic. Systems of axioms for a logic with operators “A is provable” and “p is a proof of A” are introduced, provided with Kripke semantics and decision procedure. Completeness theorems with respect to the arithmetical interpretation are proved. Download Export citation Bookmark 36 citations
(2 other versions)Review of Robert M. Solovay's Provability Interpretations of Modal Logic.George Boolos - 1981 - Journal of Symbolic Logic 46 (3):661-662.details Download Export citation Bookmark 36 citations
(1 other version)Data storage interpretation of labeled modal logic.M. A. Arslanov, S. Lempp, R. A. Shore, S. Artemov, V. Krupski, A. Dabrowski, L. S. Moss, R. Parikh, T. Eiter & G. Gottlob - 1996 - Annals of Pure and Applied Logic 78 (1-3):57-71.details Download Export citation Bookmark 3 citations

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