December 2003 A proof-theoretic study of the correspondence of classical logic and modal logic
H. Kushida, M. Okada
J. Symbolic Logic 68(4): 1403-1414 (December 2003). DOI: 10.2178/jsl/1067620195


It is well known that the modal logic S5 can be embedded in the classical predicate logic by interpreting the modal operator in terms of a quantifier. Wajsberg proved this fact in a syntactic way. Mints extended this result to the quantified version of S5; using a purely proof-theoretic method he showed that the quantified S5 corresponds to the classical predicate logic with one-sorted variable. In this paper we extend Mints’ result to the basic modal logic S4; we investigate the correspondence between the quantified versions of S4 (with and without the Barcan formula) and the classical predicate logic (with one-sorted variable). We present a purely proof-theoretic proof-transformation method, reducing an LK-proof of an interpreted formula to a modal proof.


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H. Kushida. M. Okada. "A proof-theoretic study of the correspondence of classical logic and modal logic." J. Symbolic Logic 68 (4) 1403 - 1414, December 2003.


Published: December 2003
First available in Project Euclid: 31 October 2003

zbMATH: 1056.03009
MathSciNet: MR2017363
Digital Object Identifier: 10.2178/jsl/1067620195

Rights: Copyright © 2003 Association for Symbolic Logic


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Vol.68 • No. 4 • December 2003
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