Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 68, Issue 4 (2003), 1403-1414.
A proof-theoretic study of the correspondence of classical logic and modal logic
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.
J. Symbolic Logic, Volume 68, Issue 4 (2003), 1403-1414.
First available in Project Euclid: 31 October 2003
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Kushida, H.; Okada, M. A proof-theoretic study of the correspondence of classical logic and modal logic. J. Symbolic Logic 68 (2003), no. 4, 1403--1414. doi:10.2178/jsl/1067620195. https://projecteuclid.org/euclid.jsl/1067620195