A proof-theoretic study of the correspondence of classical logic and modal logic

H. Kushida, M. Okada

Research output: Contribution to journalArticle

7 Citations (Scopus)


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 [10] proved this fact in a syntactic way. Mints [7] 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.

Original languageEnglish
Pages (from-to)1403-1414
Number of pages12
JournalJournal of Symbolic Logic
Issue number4
Publication statusPublished - 2003 Dec


ASJC Scopus subject areas

  • Philosophy
  • Logic

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