Original Article

Journal of Logic, Language and Information

, Volume 16, Issue 1, pp 35-61

A proof–theoretic study of the correspondence of hybrid logic and classical logic

  • H. KushidaAffiliated withDepartment of Philosophy, Keio University Email author 
  • , M. OkadaAffiliated withDepartment of Philosophy, Keio University

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Abstract

In this paper, we show the equivalence between the provability of a proof system of basic hybrid logic and that of translated formulas of the classical predicate logic with equality and explicit substitution by a purely proof–theoretic method. Then we show the equivalence of two groups of proof systems of hybrid logic: the group of labelled deduction systems and the group of modal logic-based systems.

Keywords

Proof theory Hybrid logic Classical logic