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

Original Article

DOI: 10.1007/s10849-006-9023-0

Cite this article as:
Kushida, H. & Okada, M. JoLLI (2007) 16: 35. doi:10.1007/s10849-006-9023-0

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 

Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  1. 1.Department of PhilosophyKeio UniversityMinatokuJapan