Article

Studia Logica

, Volume 59, Issue 3, pp 303-330

First online:

Cut-Free Tableau Calculi for some Intuitionistic Modal Logics

  • Mauro FerrariAffiliated withDipartimento di Scienze dell'Informazione, Università degli Studi di Milano

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Abstract

In this paper we provide cut-free tableau calculi for the intuitionistic modal logics IK, ID, IT, i.e. the intuitionistic analogues of the classical modal systems K, D and T. Further, we analyse the necessity of duplicating formulas to which rules are applied. In order to develop these calculi we extend to the modal case some ideas presented by Miglioli, Moscato and Ornaghi for intuitionistic logic. Specifically, we enlarge the language with the new signs Fc and CR near to the usual signs T and F. In this work we establish the soundness and completeness theorems for these calculi with respect to the Kripke semantics proposed by Fischer Servi.

intuitionistic modal logics refutation systems Kripke models duplications