Cut-free tableau calculi for some intuitionistic modal logics

Studia Logica 59 (3):303-330 (1997)
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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.

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Citations of this work

Gentzen sequent calculi for some intuitionistic modal logics.Zhe Lin & Minghui Ma - 2019 - Logic Journal of the IGPL 27 (4):596-623.

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References found in this work

First-order logic.Raymond Merrill Smullyan - 1968 - New York [etc.]: Springer Verlag.
Proof Methods for Modal and Intuitionistic Logics.Melvin Fitting - 1985 - Journal of Symbolic Logic 50 (3):855-856.
Semantical Investigations in Heyting's Intuitionistic Logic.Dov M. Gabbay - 1986 - Journal of Symbolic Logic 51 (3):824-824.
A Companion to Modal Logic.G. E. Hughes & M. J. Cresswell - 1995 - Studia Logica 54 (3):411-413.

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