Label-free proof systems for intuitionistic modal logic IS5

Authors:
Didier Galmiche;Yakoub Salhi
Affiliations:
LORIA, UHP Nancy 1, Vandoeuvre-lès-Nancy, France;LORIA, UHP Nancy 1, Vandoeuvre-lès-Nancy, France
Venue:
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
Year:
2010

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Abstract

In this paper we propose proof systems without labels for the intuitionistic modal logic IS5 that are based on a new multicontextual sequent structure appropriate to deal with such a logic. We first give a label-free natural deduction system and thus derive natural deduction systems for the classical modal logic S5 and also for an intermediate logic IM5. Then we define a label-free sequent calculus for IS5 and prove its soundness and completeness. The study of this calculus leads to a decision procedure for IS5 and thus to an alternative syntactic proof of its decidability.