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Communication Dans Un Congrès Année : 2010

Label-free Proof Systems for Intuitionistic Modal Logic IS5

Didier Galmiche
Yakoub Salhi

Résumé

In this paper we propose proof systems without labels for the intuitionistic modal logic IS5 that are based on a new multi-contextual 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.

Dates et versions

hal-00580298 , version 1 (27-03-2011)

Identifiants

Citer

Didier Galmiche, Yakoub Salhi. Label-free Proof Systems for Intuitionistic Modal Logic IS5. 16th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, LPAR-16, Apr 2010, Dakar, Senegal. pp.255-271, ⟨10.1007/978-3-642-17511-4_15⟩. ⟨hal-00580298⟩
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