Journal of Logic, Language and Information

, Volume 11, Issue 4, pp 453-470

First online:

Kripke Semantics for Modal Substructural Logics

  • Norihiro KamideAffiliated withWakayama National College of Technology

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We introduce Kripke semantics for modal substructural logics, and provethe completeness theorems with respect to the semantics. Thecompleteness theorems are proved using an extended Ishihara's method ofcanonical model construction (Ishihara, 2000). The framework presentedcan deal with a broad range of modal substructural logics, including afragment of modal intuitionistic linear logic, and modal versions ofCorsi's logics, Visser's logic, Méndez's logics and relevant logics.

completeness theorem Kripke semantics linear logic modal substructural logic relevant logic