Abstract
We introduce Kripke semantics for modal substructural logics, and prove the completeness theorems with respect to the semantics. The completeness theorems are proved using an extended Ishihara's method of canonical model construction (Ishihara, 2000). The framework presented can deal with a broad range of modal substructural logics, including a fragment of modal intuitionistic linear logic, and modal versions of Corsi's logics, Visser's logic, Mendez's logics and relevant logics.
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