Abstract
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.
Keywords completeness theorem  Kripke semantics  linear logic  modal substructural logic  relevant logic
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Reprint years 2004
DOI 10.1023/A:1019915908844
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References found in this work BETA

Semantics for Relevant Logics.Alasdair Urquhart - 1972 - Journal of Symbolic Logic 37 (1):159-169.
Logics Without the Contraction Rule.Hiroakira Ono & Yuichi Komori - 1985 - Journal of Symbolic Logic 50 (1):169-201.
Sequent-Systems and Groupoid Models. I.Kosta Došen - 1988 - Studia Logica 47 (4):353 - 385.
Weak Logics with Strict Implication.Giovanna Corsi - 1987 - Mathematical Logic Quarterly 33 (5):389-406.

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Current Trends in Substructural Logics.Katalin Bimbó - 2015 - Journal of Philosophical Logic 44 (6):609-624.

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