Grafting modalities onto substructural implication systems

Studia Logica 59 (1):65-102 (1997)
Abstract
We investigate the semantics of the logical systems obtained by introducing the modalities and into the family of substructural implication logics (including relevant, linear and intuitionistic implication). Then, in the spirit of the LDS (Labelled Deductive Systems) methodology, we "import" this semantics into the classical proof system KE. This leads to the formulation of a uniform labelled refutation system for the new logics which is a natural extension of a system for substructural implication developed by the first two authors in a previous paper.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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DOI 10.1023/A:1004947400860
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Normal Modal Substructural Logics with Strong Negation.Norihiro Kamide - 2003 - Journal of Philosophical Logic 32 (6):589-612.
Non-Normal Modalities in Variants of Linear Logic.D. Porello & N. Troquard - 2015 - Journal of Applied Non-Classical Logics 25 (3):229-255.

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