Notre Dame Journal of Formal Logic 42 (3):171-192 (2001)

Authors
Jon Michael Dunn
Indiana University, Bloomington
Katalin Bimbo
University of Alberta
Abstract
Four-valued semantics proved useful in many contexts from relevance logics to reasoning about computers. We extend this approach further. A sequent calculus is defined with logical connectives conjunction and disjunction that do not distribute over each other. We give a sound and complete semantics for this system and formulate the same logic as a tableaux system. Intensional conjunction and its residuals can be added to the sequent calculus straightforwardly. We extend a simplified version of the earlier semantics for this system and prove soundness and completeness. Then, with some modifications to this semantics, we arrive at a mathematically elegant yet powerful semantics that we call generalized Kripke semantics
Keywords substructural logics   Lambek calculi   relevance logic   lattice representation   Kripke semantics
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DOI 10.1305/ndjfl/1063372199
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Generalized Kripke Frames.Mai Gehrke - 2006 - Studia Logica 84 (2):241-275.
Four-Valued Paradefinite Logics.Ofer Arieli & Arnon Avron - 2017 - Studia Logica 105 (6):1087-1122.
Algebraic Kripke-Style Semantics for Relevance Logics.Eunsuk Yang - 2014 - Journal of Philosophical Logic 43 (4):803-826.
Current Trends in Substructural Logics.Katalin Bimbó - 2015 - Journal of Philosophical Logic 44 (6):609-624.

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