Four-valued Logic

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

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Author Profiles

Jon Michael Dunn
PhD: University of Pittsburgh; Last affiliation: Indiana University, Bloomington
Katalin Bimbo
University of Alberta

Citations of this work

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Generalized Kripke Frames.Mai Gehrke - 2006 - Studia Logica 84 (2):241-275.
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A Note on FDE “All the Way Up”.Jc Beall & Caleb Camrud - 2020 - Notre Dame Journal of Formal Logic 61 (2):283-296.

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Varieties of complex algebras.Robert Goldblatt - 1989 - Annals of Pure and Applied Logic 44 (3):173-242.
Positive modal logic.J. Michael Dunn - 1995 - Studia Logica 55 (2):301 - 317.
Algebraic analysis of entailment I.Robert K. Meyer & Richard Routley - 1972 - Logique Et Analyse 15 (59/60):407-428.
Kripke models for linear logic.Gerard Allwein & J. Michael Dunn - 1993 - Journal of Symbolic Logic 58 (2):514-545.

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