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2001 Four-valued Logic
Katalin Bimbó, J. Michael Dunn
Notre Dame J. Formal Logic 42(3): 171-192 (2001). DOI: 10.1305/ndjfl/1063372199

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 (fusion) and its residuals (implications) 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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Katalin Bimbó. J. Michael Dunn. "Four-valued Logic." Notre Dame J. Formal Logic 42 (3) 171 - 192, 2001. https://doi.org/10.1305/ndjfl/1063372199

Information

Published: 2001
First available in Project Euclid: 12 September 2003

zbMATH: 1034.03021
MathSciNet: MR2010180
Digital Object Identifier: 10.1305/ndjfl/1063372199

Subjects:
Primary: 03B47

Rights: Copyright © 2001 University of Notre Dame

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Vol.42 • No. 3 • 2001
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