Notre Dame Journal of Formal Logic

Four-valued Logic

Katalin Bimbó and J. Michael Dunn

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.

Article information

Source
Notre Dame J. Formal Logic, Volume 42, Number 3 (2001), 171-192.

Dates
First available in Project Euclid: 12 September 2003

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1063372199

Digital Object Identifier
doi:10.1305/ndjfl/1063372199

Mathematical Reviews number (MathSciNet)
MR2010180

Zentralblatt MATH identifier
1034.03021

Subjects
Primary: 03B47: Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) {For proof-theoretic aspects see 03F52}

Keywords
substructural logics Lambek calculi relevance logic lattice representation Kripke semantics

Citation

Bimbó, Katalin; Dunn, J. Michael. Four-valued Logic. Notre Dame J. Formal Logic 42 (2001), no. 3, 171--192. doi:10.1305/ndjfl/1063372199. https://projecteuclid.org/euclid.ndjfl/1063372199


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