Logic and Logical Philosophy 25 (2):143-171 (2016)

Abstract
On the sidelines of classical logic, many partial and paraconsistent three-valued logics have been developed. Most of them differ in the notion of logical consequence or in the definition of logical connectives. This article aims, firstly, to provide both a model-theoretic and a proof-theoretic unified framework for these logics and, secondly, to apply these general frameworks to several well-known three-valued logics. The proof-theoretic approach to which we give preference is sequent calculus. In this perspective, several results concerning the properties of functional completeness, cut redundancy, and proof-search procedure are shown. We also provide a general proof for the soundness and the completeness of the three sequent calculi discussed.
Keywords four-valued logic   three-valued logic   partial logic   paraconsistent logic   sequent calculus   functional completeness   cut redundancy   proof-search procedure
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DOI 10.12775/LLP.2016.003
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References found in this work BETA

Aspects of the Theory of Syntax.Noam Chomsky - 1965 - Cambridge, MA, USA: MIT Press.
A Useful Four-Valued Logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
Untersuchungen über das logische Schließen. I.Gerhard Gentzen - 1935 - Mathematische Zeitschrift 35:176–210.

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Citations of this work BETA

Neutral Free Logic: Motivation, Proof Theory and Models.Edi Pavlović & Norbert Gratzl - forthcoming - Journal of Philosophical Logic:1-36.

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