Partial and paraconsistent three-valued logics

Vincent Degauquier



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.


four-valued logic; three-valued logic; partial logic; paraconsistent logic; sequent calculus; functional completeness; cut redundancy; proof-search procedure

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ISSN: 1425-3305 (print version)

ISSN: 2300-9802 (electronic version)

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