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  1. 1 Logic and Logical Philosophy

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  1. 1 Degauquier V.

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  1. 1 2016

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Partial and paraconsistent three-valued logics

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Degauquier V.
Logic and Logical Philosophy
|
2016
|
vol. 25
|
issue 2
143–171
EN
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.
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