Partial and paraconsistent three-valued logics

• Authors: Degauquier Vincent
• Languages of publication: EN

Abstracts

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.

Keywords

EN

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

• Publisher: Uniwersytet Mikołaja Kopernika (Nicolaus Copernicus University in Toruń)
• Journal: Logic and Logical Philosophy
• Year: 2016
• Volume: 25
• Issue: 2
• Pages: 143–171

Dates

online

2016-02-27

Contributors

author

Degauquier Vincent

• Faculty of Sciences University of Namur Rue de Bruxelles 61 5000 Namur, Belgium

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Identifiers

DOI

10.12775/LLP.2016.003