PARTIAL AND PARACONSISTENT THREE-VALUED LOGICS

被引：6
|
作者：
Degauquier, Vincent [1 ]
机构：
[1] Univ Namur, Fac Sci, Rue Bruxelles 61, B-5000 Namur, Belgium
来源：
LOGIC AND LOGICAL PHILOSOPHY | 2016年 / 25卷 / 02期
关键词：
four-valued logic; three-valued logic; partial logic; paraconsistent logic; sequent calculus; functional completeness; cut redundancy; proof-search procedure;
D O I：
10.12775/LLP.2016.003
中图分类号：
B81 [逻辑学（论理学）];
学科分类号：
010104 ; 010105 ;
摘要：
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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页码：143 / 171
页数：29
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