TY - JOUR
T1 - Partial and paraconsistent three-valued logics
AU - Degauquier, Vincent
PY - 2016/6/1
Y1 - 2016/6/1
N2 - 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.
AB - 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.
KW - Cut redundancy
KW - Four-valued logic
KW - Functional completeness
KW - Paraconsistent logic
KW - Partial logic
KW - Proof-search procedure
KW - Sequent calculus
KW - Three-valued logic
UR - http://www.scopus.com/inward/record.url?scp=85029580860&partnerID=8YFLogxK
U2 - 10.12775/LLP.2016.003
DO - 10.12775/LLP.2016.003
M3 - Article
AN - SCOPUS:85029580860
SN - 1425-3305
VL - 25
SP - 143
EP - 171
JO - Logic and Logical Philosophy
JF - Logic and Logical Philosophy
IS - 2
ER -