TY - JOUR
AU - Degauquier, Vincent
PY - 2016/02/27
Y2 - 2022/01/18
TI - Partial and paraconsistent three-valued logics
JF - Logic and Logical Philosophy
JA - LLP
VL - 25
IS - 2
SE - Articles
DO - 10.12775/LLP.2016.003
UR - https://apcz.umk.pl/LLP/article/view/LLP.2016.003
SP - 143-171
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.
ER -