Partial and paraconsistent three-valued logics
Journal Title: Logic and Logical Philosophy - Year 2016, Vol 25, Issue 2
Abstract
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.
Authors and Affiliations
Vincent Degauquier
Keywords
Related Articles
- EP ID EP201816
- DOI 10.12775/LLP.2016.003
- Views 61
- Downloads 0
Refutation Systems for a System of Nonsense-Logic
In the paper rejection systems for a system of nonsense-logic are investigated. The first rejection system consists of four rejected axioms and only one rejection rule - the rule of rejection by detachment. The second o...
Tomasz Jarmużek and Marcin Tkaczyk: “Normalne logiki pozycyjne” (Normal Positional Logics), Wydawnictwo KUL, Lublin (Poland), 2015
Book Reviews: Tomasz Jarmużek and Marcin Tkaczyk, Normalne logiki pozycyjne (Normal Positional Logics), Wydawnictwo KUL, Lublin (Poland), 2015, 202 pages, ISBN 978-838061-114-6.
Trivial Dialetheism and the Logic of Paradox
In this paper we explain that the paraconsistent logic LP (Logic of Paradox) promoted by Graham Priest can only be supported by trivial dialetheists, i.e., those who believe that all sentences are dialetheias.
The Need for Pluralism of Causality
It will be shown in this article that a pluralism of causality is needed. Not only, as might be expected, for such different domains as natural sciences and humanities, but even within the domain of physics different cau...
Relational semantics for the 4-valued relevant logics BN4 and E4
The logic BN4 was defined by R.T. Brady in 1982. It can be considered as the 4-valued logic of the relevant conditional. E4 is a variant of BN4 that can be considered as the 4-valued logic of (relevant) entailment. The a...