Paraconsistency and the need for infinite semantics

Paraconsistency and the need for infinite semantics We show that most of the paraconsistent logics which have been investigated in the literature have no finite characteristic matrices, and in the most important cases not even finite characteristic non-deterministic matrices (Nmatrices). 1 Introduction over its elements. Var(ϕ) denotes the set of variables which occur in ϕ. There are many paraconsistent logics that have been devel- Definition 2.1 A (propositional) logic is a pair L =L,  , oped over the years. The simplest of them, like Asenjo– such that L is a propositional language, and  is a structural Priest’s logic LP (Asenjo 1966;Priest 1979), D’Ottaviano’s and non-trivial Tarskian consequence relation for L. logic J (D’Ottaviano 1985; Epstein 2012), and Sette’s logic P (Sette 1973), were based from the start on finite matrices Now we define the notion of “paraconsistent logic”. A (actually: three-valued matrices). However, it is known that very useful general definition can, e.g., be found in Arieli most of the paraconsistent logics that were designed on the and Avron (2015). However, for the purposes of this paper basis of other ideas, like relevance or formal inconsistency, the following much weaker notion used in Avron and Béziau do not have finite characteristic matrices. Our goal http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Soft Computing Springer Journals

Paraconsistency and the need for infinite semantics

Soft Computing , Volume OnlineFirst – Jun 6, 2018

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Engineering; Computational Intelligence; Artificial Intelligence (incl. Robotics); Mathematical Logic and Foundations; Control, Robotics, Mechatronics
ISSN
1432-7643
eISSN
1433-7479
D.O.I.
10.1007/s00500-018-3272-0
Publisher site
See Article on Publisher Site

Abstract

We show that most of the paraconsistent logics which have been investigated in the literature have no finite characteristic matrices, and in the most important cases not even finite characteristic non-deterministic matrices (Nmatrices). 1 Introduction over its elements. Var(ϕ) denotes the set of variables which occur in ϕ. There are many paraconsistent logics that have been devel- Definition 2.1 A (propositional) logic is a pair L =L,  , oped over the years. The simplest of them, like Asenjo– such that L is a propositional language, and  is a structural Priest’s logic LP (Asenjo 1966;Priest 1979), D’Ottaviano’s and non-trivial Tarskian consequence relation for L. logic J (D’Ottaviano 1985; Epstein 2012), and Sette’s logic P (Sette 1973), were based from the start on finite matrices Now we define the notion of “paraconsistent logic”. A (actually: three-valued matrices). However, it is known that very useful general definition can, e.g., be found in Arieli most of the paraconsistent logics that were designed on the and Avron (2015). However, for the purposes of this paper basis of other ideas, like relevance or formal inconsistency, the following much weaker notion used in Avron and Béziau do not have finite characteristic matrices. Our goal

Journal

Soft ComputingSpringer Journals

Published: Jun 6, 2018

References

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