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Extensions of Hałkowska–Zajac's three-valued paraconsistent logic

Extensions of Hałkowska–Zajac's three-valued paraconsistent logic  As it was proved in [4, Sect. 3], the poset of extensions of the propositional logic defined by a class of logical matrices with equationally-definable set of distinguished values is a retract, under a Galois connection, of the poset of subprevarieties of the prevariety generated by the class of the underlying algebras of the defining matrices. In the present paper we apply this general result to the three-valued paraconsistent logic proposed by Hałkowska–Zajac [2]. Studying corresponding prevarieties, we prove that extensions of the logic involved form a four-element chain, the only proper consistent extensions being the least non-paraconsistent extension of it and the classical logic. RID=""ID="" <E5>Mathematics Subject Classification (2000):</E5> 03B50, 03B53, 03G10 RID=""ID="" <E5>Key words or phrases:</E5> Many-valued logic &ndash; Paraconsistent logic &ndash; Extension &ndash; Prevariety &ndash; Distributive lattice http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Mathematical Logic Springer Journals

Extensions of Hałkowska–Zajac's three-valued paraconsistent logic

Pynko, Alexej P.
Archive for Mathematical Logic , Volume 41 (3) – Apr 1, 2002
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References (7)

Publisher
Springer Journals
Copyright
Copyright © 2002 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Mathematical Logic and Foundations; Mathematics, general; Algebra
ISSN
0933-5846
eISSN
1432-0665
DOI
10.1007/s001530100115
Publisher site
See Article on Publisher Site

Abstract

 As it was proved in [4, Sect. 3], the poset of extensions of the propositional logic defined by a class of logical matrices with equationally-definable set of distinguished values is a retract, under a Galois connection, of the poset of subprevarieties of the prevariety generated by the class of the underlying algebras of the defining matrices. In the present paper we apply this general result to the three-valued paraconsistent logic proposed by Hałkowska–Zajac [2]. Studying corresponding prevarieties, we prove that extensions of the logic involved form a four-element chain, the only proper consistent extensions being the least non-paraconsistent extension of it and the classical logic. RID=""ID="" <E5>Mathematics Subject Classification (2000):</E5> 03B50, 03B53, 03G10 RID=""ID="" <E5>Key words or phrases:</E5> Many-valued logic &ndash; Paraconsistent logic &ndash; Extension &ndash; Prevariety &ndash; Distributive lattice

Journal

Archive for Mathematical Logic – Springer Journals

Published: Apr 1, 2002

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