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ArticleOriginal scientific text

Title

A Semi-lattice of Four-valued Literal-paraconsistent-paracomplete Logics

Authors 1

Affiliations

  1. Russian Academy of Sciences, Institute of Philosophy, Moscow, Russian Federation

Abstract

In this paper, we consider the class of four-valued literal-paraconsistent-paracomplete logics constructed by combination of isomorphs of classical logic CPC. These logics form a 10-element upper semi-lattice with respect to the functional embeddinig one logic into another. The mechanism of variation of paraconsistency and paracompleteness properties in logics is demonstrated on the example of two four-element lattices included in the upper semi-lattice. Functional properties and sets of tautologies of corresponding literal-paraconsistent-paracomplete matrices are investigated. Among the considered matrices there are the matrix of Puga and da Costa's logic V and the matrix of paranormal logic P1I1, which is the part of a sequence of paranormal matrices proposed by V. Fernández.

Keywords

ENG
Four-valued logics, paraconsistent logics, paracomplete logics, isomorphisms, literal-paraconsistent-paracomplete logics, semi-lattice of logics

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Bulletin of the Section of Logic
2021/50/1
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Pages:
35-53
Main language of publication
English
Published
2020-11-13
Published online
2020-11-13

DOI: 10.18778/0138-0680.2020.24

Humanities