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

Natalya Tomova

doi:10.18778/0138-0680.2020.24

Authors

Natalya Tomova Russian Academy of Sciences, Institute of Philosophy, Goncharnaya 12/1, 109240 Moscow, Russian Federation https://orcid.org/0000-0001-9909-2504

DOI:

https://doi.org/10.18778/0138-0680.2020.24

Keywords:

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

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.

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