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A semi-lattice of four-valued literal-paraconsistent-paracomplete logics. (English) Zbl 07368981

Summary: 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 L. Z. Puga and N. C. A. da Costa’s logic V [Z. Math. Logik Grundlagen Math. 34, No. 3, 205–211 (1988; Zbl 0627.03011)] and the matrix of paranormal logic \(P^1 I^1\), which is the part of a sequence of paranormal matrices proposed by V. L. Fernández [Semântica de sociedades para lógicas \(n\)-valentes. Campinas: IFCH-UNICAMP (Master’s thesis) (2001)].

MSC:

03B53 Paraconsistent logics
03B50 Many-valued logic

Citations:

Zbl 0627.03011
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