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

Natalya Tomova

Bulletin of the Section of Logic (2021)

  • Volume: 50, Issue: 1, page 35-53
  • ISSN: 0138-0680

Abstract

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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.

How to cite

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Natalya Tomova. "A Semi-lattice of Four-valued Literal-paraconsistent-paracomplete Logics." Bulletin of the Section of Logic 50.1 (2021): 35-53. <http://eudml.org/doc/296787>.

@article{NatalyaTomova2021,
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.},
author = {Natalya Tomova},
journal = {Bulletin of the Section of Logic},
keywords = {Four-valued logics; paraconsistent logics; paracomplete logics; isomorphisms; literal-paraconsistent-paracomplete logics; semi-lattice of logics},
language = {eng},
number = {1},
pages = {35-53},
title = {A Semi-lattice of Four-valued Literal-paraconsistent-paracomplete Logics},
url = {http://eudml.org/doc/296787},
volume = {50},
year = {2021},
}

TY - JOUR
AU - Natalya Tomova
TI - A Semi-lattice of Four-valued Literal-paraconsistent-paracomplete Logics
JO - Bulletin of the Section of Logic
PY - 2021
VL - 50
IS - 1
SP - 35
EP - 53
AB - 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.
LA - eng
KW - Four-valued logics; paraconsistent logics; paracomplete logics; isomorphisms; literal-paraconsistent-paracomplete logics; semi-lattice of logics
UR - http://eudml.org/doc/296787
ER -

References

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