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Logic and Logical Philosophy

Jaśkowski's criterion and three-valued paraconsistent logics
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Jaśkowski's criterion and three-valued paraconsistent logics

Authors

  • Alexander S. Karpenko the Russian Academy of Science

DOI:

https://doi.org/10.12775/LLP.1999.006

Abstract

A survey is given of three-valued paraconsistent propositional logics connected with Jaśkowski’s criterion for constructing paraconsistent logics. Several problems are raised and four new matrix three-valued paraconsistent logics are suggested.

Author Biography

Alexander S. Karpenko, the Russian Academy of Science

Institute of Philosophy

References

Anderson, A.R., and N.D. Belnap, jr., Entailment: The Logic of Relevance and Necessity, Vol. 1. Princeton, 1975.

Arruda, A.I., “On the imaginery logic of N.A.Vasiľev”, in: Non-Classical Logics, Model Theory and Computability, North-Holland, Amsterdam, 1977, pp. 3–24.

Asenjo, F.G., La Idea de un Calculo de Antinomias, Seminario Mathematico, Universidad Nacional de La Plata, 1953.

Asenjo, F.G., and J. Tamburino., “Logic of antinomies”, Notre Dame Journal of Formal Logic 16, No 1 (1975).

Avron, A, “On the implicational connective of RM”, Notre Dame Journal of Formal Logic 27 (1986), 201–209.

Avron, A, “On the expressive power of the language of J3”, in: Stanisław Jaśkowski Memorial Symposium, Toruń, 1998, p. 42–45.

Batens, D., “Paraconsistent extensional propositional logics”, Logique et Analyse 23, No 90–91 (1980), 127–139.

Béziau, J., “What is paraconsistent logic?”, Relatorios de Pesquisa e Desenvolvimento, Dezembro de 1997 (preprint No 50/97).

Brady, R., “Completeness proofs for the systems RM3 and BN4”, Logique et Analyse 25 (1982), 51–61.

da Costa, N.C.A., “Calculus propositionnels pour les systemes formels inconsistants”, Comptes Rendus Acad. Sci. 257 (1963), 3790–3792.

da Costa N.C.A., and E.N. Alves, “Relations between paraconsistent logic and many-valued logic”, Bulletin of the Section of Logic 10 (1981), p. 185-191.

D’Ottaviano, I.M.L., and N.C.A. da Costa, “Sur un probleme de Jaśkowski”, Comptes Rendus Acad. Sci. 270A (1970), 1349–1343.

Epstein, R.L., The Semantic Foundations of Logic. Vol. 1: Propositional logic, Kluwer Academic Publishers, Dordrecht, 1990.

Jaśkowski, S., “Rachunek zdań dla systemów dedukcyjnych sprzecznych”, Studia Societatis Scientiarum Torunensis Vol. 1, No 5, Sectio A (1948). (English translation: “Propositional calculus for contadictory deductive systems”, Studia Logica 24 (1969), 143–157).

Karpenko, A.S., “A maximal paraconsistent logic: The combination of two three-valued isomorphs of classical propositional logic”, in: Proceedings of the 1st World Congress on Paraconsistency, 1999 (forthcoming).

Kleene, S.C., “On a notation for ordinal numbers”, The Journal of Symbolic Logic 3 (1938), 150–155.

Łukasiewicz, J., “O logice trójwartościowej”, Ruch Filozoficzny 5 (1920), 170–171. (English translation: “On three-valued logic”, in: J. Łukasiewicz, Selected Works, PWN, Warszawa, 1970, pp. 87–88).

Mortensen, C., “Paraconsistency and C1”, in: Paraconsistent Logic: Essays on the inconsistent (eds. G. Priest, R. Routley, J. Norman). Philosophia Verlag, Munchen, 1989, pp. 289–305.

Parks, R. Z., “A note on R-mingle and Sobociński’s three-valued logic”, Notre Dame Journal of Formal Logic 13 (1972), 227–228.

Priest, G., “Logic of paradox”, Journal of Philosophical Logic 8 (1979), 219–241.

Rozonoer, L.I., “On semantics of inconsistent formal theories”, Semiotics and Informatics 33 (1993), 71–100 (in Russian).

Sette, A.M., “On propositional calculus P1”, Mathematica Japonica 16 (1973),173–180.

Sobociński, B., “Axiomatization of a partial system of three-valued calculus of propositions”, The Journal of Computing Systems 1 (1952), 23–55.

Tamburino, J., Inconsistent systems of mathematical logic (Thesis), University of Pittsburg, 1972.

Tuziak, R., “Finitely many-valued paraconsistent systems”, Logic and Logical Philosophy 5 (1997), 121–127. DOI: http://dx.doi.org/10.12775/LLP.1997.008

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Published

2004-01-07

How to Cite

1.
KARPENKO, Alexander S. Jaśkowski’s criterion and three-valued paraconsistent logics. Logic and Logical Philosophy. Online. 7 January 2004. Vol. 7, no. 7, pp. 81-86. [Accessed 1 July 2025]. DOI 10.12775/LLP.1999.006.
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