The paraconsistent logic Z. A possible solution to Jaśkowski’s problem

Jean-Yves Béziau



We present a paraconsistent logic, called Z, based on an intuitive possible worlds semantics, in which the replacement theorem holds. We show how to axiomatize this logic and prove the completeness theorem.

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Béziau, J.-Y., 1995, Recherches sur la logique universelle, PhD, University of Paris 7.

Béziau, J.-Y., 1998, “Recherches sur la logique abstraite: les logiques normales”, Acta Universitatis Wratislaviensis, Logika 18, 105–114.

Béziau, J.-Y., 2000, “What is paraconsistent logic?”, in Frontiers of Paraconsistent Logic, D. Batens et al. (eds), Researcher Studies Press, Baldock, pp. 95-111.

Carnielli, W.A., and P.A.Veloso, 1997, “Ultrafilter logic and generic reasoning”, Computational Logic and Proof Theory, Springer, Berlin, pp. 34–53.

Chellas, B.F., 1980, Modal Logic. An Introduction, CUP, Cambridge.

da Costa, N.C.A., 1963, “Calculs propositionnels pour les systémes formels inconsistants”, Comptes Rendus de l’Académie des Sciences de Paris 257, 3790–3793.

da Costa, N.C.A., and F.A. Doria, “On Jaśkowski’s discussive logics”, Studia Logica 54, 33–60.

D’Ottaviano, I.M.L., and N.C.A. da Costa, 1970, “Sur un probleme de Jaśkowski”, Comptes Rendus de l’Académie des Sciences de Paris 270, 1349–1353.

Jaśkowski, S., 1948, “Rachunek zdań dla systemów dedukcyjnych sprzecznych”, Studia Societatis Scientiarum Torunensis, Sectio A, I(5), 55–77.

Kotas, J., and N.C.A. da Costa, 1977, “On the problem of Jaśkowski and the logics of Łukasiewicz”, in Proceedings of the First Brazilian Conference, A.I. Arruda et al. (eds), Marcel Dekker, New York, pp. 127–139.

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

Sette, A.M., E.H. Alves and G.S. Queiroz, “Brouwerian algebras and paraconsistent logic”, paper presented at the 1st World Congress on Paraconsistency, Ghent 1995.

Urbas, I., 1990, “Paraconsistency”, Studies in Soviet Thought 39, 343–354.

Urbas, I., 1996, “Dual-intuitionistic logic”, Notre Dame Journal of Formal Logic 37, 440–451.

Urchs, M., 1995, “Discursive logic: towards a logic of rational discourse”, Studia Logica 54, 231–249.

ISSN: 1425-3305 (print version)

ISSN: 2300-9802 (electronic version)

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