Paraconsistency and Sette’s calculus P1

Janusz Ciuciura

DOI: http://dx.doi.org/10.12775/LLP.2015.003

Abstract


In 1973, Sette presented a calculus, called P1, which is recognized as one of the most remarkable paraconsistent systems. The aim of this paper is to propose a new axiomatization of P1. The axiom schemata are chosen to show that P1 behaves in a paraconsistent way only at the atomic level, i.e. the rule: α, ~α / β holds in P1 only if α is not a propositional variable.


Keywords


logic; Sette’s system; P1

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References


Carnielli, W., M.E.Coniglio, and J. Marcos, “Logics of formal inconsistency”, pages 1–95 in D.M. Gabbay and F. Guenthner (eds.) Handbook of Philosophical Logic, vol. 14, Springer, 2007. DOI: 10.1007/978-1-4020-6324-4_1

da Costa, N.C.A., “On the theory of inconsistent formal systems”, Notre Dame Journal of Formal Logic, 15, 4 (1974): 497–510. DOI: 10.1305/ndjfl/1093891487

Jaśkowski, S., “A propositional calculus for inconsistent deductive systems”, Logic and Logical Philosophy, 7, 1 (1999): 35–56. DOI: 10.12775/LLP.1999.003

Karpenko, A., “Jaśkowski’s criterion and three-valued paraconsistent logics”, Logic and Logical Philosophy, 7, 1 (1999): 81–86. DOI: 10.12775/LLP.1999.006

Malinowski, G., Many-Valued Logics, Clarendon Press, Oxford, 1993.

Pynko, A.P., “Algebraic study of Sette’s maximal paraconsistent logis”, Studia Logica, 54, 1 (1995): 89–128.

Sette, A.M., “On the propositional calculus P1”, Mathematica Japonicae, 18, 3 (1973): 173–180.

Sette, A.M., and E.H. Alves “On the equivalence between some systems of non-classical logic”, Bul letin of the Section of Logic, 25, 2 (1973): 68–72.








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