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A New Formulation of Discussive Logic

Jerzy Kotas and N. C. A. da Costa
Studia Logica: An International Journal for Symbolic Logic
Vol. 38, No. 4 (1979), pp. 429-445
Published by: Springer
Stable URL: http://www.jstor.org/stable/20014963
Page Count: 17
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A New Formulation of Discussive Logic
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Abstract

S. Jaśkowski introduced the discussive propositional calculus D₂ as a basis for a logic which could be used as underlying logic of inconsistent but nontrivial theories (see, for example, N. C. A. da Casta and L. Dubikajtis, "On Jaśkowski's discussive logic," in Non-Classical Logic, Model Theory and Computability, A. I. Arruda, N. C. A da Costa and R. Chuaqui edts., North-Holland, Amsterdam, 1977, 37-56). D₂ has afterwards been extended to a first-order predicate calculus and to a higher-order logic (cf. the quoted paper). In this paper we present a natural version of D₂, in the sense of Jaśkowski and Gentzen; as a consequence, we suggest a new formulation of the discussive predicate calculus (with equality). A semantics for the new calculus is also presented.

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