Abstract
S. Jaśkowski introduced the discussive prepositional calculus D 2as a basis for a logic which could be used as underlying logic of inconsistent but nontrivial theories (see, for example, N. C. A. da Costa 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). D 2has 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 D 2, 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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References
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Kotas, J., da Costa, N.C.A. A new formulation of discussive logic. Stud Logica 38, 429–445 (1979). https://doi.org/10.1007/BF00370480
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DOI: https://doi.org/10.1007/BF00370480