Some results on Jaśkowski’s discursive logic

Lafayette de Moraes, Jair Minoro Abe

DOI: http://dx.doi.org/10.12775/LLP.2001.002

Abstract


Jaśkowski [3] presented a new propositional calculus labeled “discussive propositional calculus”, to serve as an underlying basis for inconsistent but non-trivial theories. This system was later extended to lower and higher order predicate calculus ([1], [2]). Jaśkowski’s system of discussive or discursive propositional calculus can actually be extended to predicate calculus in at least two ways. We have the intention using this calculus of building later as a basis for a discussive theory of sets. One way is that studied by Da Costa and Dubikajtis. Another one is developed in this paper as a solution to a problem formulated by Da Costa. In this work we study a first order discussive predicate calculus J∗∗ .

The paper consists of three parts. In the first part we introduce the calculus J∗∗ and, following Prof. D. Makinson’s suggestion, we show that it is not identical with the predicate calculus [2] of Da Costa and Dubikajtis. An axiomatization of J∗∗ is presented. In the second one, we introduce new discussive connectives and study some of the properties. We observe that the usual Kripke semantics can be adapted to the calculus J∗∗ .

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References


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Costa, N.C.A. da, and L. Dubikajtis, “On Jaśkowski’s discursive logic”, in Non Classical Logics, Model Theory and Computability, A.I. Arruda, N.C.A. da Costa, and R. Chuaqui (eds.), North Holland, Amsterdam, 1977, pp. 37–56.

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