### Some results on Jaśkowski’s discursive logic

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^{∗∗} .

^{∗∗}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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PDF#### References

Costa, N.C.A. da, “Remarks on Jaśkowski’s discursive logic”, Reports on Mathematical Logic 4 (1975), 7–16.

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.

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

Kotas, J., and N.C.A. da Costa, “A new formulation of discursive logic” (to appear).

Moraes, L. de, Sobre a Lógica Discursiva de Jaśkowski, Master Thesis, USP, 1970.

Santos, L.H.L. dos, “Some remarks on discursive logic”, in Non Classical Logics. Model Theory and Computability, A. Arruda, N.C.A . da Costa and R. Chuaqui (eds.), North-Holland, 1977, pp. 99–113.

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