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


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).

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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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Financed by MNiSW on the basis of agreement no. 706/P-DUN/2018 (dated 10/05/18). Project 1: “Preparation of articles in English for eight editions of the journal Logic and Logical Philosophy over the period 2018–19; Vol. 27, No. 1–4 (2018), Vol. 28, No. 1–4 (2019)”; amount from the DUN grant: 64800 zł. Project 4: “Digitalisation of eight editions of the journal Logic and Logical Philosophy over the period 2018-19; Vol. 27, No. 1–4 (2018), Vol. 28, No. 1–4 (2019)”; amount from the DUN grant: 18600 zł.


ISSN: 1425-3305 (print version)
ISSN: 2300-9802 (electronic version)

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