A new axiomatization of Jaśkowski's discussive logic
DOI:
https://doi.org/10.12775/LLP.2001.003Abstract
In 1995 N.C.A. da Costa and F. Doria proposed the modal-type elegant axiomatization of Jaśkowski’s discussive logic D2 . Yet his own problem which was formulated in 1975 in a following way: Is it possible to formulate natural and simple axiomatization for D2 , employing classical disjunction and conjunction along with discussive implication and conjunction as the only primitive connectives? — still seems left open. The matter of fact is there are some axiomatizations of D2 proposed, e.g., by T. Furmanowski (1975), J. Kotas and N.C.A. da Costa (1979), G. Achtelik, L. Dubikajtus, E. Dudek and J. Konior (1981), satisfying da Costa’s conditions, but they are rather looking very complicated and unnatural. An attempt is made to solve da Costa’s problem. The new axiomatization of D 2 is proposed essentially based on da Costa’s-Doria axiomatization from 1995.References
[Achtelik et al 1981] Achtelik, G., L. Dubikajtis, E. Dudek, and J. Konior, “On
independence of axioms of Jaśkowski s propositional calculus”, Reports on
Mathematical Logic 11, 3–11.
[da Costa, Dubikajtis 1968] da Costa, N.C.A., and L. Dubikajtis, “Sur la logique discoursive de Jaśkowski”, Bulletin Acad. Polonaise des Sciences Math., Astr. et Phys. 16, 551–557.
[da Costa 1975] da Costa, N.C.A., “Remarks on Jaśkowski’s Discussive Logic”, Reports on Mathematical Logic 4, 7–15.
[da Costa, Dubikajtis 1977] da Costa, N.C.A., and L. Dubikajtis, “On Jaśkowski’s Discussive Logic”, pages 37–56 in Non-Classical Logic. Model Theory and Computability, A.I. Arruda, N.C.A. da Costa and R. Chuaqui (eds.), North-Holland.
[da Costa, Doria 1995] da Costa, N.C.A., and F. Doria, “On Jaśkowski’sDiscussive Logic”, Studia Logica 54, 1, 33–60.
[Jaśkowski 1948] Jaśkowski, S., “Rachunek zdań dla systemów dedukcyjnych sprzecznych”, Studia Soc. Sci. Torunensis, sectio A, vol. I, no. 5. English translation [Jaśkowski 1969] and [Jaśkowski 1999a].
[Jaśkowski 1949] Jaśkowski, S., “O koniunkcji dedukcyjnej w rachunku zdań dla systemæw dedukcyjnych sprzecznych”, Studia Soc. Sci. Torunensis, sectio A, vol. I, no. 8 (1949). English translation [Jaśkowski 1999b].
[Jaśkowski 1969] Jaśkowski, S., “Propositional calculus for contradictory deductive systems”, Studia Logica XXIV, 143–157.
[Jaśkowski 1999a] Jaśkowski, S., “Propositional calculus for inconsistent deductive systems”, Logic and Logical Philosophy 7, 35–56. DOI: http://dx.doi.org/10.12775/LLP.1999.003
[Jaśkowski 1999b] Jaśkowski, S., “On the discussive conjunction in the propositional calculus for inconsistent deductive systems”, Logic and Logical Philosophy 7, 57–59. DOI: http://dx.doi.org/10.12775/LLP.1999.004
[Kotas 1971] Kotas, J., “On the algebra of classes of formulae of Jaśkowski s Disscussive System”, Studia Logica XXVII, 81–92.
[Kotas 1974] Kotas, J., “The axiomatization of S. Jaśkowski s Discussive System”, Studia Logica XXXIII, 2, 195–200.
[Kotas 1975] Kotas, J., “Discussive sentential calculus of Jaśkowski”, Studia Logica XXXIV, 2, 149–168.
[Kotas, da Costa 1979] Kotas, J., and N.C.A. da Costa, “A new formulation of Discussive Logic”, Studia Logica XXXVIII, 4, 429–445.
Downloads
Published
How to Cite
Issue
Section
Stats
Number of views and downloads: 613
Number of citations: 0
