Algebraization of Jaśkowski’s Paraconsistent Logic D2

• Authors: Janusz Ciuciura
• Languages of publication: EN

Abstracts

EN

The aim of this paper is to present an algebraic approach to Jaśkowski’s paraconsistent logic D2. We present: a D2-discursive algebra, Lindenbaum- Tarski algebra for D2 and D2-matrices. The analysis is mainly based on the results obtained by Jerzy Kotas in the 70s.

Keywords

EN

discursive (discussive) logic; discursive algebra; Jaśkowski’s logic; D2; paraconsistent logic

• Publisher: Sciendo
• Journal: Studies in Logic, Grammar and Rhetoric
• Year: 2015
• Volume: 42
• Issue: 1
• Pages: 173-193

Dates

published

2015-09-01

online

2015-11-26

Contributors

author

Janusz Ciuciura

• University of Łódź

References

• Arieli, O., Avron, A., & Zamansky, A. (2011). Ideal Paraconsistent Logics. Studia Logica, 99(1-3), 31-60.[WoS]
• Béziau, J.-Y. (2006). The paraconsistent logic Z. A possible solution to Jaśkowski’s problem. Logic and Logical Philosophy, 15(2), 99-111.
• Chellas, B. F. (1980). Modal Logic: An Introduction. Cambridge: Cambridge University Press.
• Ciuciura, J. (2008). Negations in the Adjunctive Discursive Logic. Bulletin of the Section of Logic, 3 7(3-4), 143-160.
• Ciuciura, J. (2005). On the da Costa, Dubikajtis and Kotas’ system of the discursive logic, D∗ 2. Logic and Logical Philosophy, 14(2), 235-252.
• Cvetko-Vah, K. (2011). On Strongly Symmetric Skew Lattices. Algebra universalis, 66(1-2), 99-113. [WoS][Crossref]
• da Costa, N.C.A., & Dubikajtis, L. (1977). New Axiomatization for the Discussive Propositional Calculus. In A.I. Arruda, N.C.A. da Costa, & R. Chuaqui, (Eds), Non Classical Logics, Model Theory and Computability (pp. 45-55). Amsterdam: North-Holland Publishing.
• da Costa, N.C.A., & Dubikajtis, L. (1968). Sur la logique discursive de Jaśkowski. Bulletin de L’Académie Polonaise des Sciences (Série des sciences math., astr. et phys.), 16(7), 551-557.
• Hawranek, J. (1980). A Matrix Adequate for S5 with MP and RN. Bulletin of the Section of Logic, 9(3), 122-124.
• Hughes, G.E., & Cresswell, M. J. (1996). A New Introduction to Modal Logic. London: Routledge.
• Jaśkowski, S. (1948). Rachunek zdań dla systemow dedukcyjnych sprzecznych. Societatis Scientiarum Torunensis, Sect. A, I, 5, 57-77 (in Polish).
• Jaśkowski, S. (1969). Propositional Calculus for Contradictory Deductive Systems. Studia Logica, 24, 143-157 (the first English translation of (Jaśkowski, 1948)).
• Jaśkowski, S. (1999a). A Propositional Calculus for Inconsistent Deductive Systems. Logic and Logical Philosophy, 7(1), 35-56 (the second English translation of (Jaśkowski, 1948)).
• Jaśkowski, S. (1949). O koniunkcji dyskusyjnej w rachunku zdań dla systemow dedukcyjnych sprzecznych. Societatis Scientiarum Torunensis, Sect. A, I, 8, 171-172 (in Polish).
• Jaśkowski, S. (1999b). On the Discussive Conjuntion in the Propositional Calculus for Inconsistent Deductive Systems. Logic and Logical Philosophy, 7(1), 57-59 (English translation of (Jaśkowski, 1949)).
• Jordan, P. (1949). Uber Nichtkommutative Verb¨ande. Arch. Math., 2, 56-59.
• Kotas, J. (1975a). Discussive Sentential Calculus of Jaśkowski. Studia Logica, 34(2), 149-168.
• Kotas, J. (1971). On the algebra of classes of formulae of Jaśkowski’s discussive system. Studia Logica, 27(1), 81-90.
• Kotas, J. (1975b). On Quantity of Logical Values in the Discussive D2 System and in Modular Logic. Studia Logica, 33(3), 273-275.
• Kotas, J., & da Costa, N.C.A. (1977). On Some Modal Logical Systems Defined in Connexion with Jaśkowski’s Problem. In A.I. Arruda, N.C.A. da Costa, & R. Chuaqui (Eds). Non Classical Logics, Model Theory and Computability (pp. 57-73). Amsterdam: North-Holland Publishing.
• Leech, J. (1989). Skew lattices in rings. Alg. Universalis, 26, 48-72.
• Nasieniewski, M., & Pietruszczak, A. (2012). On the weakest modal logics defining Jaśkowski’s logic D2 and the D2-consequence. Bulletin of the Section of Logic, 41(3-4), 215-232.
• Priest, G., Tanaka, K., & Weber, Z. (1996). Paraconsistent Logic. In Zalta, E.N. (Principal Ed.). Stanford Encyclopedia of Philosophy, available at http://plato.stanford.edu/entries/logic-paraconsistent/
• Rasiowa, H., (1974). An algebraic approach to non-classical logics. Studies in Logic and the Foundations of Mathematics, vol. 78. North-Holland-Warszawa- Amsterdam: PWN.

Identifiers

DOI

10.1515/slgr-2015-0036