Some new results on PCL1 and its related systems

Toshiharu Waragai, Hitoshi Omori

DOI: http://dx.doi.org/10.12775/LLP.2010.006

Abstract


In [Waragai & Shidori, 2007], a system of paraconsistent logic called PCL1, which takes a similar approach to that of da Costa, is proposed. The present paper gives further results on this system and its related systems. Those results include the concrete condition to enrich the system PCL1 with the classical negation, a comparison of the concrete notion of “behaving classically” given by da Costa and by Waragai and Shidori, and a characterisation of the notion of “behaving classically” given by Waragai and Shidori.

Keywords


paraconsistent logic; classical negation; da Costa's system C1

Full Text:

PDF

References


Arruda, A.I., 1980, “A survey of paraconsistent logic”, pp. 1–41 in: A.I. Arruda, R. Chuaqui, and N.C.A. da Costa (eds.), Mathematical Logic in Latin America: Proc. of the 4th Latin American Symposium on Mathematical Logic, North-Holand.

Béziau, J.-Y., 2002, “Are paraconsistent negations negations?”, pp. 465–486 in: W.A. Carnielli, M.E. Coniglio, and I.M.L. D’Ottaviano (eds.), Paraconsistency: The Logical Way to the Inconsistent, Proc. of the II World Congress on Paraconsistency, Marcel Dekker.

Carnielli, W.A., M.E. Coniglio, J. Marcos, 2005, “Logics of formal inconsistency”, pp. 1–93 in: D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic.

Carnielli, W.A., and J. Marcos, 1999, “Limits for paraconsistent calculi”, Notre Dame Journal of Formal Logic 40, 3: 375–390.

Carnielli, W.A., J. Marcos, 2002, “A taxonomy of C-systems”, pp. 1–94 in: W.A. Carnielli, M.E. Coniglio, and I.M.L. D’Ottaviano (eds.), Paraconsistency: The Logical Way to the Inconsistent, Proc. of the II World Congress on Paraconsistency, Marcel Dekker.

da Costa, N.C.A., 1974, “On the theory of inconsistent formal systems”, Notre Dame Journal of Formal Logic 15, 4: 497–510.

da Costa, N.C.A., and M. Guillaume, 1965, “Négations composées et loi de Peirce dans les systèmes C n ”, Portugaliae Mathematica 24, 4: 201–210.

Guillaume, M., 2007, “Da Costa 1964 logical seminar: revised memories”, pp. 3–62 in: J.-Y. Béziau, W.A. Carnielli and D. Gabbay (eds.), Handbook of Paraconsistency, College Publications.

Jaśkowski, S., 1948, “Rachunek zdań dla systemów dedukcyjnych sprzecznych”, Studia Societatis Scientiarum Torunensis, Sectio A, Vol. I, No. 5: 57–77.

Jaśkowski, S., 1949, “O koniunkcji dyskusyjnej w rachunku zdań dla systemów dedukcyjnych sprzecznych”, Studia Societatis Scientiarum Torunensis, Sectio A, Vol. I, No. 8: 171–172.

Jaśkowski, S., 1999, “A propositional calculus for inconsistent deductive systems”, Logic and Logical Philosophy 7: 35–56; translation of [Jaśkowski, 1948] by O. Wojtasiewicz with corrections and notes by J. Perzanowski.

Jaśkowski, S., 1999, “On the discussive conjunction in the propositional calculus for inconsistent deductive systems”, Logic and Logical Philosophy 7: 57–59; translation of [Jaśkowski, 1949] by J. Perzanowski.

Kleene, S.C., 1967, Introduction to Metamathematics, Amsterdam, North-Holland.

Kotas, J., 1975, “Discussive sentential calculus of Jaśkowski”, Studia Logica 34, 2: 149–168.

Marcos, J., 2005a, “Modality and paraconsistency”, pp. 213–222 in: M. Bilvoka and L. Behounek (eds.), The Logica Yearbook 2004, Filosofia.

Marcos, J., 2005b, “Nearly every normal modal logic is paranormal”, Logique et Analyse 48: 279–300.

Marcos, J., 2005c, “On a problem of da Costa”, pp. 53–69 in: G. Sica (ed.), Essays on the Foundations of Mathematics and Logic, vol. 2, Monza: Polimetrica.

Omori, H., and T. Waragai, 2010, “Propagation of consistency in some systems of paraconsistent logic”, to be presented to LRR10, Ghent, Belgium.

Priest, G., and R. Routley, 1984, “Introduction: Paraconsistent Logics”, Studia Logica 43, 1–2: 3–16.

Rasiowa, H., and R. Sikorski, 1970, The Mathematics of Metamathematics, Warszawa, Polish Scientific Publishers.

Urbas, I., 1989, “Paraconsistency and the C-systems of da Costa”, Notre Dame Journal of Formal Logic 30, 4: 583–597.

Waragai, T., and T. Shidori, 2007, “A system of paraconsistent logic that has the notion of ‘behaving classically’ in terms of the law of double negation and its relation to S5”, pp. 177–187 in: J.-Y. Béziau, W.A. Carnielli and D. Gabbay (eds.), Handbook of Paraconsistency, College Publications.








Print ISSN: 1425-3305
Online ISSN: 2300-9802

Partnerzy platformy czasopism