A Note on Ciuciura’s mbC1

Authors

  • Hitoshi Omori Ruhr-Universität Bochum, Department of Philosophy I

DOI:

https://doi.org/10.18778/0138-0680.48.3.01

Keywords:

paraconsistent logic, non-deterministic semantics contra-classical logic

Abstract

This note offers a non-deterministic semantics for mbC1, introduced by Janusz Ciuciura, and establishes soundness and (strong) completeness results with respect to the Hilbert-style proof system. Moreover, based on the new semantics, we briefly discuss an unexplored variant of mbC1 which has a contra-classical flavor.

References

A. Avron, Non-deterministic Matrices and Modular Semantics of Rules, [in:] J.-Y. Béziau (ed.), Logica Universalis, Birkhüser Verlag, 2005, pp. 149–167.
Google Scholar

A. Avron, Non-deterministic Semantics for Families of Paraconsistent Logics, [in:] J. Y. Béziau, W. A. Carnielli and D. Gabbay (eds.), Handbook of Paraconsistency, College Publications, 2007, pp. 285–320.
Google Scholar

A. Avron and B. Konikowska, Multi-valued calculi for logics based on non-determinism, Logic Journal of IGPL, Vol. 13, No. 4 (2005), pp. 365–387.
Google Scholar

A. Avron and I. Lev, Non-Deterministic Multiple-valued Structures, Journal of Logic and Computation, Vol. 15, No. 3 (2005), pp. 241–261.
Google Scholar

A. Avron and A. Zamansky, Non-Deterministic Semantics for Logical Systems, [in:] D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, Vol. 16, Springer, 2011, pp. 227–304.
Google Scholar

J. Cantwell, The Logic of Conditional Negation, Notre Dame Journal of Formal Logic, Vol. 49 (2008), pp. 245–260.
Google Scholar

W. Carnielli, M. Coniglio and J. Marcos, Logics of Formal Inconsistency, [in:] D. Gabbay and F. Guenthner (eds.), Handbook of Philosphical Logic, Vol. 14, Dordrecht: Springer-Verlag, 2007, pp. 1–93.
Google Scholar

W. Carnielli and J. Marcos, A Taxonomy of C-systems, [in:] W. A. Carnielli and M. E. Coniglio and I. M. L. d’Ottaviano (eds.), Paraconsistency: The Logical Way to the Inconsistent, Proceedings of the II World Congress on Paraconsistency, Marcel Dekker, 2002, pp. 1–94.
Google Scholar

W. Carnielli, J. Marcos and S. de Amo, Formal Inconsistency and Evolutionary Databases, Logic and Logical Philosophy, Vol. 8 (2000), pp. 115–152.
Google Scholar

J. Ciuciura, Paraconsistent heap. A Hierarchy of mbCn-systems, Bulletin of the Section of Logic, Vol. 43, No. 3/4 (2014), pp. 173–182.
Google Scholar

L. Humberstone, Negation by iteration, Theoria, Vol. 61, No. 1 (1995), pp. 1–24.
Google Scholar

L. Humberstone, Contra-classical logics, Australasian Journal of Philosophy, Vol. 78, No. 4 (2000), pp. 438–474.
Google Scholar

N. Kamide, Paraconsistent Double Negations as Classical and Intuitionistic Negations, Studia Logica, Vol. 105, No. 6 (2017), pp. 1167–1191.
Google Scholar

G. Olkhovikov, On a new three-valued paraconsistent logic, IfCoLog Journal of Logics and their Applications, Vol. 3, No. 3 (2016), pp. 317–334.
Google Scholar

H. Omori, From paraconsistent logic to dialetheic logic, [in:] Holger Andreas and Peter Verd´ee (eds.), Logical Studies of Paraconsistent Reasoning in Science and Mathematics, Springer, 2016, pp. 111–134.
Google Scholar

H. Omori, Sette’s Logics, Revisited, [in:] A. Baltag, J. Seligman and T. Yamada (eds.), Proceedings of LORI 2017, 2017, pp. 451–465.
Google Scholar

H. Omori and H. Wansing, On Contra-classical variants of Nelson logic N4 and its classical extension, The Review of Symbolic Logic, Vol. 11, No. 4 (2018), pp. 805–820.
Google Scholar

F. Paoli, Bilattice Logics and Demi-Negation, [in:] Hitoshi Omori and Heinrich Wansing (eds.), New Essays on Belnap-Dunn Logic, Synthese Library, Springer, forthcoming.
Google Scholar

A. Sette, On the propositional calculus P1, Mathematica Japonicae, Vol. 16 (1973), pp. 173–180.
Google Scholar

W. Heinrich, Connexive Logic, [in:] Edward N. Zalta, The Stanford Encyclopedia of Philosophy, 2014, Fall 2014, http://plato.stanford.edu/archives/fall2014/entries/logic-connexive/
Google Scholar

T. Waragai and H. Omori, Some New Results on PCL1 and its Related Systems, Logic and Logical Philosophy, Vol. 19, No. 1/2 (2010), pp. 129–158.
Google Scholar

T. Waragai and T. Shidori, 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, [in:] J.-Y. B´eziau, W. A. Carnielli and D. Gabbay (eds.), Handbook of Paraconsistency, 2007, College Publications, pp. 177–187.
Google Scholar

Downloads

Published

2019-10-30

How to Cite

Omori, H. (2019). A Note on Ciuciura’s mbC1. Bulletin of the Section of Logic, 48(3), 161–171. https://doi.org/10.18778/0138-0680.48.3.01

Issue

Section

Research Article