A Note on Ciuciura’s mbC1

Hitoshi Omori

Bulletin of the Section of Logic (2019)

  • Volume: 48, Issue: 3, page 161-171
  • ISSN: 0138-0680

Abstract

top
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.

How to cite

top

Hitoshi Omori. "A Note on Ciuciura’s mbC1." Bulletin of the Section of Logic 48.3 (2019): 161-171. <http://eudml.org/doc/295519>.

@article{HitoshiOmori2019,
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.},
author = {Hitoshi Omori},
journal = {Bulletin of the Section of Logic},
keywords = {paraconsistent logic; non-deterministic semantics contra-classical logic},
language = {eng},
number = {3},
pages = {161-171},
title = {A Note on Ciuciura’s mbC1},
url = {http://eudml.org/doc/295519},
volume = {48},
year = {2019},
}

TY - JOUR
AU - Hitoshi Omori
TI - A Note on Ciuciura’s mbC1
JO - Bulletin of the Section of Logic
PY - 2019
VL - 48
IS - 3
SP - 161
EP - 171
AB - 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.
LA - eng
KW - paraconsistent logic; non-deterministic semantics contra-classical logic
UR - http://eudml.org/doc/295519
ER -

References

top
  1. A. Avron, Non-deterministic Matrices and Modular Semantics of Rules, [in:] J.-Y. Béziau (ed.), Logica Universalis, Birkhüser Verlag, 2005, pp. 149–167. 
  2. 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. 
  3. 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. 
  4. A. Avron and I. Lev, Non-Deterministic Multiple-valued Structures, Journal of Logic and Computation, Vol. 15, No. 3 (2005), pp. 241–261. 
  5. 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. 
  6. J. Cantwell, The Logic of Conditional Negation, Notre Dame Journal of Formal Logic, Vol. 49 (2008), pp. 245–260. 
  7. 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. 
  8. 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. 
  9. W. Carnielli, J. Marcos and S. de Amo, Formal Inconsistency and Evolutionary Databases, Logic and Logical Philosophy, Vol. 8 (2000), pp. 115–152. 
  10. J. Ciuciura, Paraconsistent heap. A Hierarchy of mbCn-systems, Bulletin of the Section of Logic, Vol. 43, No. 3/4 (2014), pp. 173–182. 
  11. L. Humberstone, Negation by iteration, Theoria, Vol. 61, No. 1 (1995), pp. 1–24. 
  12. L. Humberstone, Contra-classical logics, Australasian Journal of Philosophy, Vol. 78, No. 4 (2000), pp. 438–474. 
  13. N. Kamide, Paraconsistent Double Negations as Classical and Intuitionistic Negations, Studia Logica, Vol. 105, No. 6 (2017), pp. 1167–1191. 
  14. G. Olkhovikov, On a new three-valued paraconsistent logic, IfCoLog Journal of Logics and their Applications, Vol. 3, No. 3 (2016), pp. 317–334. 
  15. 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. 
  16. H. Omori, Sette’s Logics, Revisited, [in:] A. Baltag, J. Seligman and T. Yamada (eds.), Proceedings of LORI 2017, 2017, pp. 451–465. 
  17. 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. 
  18. F. Paoli, Bilattice Logics and Demi-Negation, [in:] Hitoshi Omori and Heinrich Wansing (eds.), New Essays on Belnap-Dunn Logic, Synthese Library, Springer, forthcoming. 
  19. A. Sette, On the propositional calculus P1, Mathematica Japonicae, Vol. 16 (1973), pp. 173–180. 
  20. 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/ 
  21. 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. 
  22. 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. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.