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Synthese

, Volume 193, Issue 1, pp 1–14 | Cite as

Paraconsistent dynamics

  • Patrick Girard
  • Koji Tanaka
Article

Abstract

It has been an open question whether or not we can define a belief revision operation that is distinct from simple belief expansion using paraconsistent logic. In this paper, we investigate the possibility of meeting the challenge of defining a belief revision operation using the resources made available by the study of dynamic epistemic logic in the presence of paraconsistent logic. We will show that it is possible to define dynamic operations of belief revision in a paraconsistent setting.

Keywords

Paraconsistent logic Dynamic epistemic logic Public announcement Belief revision 

References

  1. Arieli, O., Avron, A., & Zamansky, A. (2011). Ideal paraconsistent logics. Studia Logica, 99, 31–60.CrossRefGoogle Scholar
  2. Avron, A. (1986). On an implication connective of RM. Notre Dame Journal of Formal Logic, 27, 201–209.CrossRefGoogle Scholar
  3. Baltag, A., & Smets, S. (2008). A qualitative theory of dynamic interactive belief revision. Text in Logic and Games, 3, 9–58.Google Scholar
  4. Beall, J., Forster, T., & Seligman, J. (2013). A mote on freedom from detachment in the logic of paradox. Notre Dame Journal of Formal Logic, 54(1), 15–20.CrossRefGoogle Scholar
  5. Brown, B., & Priest, G. (2004). Chunk and permeate—part I: The infinitesimal calculus. Journal of Philosophical Logic, 33, 379–388.CrossRefGoogle Scholar
  6. D’Ottaviano, I. M. L., & da Costa, N. (1970). Sur un problème de Jaśkowski. Comptes Rendus de l’Académie des Sciences de Paris, 270, 1349–1353.Google Scholar
  7. Fagin, R., Halpern, J., Moses, Y., & Vardi, M. (1995). Reasoning about knowledge. Cambridge: MIT Press.Google Scholar
  8. Girard, P., & Rott, H. (2014). Belief revision and dynamic logic. In A. Baltag & S. Smets (Eds.), Johan van Benthem on logic and information dynamics. Dordrecht: Springer.Google Scholar
  9. Kooi, B. (2007). Expressivity and completeness for public update logics via reductions axioms. Journal of Applied Non-Classical Logics, 17(2), 231–253.CrossRefGoogle Scholar
  10. Mares, E. (2002). A paraconsistent theory of belief revision. Erkenntnis, 56, 229–246.CrossRefGoogle Scholar
  11. Priest, G. (1979). Logic of paradox. Journal of Philosophical Logic, 8, 219–241.CrossRefGoogle Scholar
  12. Priest, G. (1987). In contradiction. Dordrecht: Martinus Nijhoff Publishers.CrossRefGoogle Scholar
  13. Priest, G. (2002). Paraconsistent logic. In D. Gabbay & F. Guenthner (Eds.), Handbook of philosophical logic (2nd ed., pp. 287–393). Dordrecht: Kluwer Academic Publishers.CrossRefGoogle Scholar
  14. Priest, G. (2006). Doubt truth to be a liar. Oxford: Oxford University Press.Google Scholar
  15. Priest, G. (2008). An introduction to non-classical logic (2nd ed.). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  16. Priest, G., Tanaka, K., & Weber, Z. (2013). Paraconsistent logic. In N. Z. Edward (Ed.), Stanford encyclopedia of philosophy. Stanford: Stanford University.Google Scholar
  17. Plaza, J. (2007). Logics of public communications. Synthese, 158(2), 165–179.CrossRefGoogle Scholar
  18. Pratt VR. (1976). Semantical considerations on Floyd-Hoare Logic. Proceedings of the 17th Annual IEEE symposium on foundations of computer science, pp. 109–121.Google Scholar
  19. Restall G, & Slaney J. (1995). Realistic belief revision, Proceedings of the second world conference on foundations of artificial intelligence, pp. 367–378.Google Scholar
  20. Rott, H. (2009). Towards mathematical philosophy. Shifting priorities: Simple representations for twenty-seven iterated theory change operators (pp. 269–296). Dordrecht: Springer.Google Scholar
  21. Tanaka, K. (2005). The AGM theory and inconsistent belief change. Logique et Analyse, 48, 113–150.Google Scholar
  22. van Benthem J. (2006). One is a lonely number: On the logic of communication. In Z. Chatzidakis, P. Koepke, W. Pohlers (Eds.), Logic colloquium ‘02, vol. 27 of lecture notes in logic. Association for Symbolic Logic: Poughkeepsie.Google Scholar
  23. van Benthem, J. (2007). Dynamic logic for belief revision. Journal of Applied Non-Classical Logics, 17, 1–27.Google Scholar
  24. Wassermann, R. (2011). On AGM for non-classical logics. Journal of Philosophical Logic, 40, 271–294.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of AucklandAucklandNew Zealand
  2. 2.School of PhilosophyAustralian National UniversityCanberraAustralia

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