Abstract
We introduce a notion of bisimulation for contingency logic interpreted on neighbourhood structures, characterise this logic as bisimulation-invariant fragment of modal logic and of first-order logic, and compare it with existing notions in the literature.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Brogan, A.P.: Aristotle’s logic of statements about contingency. Mind 76(301), 49–61 (1967)
Chellas, B.F.: Modal Logic, An Intoduction. Cambridge University Press, Cambridge (1980)
Cirstea, C., Kurz, A., Pattinson, D., Schröder, L., Venema, Y.: Modal logics are coalgebraic. Comput. J. 54(1), 31–41 (2008)
Fan, J.: Logical studies for non-contingency operator. Ph.D. thesis, Peking University (2015). (in Chinese)
Fan, J.: A note on non-contingency logic (manuscript) (2016). https://www.researchgate.net/publication/305091939
Fan, J., van Ditmarsch, H.: Neighborhood contingency logic. In: Banerjee, M., Krishna, S.N. (eds.) ICLA 2015. LNCS, vol. 8923, pp. 88–99. Springer, Heidelberg (2015). doi:10.1007/978-3-662-45824-2_6
Fan, J., Wang, Y., van Ditmarsch, H.: Almost necessary. In: Proceedings of 10th Advances in Modal Logic (AiML), pp. 178–196 (2014)
Fan, J., Wang, Y., van Ditmarsch, H.: Contingency and knowing whether. Rev. Symbolic Logic 8(1), 75–107 (2015)
Hansen, H.H., Kupke, C., Pacuit, E.: Neighbourhood structures: bisimilarity and basic model theory. Logical Methods Comput. Sci. 5(2) (2009). (paper 2)
van der Hoek, W., Lomuscio, A.: A logic for ignorance. Electron. Notes Theor. Comput. Sci. 85(2), 117–133 (2004)
Humberstone, L.: The logic of non-contingency. Notre Dame J. Formal Logic 36(2), 214–229 (1995)
Kuhn, S.: Minimal non-contingency logic. Notre Dame J. Formal Logic 36(2), 230–234 (1995)
Montague, R.: Universal grammar. Theoria 36, 373–398 (1970)
Montgomery, H., Routley, R.: Contingency and non-contingency bases for normal modal logics. Logique et Analyse 9, 318–328 (1966)
Pattinson, D.: Coalgebraic modal logic: soundness, completeness and decidability of local consequence. Theor. Comput. Sci. 309(1–3), 177–193 (2003)
Pizzi, C.: Contingency logics and propositional quantification. Manuscrito 22(2), 283 (1999)
Scott, D.: Advice on modal logic. In: Lambert, K. (ed.) Philosophical Problems in Logic: Some Recent Developments, pp. 143–173. Kluwer, Dordrecht (1970)
Steinsvold, C.: A note on logics of ignorance and borders. Notre Dame J. Formal Logic 49(4), 385–392 (2008)
Wang, Y.: Beyond knowing that: a new generation of epistemic logics. In: van Ditmarsch, H., Sandu, G. (eds.) Jaakko Hintikka on Knowledge and Game Theoretical Semantics. Outstanding Contributions to Logic. Springer (2016, to appear)
Zolin, E.: Completeness and definability in the logic of noncontingency. Notre Dame J. Formal Logic 40(4), 533–547 (1999)
Acknowledgments
Zeinab Bakhtiari and Hans van Ditmarsch gratefully acknowledge support from European Research Council grant EPS 313360. We thank Jie Fan, Yanjing Wang and the anonymous referees for their comments which helped improve the paper substantially.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer-Verlag GmbH Germany
About this paper
Cite this paper
Bakhtiari, Z., van Ditmarsch, H., Hansen, H.H. (2017). Neighbourhood Contingency Bisimulation. In: Ghosh, S., Prasad, S. (eds) Logic and Its Applications. ICLA 2017. Lecture Notes in Computer Science(), vol 10119. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-54069-5_5
Download citation
DOI: https://doi.org/10.1007/978-3-662-54069-5_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-54068-8
Online ISBN: 978-3-662-54069-5
eBook Packages: Computer ScienceComputer Science (R0)