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Indian Conference on Logic and Its Applications

ICLA 2015: Logic and Its Applications pp 88–99Cite as

Neighborhood Contingency Logic

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 8923)

Abstract

A formula is contingent, if it is possibly true and possibly false; a formula is non-contingent, if it is not contingent, i.e., if it is necessarily true or necessarily false. In this paper, we propose a neighborhood semantics for contingency logic, in which the interpretation of the non-contingency operator is consistent with its philosophical intuition. Based on this semantics, we compare the relative expressivity of contingency logic and modal logic on various classes of neighborhood models, and investigate the frame definability of contingency logic. We present a decidable axiomatization for classical contingency logic (the obvious counterpart of classical modal logic), and demonstrate that for contingency logic, neighborhood semantics can be seen as an extension of Kripke semantics.

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  • DOI: 10.1007/978-3-662-45824-2_6
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References

  1. Areces, C., Figueira, D.: Which semantics for neighbourhood semantics? In: IJCAI, pp. 671–676 (2009)

    Google Scholar 

  2. Brogan, A.: Aristotle’s logic of statements about contingency. Mind 76(301), 49–61 (1967)

    CrossRef  Google Scholar 

  3. Chellas, B.F.: Modal Logic: An Introduction. Cambridge University Press (1980)

    Google Scholar 

  4. Cresswell, M.: Necessity and contingency. Studia Logica 47, 145–149 (1988)

    CrossRef  MATH  MathSciNet  Google Scholar 

  5. Fan, J., Wang, Y., van Ditmarsch, H.: Almost necessary. Advances in Modal Logic 10, 178–196 (2014)

    Google Scholar 

  6. Fan, J., Wang, Y., van Ditmarsch, H.: Contingency and knowing whether (to appear, 2014)

    Google Scholar 

  7. Hansen, H.H., Kupke, C., Pacuit, E.: Neighbourhood structures: Bisimilarity and basic model theory. Logical Methods in Computer Science 5(2), 1–38 (2009)

    CrossRef  MathSciNet  Google Scholar 

  8. van der Hoek, W., Lomuscio, A.: A logic for ignorance. Electronic Notes in Theoretical Computer Science 85(2), 117–133 (2004)

    CrossRef  Google Scholar 

  9. Ma, M., Sano, K.: How to update neighborhood models. In: Grossi, D., Roy, O., Huang, H. (eds.) LORI. LNCS, vol. 8196, pp. 204–217. Springer, Heidelberg (2013)

    CrossRef  Google Scholar 

  10. Montague, R.: Universal grammar. Theoria 36, 373–398 (1970)

    CrossRef  MathSciNet  Google Scholar 

  11. Montgomery, H., Routley, R.: Contingency and non-contingency bases for normal modal logics. Logique et Analyse 9, 318–328 (1966)

    MATH  MathSciNet  Google Scholar 

  12. Pacuit, E.: Neighborhood semantics for modal logic: An introduction. ESSLLI Lecture (2007), http://web.pacuit.org/papers/nbhdesslli.pdf

  13. Scott, D.: Advice on modal logic. In: Philosophical Problems in Logic: Some Recent Developments, pp. 143–173 (1970)

    Google Scholar 

  14. Steinsvold, C.: A note on logics of ignorance and borders. Notre Dame Journal of Formal Logic 49(4), 385–392 (2008)

    CrossRef  MATH  MathSciNet  Google Scholar 

  15. Wheeler, G.: AGM belief revision in monotone modal logics. In: Proc. of LPAR 2010 (2010)

    Google Scholar 

  16. Zolin, E.: Completeness and definability in the logic of noncontingency. Notre Dame Journal of Formal Logic 40(4), 533–547 (1999)

    CrossRef  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Philosophy, Peking University, China

    Jie Fan

  2. LORIA, CNRS, Université de Lorraine, France

    Hans van Ditmarsch

Authors
  1. Jie Fan
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  2. Hans van Ditmarsch
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, 208016, Kanpur, India

    Mohua Banerjee

  2. Department of Computer Science and Engineering, Indian Institute of Technology Bombay, Powai, 400076, Mumbai, India

    Shankara Narayanan Krishna

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Fan, J., van Ditmarsch, H. (2015). Neighborhood Contingency Logic. In: Banerjee, M., Krishna, S.N. (eds) Logic and Its Applications. ICLA 2015. Lecture Notes in Computer Science, vol 8923. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45824-2_6

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  • DOI: https://doi.org/10.1007/978-3-662-45824-2_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-45823-5

  • Online ISBN: 978-3-662-45824-2

  • eBook Packages: Computer ScienceComputer Science (R0)