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Studia Logica

, Volume 103, Issue 2, pp 239–263 | Cite as

In the Mood for S4: The Expressive Power of the Subjunctive Modal Language in Weak Background Logics

  • Rohan FrenchEmail author
Article

Abstract

Our concern here is with the extent to which the expressive equivalence of Wehmeier’s Subjunctive Modal Language (SML) and the Actuality Modal Language (AML) is sensitive to the choice of background modal logic. In particular we will show that, when we are enriching quantified modal logics weaker than S5, AML is strictly expressively stronger than SML, this result following from general considerations regarding the relationship between operators and predicate markers. This would seem to complicate arguments given in favour of SML which rely upon its being expressively equivalent to AML.

Keywords

Expressive power Actuality operator Subjunctive modal logic 

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References

  1. 1.
    Armstrong, D., A Combinatorial Theory of Possibility, Cambridge University Press, New York, 1989.Google Scholar
  2. 2.
    Bonnay D., Egré P.: Inexact knowledge with introspection. Journal of Philosophical Logic 38, 179–227 (2009)CrossRefGoogle Scholar
  3. 3.
    Chellas, B. F., Modal Logic: An Introduction, Cambridge University Press, Cambridge, 1980.Google Scholar
  4. 4.
    French R.: An argument against general validity?. Thought 1, 4–9 (2012)Google Scholar
  5. 5.
    French R.: Expressive power, mood, and actuality. Synthese 190, 1689–1699 (2013)CrossRefGoogle Scholar
  6. 6.
    Gabbay, D. M., V. Shehtman, and D. Skvortsov, Quantification in Nonclassical Logic Volume 1, Studies in Logic and the Foundations of Mathematics, Elsevier Amsterdam, 2009.Google Scholar
  7. 7.
    Gregory D.: Completeness and decidability results for some propositional modal logics containing “Actually” operators. Journal of Philosophical Logic. 30, 57–78 (2001)CrossRefGoogle Scholar
  8. 8.
    Hazen A. P., B. G. Rin, Wehmeier K. F.: Actuality in propositional modal logic. Studia Logica 101, 487–503 (2013)CrossRefGoogle Scholar
  9. 9.
    Humberstone L.: Scope and subjunctivity. Philosophia 12, 99–126 (1982)CrossRefGoogle Scholar
  10. 10.
    Humberstone L.: Two-dimensional adventures. Philosophical Studies 118, 17–65 (2004)CrossRefGoogle Scholar
  11. 11.
    Kamp H.: Formal Properties of ‘Now’. Theoria 37, 227–273 (1971)CrossRefGoogle Scholar
  12. 12.
    Lewis D. K.: Counterfactuals and comparative possibility. Journal of Philosophical Logic 2, 418–446 (1973)CrossRefGoogle Scholar
  13. 13.
    Linksy B., Zalta E.: In defense of the simplest quantified modal logic. Philosophical Perspectives 8, 431–458 (1994)CrossRefGoogle Scholar
  14. 14.
    Salmon N.: The logic of what might have been. Philosophical Review. 98, 3–34 (1989)CrossRefGoogle Scholar
  15. 15.
    Stephanou Y.: Indexed actuality. Journal of Philosophical Logic 30, 355–393 (2001)CrossRefGoogle Scholar
  16. 16.
    Stephanou Y.: First-order modal logic with an ‘Actually’ operator. Notre Dame Journal of Formal Logic 46, 381–405 (2005)CrossRefGoogle Scholar
  17. 17.
    Wehmeier, K. F., World travelling and mood swings, in B. Löwe, T. Räsch, and W. Malzkorn, (eds.), Foundations of the Formal Sciences II, Kluwer, 2003, pp. 257–260.Google Scholar
  18. 18.
    Wehmeier K. F.: In the mood. Journal of Philosophical Logic. 33, 607–630 (2004)CrossRefGoogle Scholar
  19. 19.
    Wehmeier, K. F., Modality, mood, and descriptions, in R. Kahle, (ed.), Intensionality—an Interdisciplinary Discussion, AK Peters, Wellesley, Mass., 2005, pp. 187–216.Google Scholar
  20. 20.
    Wehmeier K. F.: Subjunctivity and cross-world predication. Philosophical Studies. 159, 107–122 (2012)CrossRefGoogle Scholar
  21. 21.
    Wehmeier K. F.: Subjunctivity and conditionals. The Journal of Philosophy 110, 117–142 (2013)Google Scholar
  22. 22.
    Williamson T.: Bare possibilia. Erkenntnis 48, 257–273 (1998)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of PhilosophyMonash UniversityClaytonAustralia

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