Advertisement

The Logic of Obligation as Weakest Permission

(Short Version)
  • Olivier Roy
  • Albert J. J. Anglberger
  • Norbert Gratzl
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7393)

Abstract

This paper studies the following interpretation of obligations: A person i ought to do A in a situation S just in case everything else i may (and can) do in S is consistent with A. In such a case A can be called the weakest permission that i has in S. We show that, under this interpretation, obligation and permission are not dual notions, and that it gives rise to an interesting interplay between deontic and alethic notions. We also discuss the logics adequacy w.r.t. the paradoxes of (classic) deontic logic and provide a sound and complete axiomatization for it. We finally show that practical, rational recommendations in games provide a natural, concrete application of such an understanding of obligations and permissions.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Anderson, A.R.: A Reduction of Deontic Logic to Alethic Modal Logic. Mind 67, 100–103 (1958)CrossRefGoogle Scholar
  2. 2.
    Aumann, R.J.: Interactive epistemology I: Knowledge. International Journal of Game Theory 28, 263–300 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Bacharach, M.: Beyond Individual Choices: Teams and Frames in Game Theory, Gold, N., Sugden, R. (eds.). Princeton University Press, Princeton (2006) Google Scholar
  4. 4.
    Blackburn, P., van Benthem, J., Wolter, F. (eds.): Handbook of Modal Logic. Elsevier (November 2006)Google Scholar
  5. 5.
    Braham, M., van Hees, M.: The Formula of Universal Law: A Reconstruction. Working paper (2011)Google Scholar
  6. 6.
    Brandenburger, A.: The power of paradox: some recent developments in interactive epistemology. International Journal of Game Theory 35, 465–492 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Brink, D.O.: Moral conflict and its structure. The Philosophical Review 103(2), 215–247 (1994)CrossRefGoogle Scholar
  8. 8.
    Chellas, B.F.: Modal Logic: An Introduction. Cambridge University Press (1980)Google Scholar
  9. 9.
    Donagan, A.: Consistency in rationalist moral systems. The Journal of Philosophy 81(6), 291–309 (1984)CrossRefGoogle Scholar
  10. 10.
    Finetti, B.: Theory of Probability, vol. 1 and 2. Wiley, New York (1974)zbMATHGoogle Scholar
  11. 11.
    Hansson, S.O.: Semantics for more plausible deontic logics. Journal of Applied Logic 2, 3–18 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Horty, J.: Reasons as defaults. To appear at Oxford UP (2011)Google Scholar
  13. 13.
    Kooi, B., Tamminga, A.: Moral conflicts between groups of agents. Journal of Philosophical Logic 37(1), 1–21 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    McNamara, P.: Deontic logic. In: Zalta, E.N. (ed.) Standford Encyclopedia of Philosophy, Spring edn. (2006), http://plato.stanford.edu/archives/spr2006/entries/logic-deontic/
  15. 15.
    Meyer, J.-J.C.: A simple solution to the “deepest” paradox in deontic logic. Logique et Analyse 117-118, 81–90 (1987)Google Scholar
  16. 16.
    Meyer, J.-J.C.: A different approach to Deontic Logic: Deontic Logic Viewed as a Variant of Dynamic Logic. Notre Dame Journal of Formal Logic 29, 109–136 (1988)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Roy, O., Pacuit, E.: Interactive rationality and the dynamics of reasons. Under Review (2011)Google Scholar
  18. 18.
    Tamminga, A.: Deontic logic for strategic games. Erkenntnis, 1–18, doi:10.1007/s10670-011-9349-0Google Scholar
  19. 19.
    van Benthem, J.: Logical Dynamics of Information and Interaction. Cambridge University Press (2010)Google Scholar
  20. 20.
    van Benthem, J., Grossi, D., Liu, F.: Deontics = Betterness + Priority. In: Governatori, G., Sartor, G. (eds.) DEON 2010. LNCS, vol. 6181, pp. 50–65. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  21. 21.
    von Wright, G.H.: Deontic Logic. Mind 60, 1–15 (1951)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Olivier Roy
    • 1
  • Albert J. J. Anglberger
    • 1
  • Norbert Gratzl
    • 1
  1. 1.Munich Center for Mathematical PhilosophyLMU MunichGermany

Personalised recommendations