Journal of Philosophical Logic

, Volume 38, Issue 1, pp 83–125 | Cite as

Everything Else Being Equal: A Modal Logic for Ceteris Paribus Preferences

Article

Abstract

This paper presents a new modal logic for ceteris paribus preferences understood in the sense of “all other things being equal”. This reading goes back to the seminal work of Von Wright in the early 1960’s and has returned in computer science in the 1990’s and in more abstract “dependency logics” today. We show how it differs from ceteris paribus as “all other things being normal”, which is used in contexts with preference defeaters. We provide a semantic analysis and several completeness theorems. We show how our system links up with Von Wright’s work, and how it applies to game-theoretic solution concepts, to agenda setting in investigation, and to preference change. We finally consider its relation with infinitary modal logics.

Keywords

Ceteris paribus Preference logic Modal logic Dynamic logic Philosophy of action Game theory 

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References

  1. 1.
    van Benthem, J. (1987). Verisimilitude and conditionals. In T. Kuipers (Ed.), What is closer-to-the-truth? (pp. 103–128). Amsterdam: Rodopi.Google Scholar
  2. 2.
    van Benthem, J. (2007). Dynamic logic for belief revision. Journal of Applied Non-classical Logic, 17(2), 129–155.CrossRefGoogle Scholar
  3. 3.
    van Benthem, J. (2008). For better or for worse: Dynamic logics of preference. Tech. rep., ILLC, Prepublication Series, PP-2008-16, In T. Grüne-Yanoff, & S. O. Hansson (Eds.), Preference change, Springer, Dordrecht (in press).Google Scholar
  4. 4.
    van Benthem, J., & Liu, F. (2007). The dynamics of preference upgrade. Journal of Applied Non-Classical Logics, 17(2), 157–182.CrossRefGoogle Scholar
  5. 5.
    van Benthem, J., van Otterloo, S., & Roy, O. (2006). Preference logic, conditionals, and solution concepts in games. In H. Lagerlund, S. Lindström, & R. Sliwinski (Eds.), Modality matters: Twenty-five essays in honour of krister segerberg. Uppsala, Uppsala Philosophical Studies.Google Scholar
  6. 6.
    Blackburn, P., de Rijke, M., & Venema, Y. (2001). Modal logic. Cambridge: Cambridge University Press.Google Scholar
  7. 7.
    Boutilier, C. (1994). Toward a logic for qualitative decision theory. In J. Doyle, E. Sandewall, & P. Torasso (Eds.), Principles of knowledge representation and reasoning (pp. 75–86). citeseer.ist.psu.edu/boutilier92toward.html.
  8. 8.
    de Bruin, B. (2004). Explaining games: On the logic of game theoretic explanation. PhD thesis, Institute for Logic, Language and Computation (ILLC).Google Scholar
  9. 9.
    Cartwright, N. (1983). How the laws of physics lie. Oxford: Clarendon Press.Google Scholar
  10. 10.
    Castañeda, H. N. (1958). On the logic of ‘better’ review. Philosophy and Phenomenological Research, 19(2), 266.CrossRefGoogle Scholar
  11. 11.
    van Ditmarsch, H., Kooi, B., & van der Hoek, W. (2007). Dynamic epistemic logic. Synthese Library (Vol. 337). Heidelberg: Springer.Google Scholar
  12. 12.
    Doyle, J., & Wellman, M. P. (1994). Representing preferences as ceteris paribus comparatives. In Decision-theoretic planning: Papers from the 1994 Spring AAAI Symposium, AAAI Press, Menlo Park (pp. 69–75). citeseer.ist.psu.edu/doyle94representing.html.Google Scholar
  13. 13.
    Fodor, J. A. (1991). You can fool some of the people all of the time, everything else being equal; hedged laws and psychological explanations. Mind, 100(1), 19–34.CrossRefGoogle Scholar
  14. 14.
    Gabbay, D. M. (1981). An irreflexivity lemma with applications to axiomatizations of conditions on linear frames. In U. Mönnich (Ed.), Aspects of philosophical logic (pp. 67–89). Dordrecht: Reidel.Google Scholar
  15. 15.
    Girard, P. (2008). Modal logic for belief and preference change. PhD thesis, Stanford University.Google Scholar
  16. 16.
    Grüne-Yanoff, T., & Hansson, S. O. (Eds.) (2008). Preference change. Dordrectht: Springer (in press).Google Scholar
  17. 17.
    Halldén, S. (1957). On the logic of ‘better’. No. 2 in Library of Theoria. Lund: Library of Theoria.Google Scholar
  18. 18.
    Halpern, J. Y. (1997). Defining relative likelihood in partially-ordered preferential structure. Journal of Artificial Intelligence Research, 7, 1–24.Google Scholar
  19. 19.
    Hansson, S. O. (2001). Preference logic. In D. Gabbay, & F. Guenthner (Eds.), Handbook of philosophical logic (2nd ed.) (Vol. 4, chap. 4, pp. 319–393). Deventer: Kluwer.Google Scholar
  20. 20.
    Harrenstein, B. P., van der Hoek, W., Meyer, J. J. C., & Witteveen, C. (2003). A modal interpretation of nash-equilibrium. Fundamenta Informaticae, 2(4), 281–321.Google Scholar
  21. 21.
    Herzig, A., Lang, J., & Polacsek, T. (2000). A modal logic for epistemic tests. In Proceeding of ECAI’2000. Berlin.Google Scholar
  22. 22.
    Jennings, R. E. (1967). Preference and choice as logical correlates. Mind, 76(304), 556–567.CrossRefGoogle Scholar
  23. 23.
    Kozen, D., & Parikh, R. (1984). A decision procedure for the propositional μ-calculus. In Proceedings of the carnegie mellon workshop on logic of programs (pp. 313–325). London: Springer-Verlag.Google Scholar
  24. 24.
    Lakatos, I. (1978). The methodology of scientific research programmes (Vol. 1). Cambridge: Cambridge University Press.Google Scholar
  25. 25.
    Lang, J., van der, Torre, L., & Weydert, E. (2003). Hidden uncertainty in the logical representation of desires. In Proceedings of eighteenth international joint conference on artificial intelligence (IJCAI’03). citeseer.ist.psu.edu/667828.html.
  26. 26.
    Liu, F. (2008). Changing for the better: Preference dynamics and agent diversity. PhD thesis, Institute for logic, language and computation (ILLC).Google Scholar
  27. 27.
    Liu, F., & de Jongh, D. (2006). Optimality, belief and preference. Tech. rep., ILLC, Prepublication Series, PP-2006-38.Google Scholar
  28. 28.
    Murakami, Y. (1968). Logic and social choice. Monographs in modern logic. Mineola: Dover.Google Scholar
  29. 29.
    Olsson, E. J., & Westlund, D. (2006). On the role of the research agenda in epistemic change. Erkenntnis, 65(2), 165–183.CrossRefGoogle Scholar
  30. 30.
    van Otterloo, S. (2005). A strategic analysis of multi-agent protocols. PhD thesis, University of Liverpool.Google Scholar
  31. 31.
    Persky, J. (1990). Retrospectives: Ceteris paribus. The Journal of Economic Perspectives, 4(2), 187–193.Google Scholar
  32. 32.
    Roy, O. (2008). Thinking before acting: Intentions, logic, rational choice. PhD thesis, Institute for logic, language and computation (ILLC).Google Scholar
  33. 33.
    Schiffer, S. (1991). Ceteris paribus laws. Mind, 100(1), 1–17.CrossRefGoogle Scholar
  34. 34.
    Segerberg, K. (1971). An essay in classical modal logic. Filosofiska Studier, (Vol. 13). Uppsala: Filosofiska föreningen och Filosofiska institutionen vid Uppsala universitet.Google Scholar
  35. 35.
    Väänänen, J. (2007). Dependence logic: A new approach to independence friendly logic, London Mathematical Society Student Texts. Cambridge: Cambridge University Press.Google Scholar
  36. 36.
    von Wright, G. H. (1963). The logic of preference. Edinburgh: Edinburgh University Press.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Johan van Benthem
    • 1
    • 2
  • Patrick Girard
    • 2
    • 3
  • Olivier Roy
    • 1
    • 4
  1. 1.Institute for Logic, Language and ComputationUniversity of AmsterdamAmsterdamThe Netherlands
  2. 2.Stanford UniversityStanfordUSA
  3. 3.University of AucklandAucklandNew Zealand
  4. 4.Faculty of PhilosophyUniversity of GroningenGroningenThe Netherlands

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