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A simple modal logic for belief revision

Author

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  • Giacomo Bonanno

    (Department of Economics, University of California Davis)

Abstract

We propose a logic based on three modal operators, representing intial beliefs, information and revised beliefs. Three simple and transparent axioms are used to provide a sound and complete axiomatization of the qualitative part of Bayes'' rule. Some theorems of this logic are derived concerning the interaction between current beliefs and future beliefs. Information flows and iterated revision are also discussed.

Suggested Citation

  • Giacomo Bonanno, 2004. "A simple modal logic for belief revision," Working Papers 164, University of California, Davis, Department of Economics.
    • Handle: RePEc:cda:wpaper:164
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    File URL: https://repec.dss.ucdavis.edu/files/uYgdYbJoFVpXk4DZFxbafxM5/04-5.pdf
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    References listed on IDEAS

    as
    1. Battigalli, Pierpaolo & Bonanno, Giacomo, 1999. "Recent results on belief, knowledge and the epistemic foundations of game theory," Research in Economics, Elsevier, vol. 53(2), pages 149-225, June.
    2. Fudenberg, Drew & Tirole, Jean, 1991. "Perfect Bayesian equilibrium and sequential equilibrium," Journal of Economic Theory, Elsevier, vol. 53(2), pages 236-260, April.
    3. Battigalli, Pierpaolo & Bonanno, Giacomo, 1997. "The Logic of Belief Persistence," Economics and Philosophy, Cambridge University Press, vol. 13(1), pages 39-59, April.
    4. Board, Oliver, 2004. "Dynamic interactive epistemology," Games and Economic Behavior, Elsevier, vol. 49(1), pages 49-80, October.
    5. Battigalli, Pierpaolo, 1996. "Strategic Independence and Perfect Bayesian Equilibria," Journal of Economic Theory, Elsevier, vol. 70(1), pages 201-234, July.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Giacomo Bonanno, 2005. "Temporal interaction of information and belief," Working Papers 541, University of California, Davis, Department of Economics.
    2. Billot, Antoine & Vergnaud, Jean-Christophe & Walliser, Bernard, 2015. "Multiagent belief revision," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 47-57.
    3. Giacomo Bonanno, 2007. "Four Logics for Minimal Belief Revision," Working Papers 209, University of California, Davis, Department of Economics.
    4. Giacomo Bonanno, 2006. "Axiomatization of the AGM theory of belief revision in a temporal logic," Working Papers 254, University of California, Davis, Department of Economics.
    5. Antoine Billot & Jean-Christophe Vergnaud & Bernard Walliser, 2008. "Multiplayer belief revision," Post-Print halshs-00344461, HAL.
    6. Giacomo Bonanno, 2005. "Temporal interaction of information and belief," Working Papers 141, University of California, Davis, Department of Economics.
    7. Giacomo Bonanno, 2007. "Four Logics for Minimal Belief Revision," Working Papers 76, University of California, Davis, Department of Economics.

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    More about this item

    Keywords

    Bayes rule; belief revision; intertemporal beliefs;
    All these keywords.

    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other

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