Abstract
We propose a modal logic based on three operators, representing intial beliefs, information and revised beliefs. Three simple 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.
I am grateful to two anonymous reviewers for helpful and constructive comments. A first draft of this paper was presented at the Sixth Conference on Logic and the Foundations of Game and Decision Theory (LOFT6), Leipzig, July 2004.
I am grateful to two anonymous reviewers for helpful and constructive comments. A first draft of this paper was presented at the Sixth Conference on Logic and the Foundations of Game and Decision Theory (LOFT6), Leipzig, July 2004.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alchourron, C., P. Gärdenfors and D. Makinson: 1985, ‘On the Logic of Theory Change; Partial Meet Contraction and Revision Functions’, The Journal of Symbolic Logic 50, 510–530.
Battigalli, P.: 1996, ‘Strategic Independence and Perfect Bayesian Equilibria’, Journal of Economic Theory 70, 201–234.
Battigalli, P. and G. Bonanno: 1992, ‘The Logic of Belief Persistence’, Economics and Philosophy 13, 39–59.
Battigalli, P. and G. Bonanno: 1999, ‘Recent Results on Belief, Knowledge and the Epistemic Foundations of Game Theory’, Research in Economics 53, 149–225.
Blackburn, P., M. de Rijke, and Y. Venema: 2001, Modal Logic, Cambridge University Press.
Board, O.: 2004, ‘Dynamic Interactive Epistemology’, Games and Economic Behavior 49, 49–80.
Bonanno, G.: 1993, ‘Rational Belief Equilibria’, Economic Notes 22, 430–463.
Brown, P. M.: 1976, ‘Conditionalization and Expected Utility’, Philosophy of Science 43, 415–419.
Chellas, B.: 1984, Modal Logic; An Introduction, Cambridge University Press.
Dekel, E. and F. Gul: 1997, ‘Rationality and Knowledge in Game Theory’, in: D. M. Kreps, and K. F. Wallis (eds.), Advances in Economic Theory, Seventh World Congress, Cambridge University Press, 87–172.
van Ditmarsch, H. and W. van der Hoek: 2004, Dynamic epistemic logic, working paper.
Friedman, N. and J. Halpern: 1999, ‘Belief Revision: A Critique’, Journal of Logic, Language, and Information 8, 401–420.
Fudenberg, D. and J. Tirole: 1991, ‘Perfect Bayesian Equilibrium and Sequential Equilibrium’, Journal of Economic Theory 53, 236–260.
Fuhrmann, A.: 1989, ‘Reflective Modalities and Theory Change’, Synthese 81, 115–134.
Fuhrmann, A.: 1991, ‘On the Modal Logic of Theory Change’, in A. Fuhrmann (ed.), The logic of theory change, Lecture notes in Artificial Intelligence No. 465, Springer-Verlag, Berlin, 259–281.
Gärdenfors, P.: 1988, Knowledge in Flux: Modeling the Dynamics of Epistemic States, MIT Press.
Goranko, V. and S. Passy: 1992, ‘Using the Universal Modality: Gains and Questions’, Journal of Logic and Computation 2, 5–30.
Hansson, S. O.: 1994, ‘Taking Belief Bases Seriously’, in D. Prawitz and D. Westerståhl (eds.), Logic and Philosophy of Science in Uppsala, Kluwer, 13–28.
Harman, G.: 1986, Change in View: Principles of Reasoning, MIT Press.
Hintikka, J.: 1962, Knowledge and Belief, Cornell University Press.
van der Hoek, W.: 1993, ‘Systems for Knowledge and Belief’, Journal of Logic and Computation, 3, 173–195.
van der Hoek, W. and M. Pauly: forthcoming ‘Game Theory’, in: J. van Benthem, P. Blackburn, and F. Wolter (eds.), Handbook of Modal Logic.
Howson, C, and P. Urbach: 1989, Scientific Reasoning, Open Court.
Jeffrey, R.: 1983, The Logic of Decision, 2nd ed. University of Chicago Press.
Kreps, D. and R, Wilson: 1982, ‘Sequential Equilibria’, Econometrica, 50, 863–894.
Kripke, S.: 1963, A Semantical Analysis of Modal Logic I: Normal Propositional Calculi’, Zeitschrift für Mathematische Logik and Grundlagen der Mathematik 9, 67–96.
Levi, I.: 1988, ‘Iteration of conditionals and the Ramsey test’, Synthese 76, 49–81.
Liau, C.-J.: 2003, ‘Belief, Information Acquisition, and Trust in Multi-Agent Systems — A Modal Logic Formulation, Artificial Intelligence 149, 31–60.
Maher, P.: 1993, Betting on Theories, Cambridge University Press.
Rott, H.: 1991, ‘Two Methods of Constructing Contractions and Revisions of Knowledge Systems’, Journal of Philosophical Logic 20, 149–173.
Segerberg, K.: 1999, ‘Two traditions in the Logic of Belief: Bringing them Together’, in: H. J, Ohlbach and U. Reyle (eds.), Logic, Language and Reasoning, Kluwer Academic Publishers. pp. 135–147.
Teller, P.: 1973, ‘Conditionalization and Observation’, Synthese, 26, 218–258.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer
About this chapter
Cite this chapter
Bonanno, G. (2005). A Simple Modal Logic for Belief Revision. In: Uncertainty, Rationality, and Agency. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4631-6_6
Download citation
DOI: https://doi.org/10.1007/1-4020-4631-6_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-4630-8
Online ISBN: 978-1-4020-4631-5
eBook Packages: Computer ScienceComputer Science (R0)