Abstract
We study belief change in the branching-time structures introduced in Bonanno (Artif Intell 171:144–160, 2007). First, we identify a property of branching-time frames that is equivalent (when the set of states is finite) to AGM-consistency, which is defined as follows. A frame is AGM-consistent if the partial belief revision function associated with an arbitrary state-instant pair and an arbitrary model based on that frame can be extended to a full belief revision function that satisfies the AGM postulates. Second, we provide a set of modal axioms that characterize the class of AGM-consistent frames within the modal logic introduced in Bonanno (Artif Intell 171:144–160, 2007). Third, we introduce a generalization of AGM belief revision functions that allows a clear statement of principles of iterated belief revision and discuss iterated revision both semantically and syntactically.
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Alchourrón, C., Gärdenfors, P., & Makinson, D. (1985). On the logic of theory change: Partial meet contraction and revision functions. The Journal of Symbolic Logic, 50, 510–530.
Baltag, A., & Moss, L. S. (2004). Logics for epistemic programs. Synthese, 139, 165–224.
Board, O. (2004). Dynamic interactive epistemology. Games and Economic Behavior, 49, 49–80.
Bonanno, G. (2007). Axiomatic characterization of the AGM theory of belief revision in a temporal logic. Artificial Intelligence, 171, 144–160.
Bonanno, G. (2008). Belief revision in a temporal framework. In K. R. Apt, & R. van Rooij (Eds.), New perspectives on games and interaction. Texts in logic and games series (Vol. 4, pp. 45–79). Amsterdam University Press.
Bonanno, G. (2009). Rational choice and AGM belief revision. Artificial Intelligence, 173, 1194–1203.
Booth, R., & Meyer, T. (2006). Admissible and restrained revision. Journal of Artificial Intelligence Research, 26, 127–151.
Boutilier, C. (1996). Iterated revision and minimal change of conditional beliefs. Journal of Philosophical Logic, 25, 263–305.
Darwiche, A., & Pearl, J. (1997). On the logic of iterated belief revision. Artificial Intelligence, 89, 1–29.
de Rijke, M. (1994). Meeting some neighbours: A dynamic modal logic meets theories of change and knowledge representation. In J. van Eijck, & A. Visser (Eds.), Logic and information flow (pp. 170–196). MIT Press.
Fagin, R., Halpern, J., Moses, Y., & Vardi, M. (1995). Reasoning about knowledge. MIT Press.
Friedman, N., & Halpern, J. (1999). Belief revision: A critique. Journal of Logic, Language, and Information, 8, 401–420.
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, pp. 259–281). Springer-Verlag.
Gärdenfors, P. (1988). Knowledge in flux: Modeling the dynamics of epistemic states. MIT Press.
Hansson, B. (1968). Choice structures and preference relations. Synthese, 18, 443–458.
Hintikka, J. (1962). Knowledge and belief. Cornell University Press.
Humberstone, L. (1987). The modal logic of ‘all and only’. Notre Dame Journal of Formal Logic, 28, 177–188.
Jin, Y., & Thielscher, M. (2007). Iterated belief revision, revised. Artificial Intelligence, 171, 1–18.
Katsuno, H., & Mendelzon, A. O. (1992). On the difference between updating a knowledge base and revising it. In P. Gärdenfors (Ed.), Belief revision (pp. 183–203). Cambridge University Press.
Kripke, S. (1963). A semantical analysis of modal logic I: Normal propositional calculi. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 9, 67–96.
Leitgeb, H., & Segerberg, K. (2007). Dynamic doxastic logic: Why, how and where to? Synthese, 155, 167–190.
Levesque, H. (1990). All I know: A study in autoepistemic logic. Artificial Intelligence, 5, 263–309.
Nayak, A., Pagnucco, M., & Peppas, P. (2003). Dynamic belief revision operators. Artificial Intelligence, 146, 193–228.
Parikh, R., & Ramanujam, R. (2003). A knowledge based semantics of messages. Journal of Logic, Language, and Information, 12, 453–467.
Plaza, J. (1989). Logics of public communications. In M. L. Emrich, M. S. Pfeifer, M. Hadzikadic, & Z. W. Ras (Eds.), Proceedings of the fourth international symposium on methodologies for intelligent systems (pp. 201–216). Oak Ridge National Laboratory. Reprinted in Synthese, 158, 165–179 (2007).
Rabinowicz, W. (1995). Stable revision, or is Preservation worth preserving? In A. Fuhrmann, & H. Rott (Eds.), Logic, action and information: Essays on logic in philosophy and artificial intelligence (pp. 101–128). Berlin.
Rott, H. (1999). Coherence and conservatism in the dynamics of belief. Erkenntnis, 50, 387–412.
Segerberg, K. (1995). Belief revision from the point of view of doxastic logic. Bulletin of the IGPL, 3, 535–553.
Segerberg, K. (1999). Two traditions in the logic of belief: Bringing them together. In H. J. Ohlbach, & U. Reyle (Eds.), Logic, language and reasoning (pp. 135–147). Kluwer Academic Publishers.
Stalnaker, R. (2009). Iterated belief revision. Erkenntnis, 70, 189–209.
van Benthem, J. (2007). Dynamic logics for belief revision. Journal of Applied Non-Classical Logics, 17, 129–155.
van Benthem, J., & Dégremont, C. (2010). Multi-agent belief dynamics: Bridges between dynamic doxastic and doxastic temporal logics. In G. Bonanno, W. van der Hoek, & B. Lö we (Eds.), Logic and the foundations of the theory of games and decisions (LOFT8) (pp. 153–175). Springer.
van Benthem J., Gerbrandy, J., Hoshi, T., & Pacuit, E. (2009). Merging frameworks for interaction. Journal of Philosophical Logic, 38, 491–526.
van Benthem, J., & Pacuit, E. (2006). The tree of knowledge in action: Towards a common perspective. In G. Governatori, I. Hodkinson, & Y. Venema (Eds.), Advances in modal logic (Vol. 6, pp. 87–106). College Publications.
van Ditmarsch, H. (2005). Belief change and dynamic logic. In J. Delgrande, J. Lang, H. Rott, & J.-M. Tallon (Eds.), Belief change in rational agents. (Electronic) Proceedings of Dagstuhl Seminar 05321, IBFI. Germany: Schloss Dagstuhl. http://drops.dagstuhl.de/portals/index.php?semnr=05321. Accessed 19 May 2011.
van Ditmarsch, H. (2005). Prolegomena to dynamic logic for belief revision. Synthese, 147, 229–275.
van Ditmarsch, H., van der Hoek, W., & Kooi, B. (2008). Dynamic epistemic logic. Springer.
Zvesper, J. (2007). How to keep on changing your mind, dynamically. In J. van Benthem, S. Ju, & F. Veltman (Eds.), A meeting of the minds. Proceedings of the workshop on logic, rationality and interaction. Texts in computer science (Vol. 8, pp. 291–306). College Publications.
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Bonanno, G. Belief Change in Branching Time: AGM-consistency and Iterated Revision. J Philos Logic 41, 201–236 (2012). https://doi.org/10.1007/s10992-011-9202-6
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DOI: https://doi.org/10.1007/s10992-011-9202-6