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Towards a “Sophisticated” Model of Belief Dynamics. Part II: Belief Revision.

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Abstract

In the companion paper (Towards a “sophisticated” model of belief dynamics. Part I), a general framework for realistic modelling of instantaneous states of belief and of the operations involving them was presented and motivated. In this paper, the framework is applied to the case of belief revision. A model of belief revision shall be obtained which, firstly, recovers the Gärdenfors postulates in a well-specified, natural yet simple class of particular circumstances; secondly, can accommodate iterated revisions, recovering several proposed revision operators for iterated revision as special cases; and finally, offers an analysis of Rott’s recent counterexample to several Gärdenfors postulates [32], elucidating in what sense it fails to be one of the special cases to which these postulates apply.

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References

  1. Carlos E., Alchourron , Peter Gärdenfors and David Makinson (1985). ‘The logic of theory change: Partial meet contraction and revision functions’, The Journal of Symbolic Logic 50: 510–530

    Google Scholar 

  2. Baltag , Alexandru and Lawrence S. Moss (2004). ‘Logic for epistemic programs’. Synthese 60: 1–59

    Google Scholar 

  3. Baltag, Alexandru, Lawrence S. Moss, and Slawomir Solecki, ‘The logic of common knowledge, public announcements and private suspicions’, in I. Gilboa, (ed.), Proceedings of the 7th Conference on Theoretical Aspects of Rationality and Knowledge (TARK’98), 1998, pp. 43–56.

  4. Baltag, Alexandru, and Sonja Smets, ‘Dynamic belief revision over multiagent plausibility models’, in Giacomo Bonanno, Wiebe van der Hoek, and Michael Wooldridge, (eds.), Proceedings of the 7th Conference on Logic and the Foundations of Game and Decision Theory (LOFT06), 2006, pp. 11–24.

  5. Baltag, Alexandru, and Sonja Smets, ‘The logic of conditional doxastic actions: A theory of dynamic multi-agent belief revision’, in S. Artemov, and R. Parikh, (eds.), Proceedings of the Workshop on Rationality and Knowledge ESSLLI 2006, 2006, pp. 13–30.

  6. Blackburn , Patrick , Maarten de Rijke and Yde Venema (2001). Modal Logic. Cambridge University Press, Cambridge

    Google Scholar 

  7. Darwiche , Adnan and Judea Pearl (1997). ‘On the logic of iterated belief revision’. Artificial Intelligence 89: 1–29

    Article  Google Scholar 

  8. Fagin , Ronald and Joseph Y. Halpern (1988). ‘Belief, awareness, and limited reasoning’. Artificial Intelligence 34: 39–76

    Article  Google Scholar 

  9. Joseph Y. Halpern , Friedman and Nir (1999). ‘Belief revision: a critique’. Journal of Logic, Language, and Information 8: 401–420

    Article  Google Scholar 

  10. Willem Groeneveld , Gerbrandy and Jelle (1997). ‘Reasoning about information change’. Journal of Logic, Language, and Information 6: 147–169

    Article  Google Scholar 

  11. Gärdenfors and Peter (1988). Knowledge in Flux : Modeling the Dynamics of Epistemic States. MIT Press, Cambridge, MA

    Google Scholar 

  12. Gärdenfors, Peter, and Hans Rott, ‘Belief revision’, in Gabbay, Hogger, and Robinson, (eds.), Handbook of Logic in AI and Logic Programming, vol. 4, Oxford University Press, Oxford, 1995.

  13. Grove and Adam (1988). ‘Two modelings for theory change’. Journal of Philosophical Logic 17: 157–170

    Article  Google Scholar 

  14. Halpern, Joseph Y., and Leandro Chaves Rêgo, ‘Interactive awareness revisited’, in Proceedings of Tenth Conference on Theoretical Aspects of Rationality and Knowledge, 2005, pp. 78–91.

  15. Sven Ove and Hansson (2003). ‘Ten philosophical problems in belief revision’. Journal of Logic and Computution 13: 37–49

    Article  Google Scholar 

  16. Heifetz A., Meier M. and Schipper B. (2006). ‘Interactive unawareness’. Journal of Economic Theory 130: 78–94

    Article  Google Scholar 

  17. Heifetz, A., M. Meier, and B. Schipper, ‘Awareness, beliefs and games’, in Theoretical Aspects of Rationality and Knowledge XI, vol. XI, 2007.

  18. Henkin, Leon, J. Donald Monk, and Alfred Tarski, Cylindrical Algebras. Part I, North-Holland, 1985.

  19. Hill, Brian, Jouer avec le Faux. Recherches sur les processus mentaux à l’oeuvre dans la lecture des textes de fiction, Doctorate thesis, University Paris 1 Panthéon- Sorbonne, 2006.

  20. Hill, Brian, ‘Living without state-independence of utilities’, Tech. rep., GREGHEC, 2007. 874/2007.

  21. Hill, Brian, ‘The logic of awareness change’, in Proceedings of ILCLI International Worskop on Logic and Philosophy of Knowledge, Communication and Action, University of the Basque Country Press, 2007.

  22. Hill, Brian, ‘Logicality: from a local point of view’, Yeditepe’de Felsefe Yearbook, 6 (2007).

  23. Hintikka and Jaakko (1975). ‘Impossible possible worlds vindicated’. Journal of Philosophical Logic, 4: 475–484

    Article  Google Scholar 

  24. Amos Tversky , Kahneman and Daniel (1979). ‘Prospect theory: An analysis of decision under risk’. Econometrica 47: 263–291

    Article  Google Scholar 

  25. Konieczny , Sébastien and Ramón Pino Pérez (2000). ‘A framework for iterated revision’. Journal of Applied Non-Classical Logics 10(3-4): 339–367

    Google Scholar 

  26. Koppelberg, S., ‘General theory of boolean algebras’, in J. D. Monk, and R. Bonnet, (eds.), Handbook of Boolean Algebras, vol. 1, North Holland, 1989.

  27. David K. and Lewis (1973). Counterfactuals. Harvard University Press, Cambridge, Massachusetts

    Google Scholar 

  28. Abhaya C. and Nayak (1994). ‘Iterated belief change based on epistemic entrenchment’. Erkenntnis 41: 353–390

    Article  Google Scholar 

  29. Rabinowicz, Wlodzimierz, ‘Stable revision, or is preservation worth preserving’, in André Fuhrmann, Hans Rott, (eds.), Logic, Action and Information: Essays on Logic in Philosophy and Artificial Intelligence, De Gruyter, Berlin, (1995), pp. 101–128.

  30. Rott and Hans (2001). Change, Choice and Inference, vol. 42 of Oxford Logic Guides. Clarendon Press, Oxford

    Google Scholar 

  31. Rott and Hans (2003). ‘Coherence and conservatism in the dynamics of belief. part ii: Iterated belief change without dispositional coherence’. Journal of Logic and Computation 13: 111–145

    Article  Google Scholar 

  32. Rott and Hans (2004). ‘A counterexample to six fundamental principles of belief formation’. Synthese 139: 225–240

    Article  Google Scholar 

  33. Rott, Hans, ‘A counterexample to six fundamental principles of belief formation’, Synthese 139 (2004), 225–240. Retrieved February 20, 2006, from http://www.uniregensburg.de/Fakultaeten/phil_Fak_I/Philosophie/theo_neu/RottV/Index_HRott.htm.

  34. Rott, Hans, ‘Shifting priorities: Simple representations for twenty-seven iterated theory change operators’, in Modality Matters: Twenty-Five Essays in Honour of Krister Segerberg, vol. 53, Uppsala Philosophical Studies, 2006, pp. 359–384.

  35. Savage, Leonard, The Foundations of Statistics, Dover, New York, 1954. 2nd edn 1971.

  36. Segerberg and Krister (1998). ‘Irrevocable belief revision in dynamic doxastic logic’. Notre Dame Journal of Formal Logic 39: 287–306

    Article  Google Scholar 

  37. Spohn, Wolfgang, ‘Ordinal conditional functions’, in William L Harper, and Brian Skyrms, (eds.), Causation in Decision, Belief Change and Statistics, vol. II, Reidel, Dordrecht, 1988, pp. 105–134.

  38. Robert C. and Stalnaker (1984). Inquiry. MIT Press, Cambridge, MA

    Google Scholar 

  39. Daniel Kahneman, Tversky and Amos (1986). ‘Rational choice and the framing of decisions’. Journal of Business 59: 251–278

    Article  Google Scholar 

  40. van Benthem, Johan, ‘Dynamic logic for belief change’, Journal of Applied Nonclassical Logics 17 (2007), 2007.

  41. Hans P. (2001). ‘Knowledge games’. Bulletin of Economic Research 53: 249–273

    Article  Google Scholar 

  42. van Ditmarsch, Hans P., ‘Prolegomena to dynamic logic of belief revision’, Synthese 147 (2005), 229–275.

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Hill, B. Towards a “Sophisticated” Model of Belief Dynamics. Part II: Belief Revision.. Stud Logica 89, 291–323 (2008). https://doi.org/10.1007/s11225-008-9130-9

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