Studia Logica

, Volume 89, Issue 1, pp 81–109 | Cite as

Towards a “Sophisticated” Model of Belief Dynamics. Part I: The General Framework

  • Brian Hill


It is well-known that classical models of belief are not realistic representations of human doxastic capacity; equally, models of actions involving beliefs, such as decisions based on beliefs, or changes of beliefs, suffer from a similar inaccuracies. In this paper, a general framework is presented which permits a more realistic modelling both of instantaneous states of belief, and of the operations involving them. This framework is motivated by some of the inadequacies of existing models, which it overcomes, whilst retaining technical rigour in so far as it relies on known, natural logical and mathematical notions. The companion paper (Towards a “sophisticated” model of belief dynamics. Part II) contains an application of this framework to the particular case of belief revision.


Representations of belief bounded rationality logical omniscience awareness logical locality belief dynamics iterated revision Gärdenfors postulates rational choice theory framing effect 


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  1. 1.
    Baltag, Alexandru and Lawrence S Moss (2004). ‘Logic for epistemic programs’. Synthese 60: 1–59 Google Scholar
  2. 2.
    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.Google Scholar
  3. 3.
    Baltag, Alexandru, and Sonja Smets, ‘Dynamic belief revision over multi-agent 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.Google Scholar
  4. 4.
    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.Google Scholar
  5. 5.
    Blackburn, Patrick, Maarten De Rijke and Yde Venema (2001). Modal Logic. University Press, CambridgeCrossRefGoogle Scholar
  6. 6.
    Fagin, Ronald and Joseph Y Halpern (1988). ‘Belief, awareness, and limited reasoning’. Artificial Intelligence 34: 39–76 CrossRefGoogle Scholar
  7. 7.
    Gerbrandy, Jelle and Willem Groeneveld (1997). ‘Reasoning about information change’. Journal of Logic, Language, and Information 6: 147–169 CrossRefGoogle Scholar
  8. 8.
    Gärdenfors and Peter (1988). Knowledge in Flux : Modeling the Dynamics of Epistemic States. MIT Press, Cambridge, MA Google Scholar
  9. 9.
    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.Google Scholar
  10. 10.
    Heifetz A., Meier M., Schipper B. (2006). ‘Interactive unawareness’. Journal of Economic Theory 130: 78–94 CrossRefGoogle Scholar
  11. 11.
    Heifetz, A., M. Meier, and B. Schipper, ‘Awareness, beliefs and games’, in Theoretical Aspects of Rationality and Knowledge XI, vol. XI, 2007.Google Scholar
  12. 12.
    Henkin, Leon, J. Donald Monk, and Alfred Tarski, Cylindrical Algebras. Part I, North-Holland, 1985.Google Scholar
  13. 13.
    Hill, Brian, Jouer avec le Faux. Recherches sur les processus mentaux à l’œuvre dans la lecture des textes de fiction, Doctorate thesis, University Paris 1 Panthé-Sorbonne, 2006.Google Scholar
  14. 14.
    Hill, Brian, ‘Living without state-independence of utilities’, Tech. rep., GREGHEC, 2007. 874/2007.Google Scholar
  15. 15.
    Hill, Brian, ‘The logic of awareness change’, in Proceedings of ILCLI InternationalWorskop on Logic and Philosophy of Knowledge, Communication and Action, University of the Basque Country Press, 2007.Google Scholar
  16. 16.
    Hill, Brian, ‘Logicality: from a local point of view’, Yeditepe’de Felsefe Yearbook, 6 (2007).Google Scholar
  17. 17.
    Hill, Brian, ‘Towards a “sophisticated” model of belief dynamics. Part II: Belief revision’, Studia Logica, 89 (2008).Google Scholar
  18. 18.
    Hintikka and Jaakko (1975). ‘Impossible possible worlds vindicated’. Journal of Philosophical Logic 4: 475–484 CrossRefGoogle Scholar
  19. 19.
    Koppelberg, S., ‘General theory of boolean algebras’, in J. D. Monk, and R. Bonnet, (eds.), Handbook of Boolean Algebras, vol. 1, North Holland, 1989.Google Scholar
  20. 20.
    Rott and Hans (2004). ‘A counterexample to six fundamental principles of belief formation’. Synthese 139: 225–240 CrossRefGoogle Scholar
  21. 21.
    Rott, Hans, ‘A counterexample to six fundamental principles of belief formation’, Synthese, 139 (2004), 225–240. Retrieved February 20, 2006, from
  22. 22.
    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.Google Scholar
  23. 23.
    Savage, Leonard, The Foundations of Statistics, Dover, New York, 1954. 2nd edn 1971.Google Scholar
  24. 24.
    Stalnaker, and Robert C. (1984). Inquiry. MIT Press, Cambridge, MA Google Scholar
  25. 25.
    Van Benthem, Johan, ‘Dynamic logic for belief change’, Journal of Applied Non-classical Logics, 17 (2007), 2007.Google Scholar
  26. 26.
    Van Ditmarsch, Hans P (2001). ‘Knowledge games’. Bulletin of Economic Research 53: 249–273 CrossRefGoogle Scholar

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© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.GREGHEC and IHPSTHEC ParisJouy-en-JosasFrance

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