Procedural Information and the Dynamics of Belief

  • Eric PacuitEmail author
Part of the Logic, Argumentation & Reasoning book series (LARI, volume 3)


This paper surveys recent dynamic logics of knowledge and belief for a single agent. Many of the recent developments in this area have been driven by analyzing concrete examples. These range from toy examples, such as the infamous muddy children puzzle, to philosophical quandaries, such as Fitch’s Paradox , to everyday examples of social interaction . Different logical systems are then judged, in part, on how well they conform to the analyst’s intuitions about the relevant set of examples. But this raises an important methodological issue: Implicit assumptions about what the actors know and believe about the situation being modeled often guide the analyst’s intuitions. In many cases, it is crucial to make these underlying assumptions explicit. The primary goal of this paper is to demonstrate how this “meta-information ” can be made explicit in the formal models of knowledge and belief .


Logic Logic Belief Revision Plausibility Model Dynamic Logic Public Announcement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. T. Ågotnes, N. Alechina, The dynamics of syntactic knowledge. J. Log. Comput. 17(1), 83–116 (2007)CrossRefGoogle Scholar
  2. C.E. Alchourrón, P. Gärdenfors, D. Makinson, On the logic of theory change: partial meet contraction and revision functions. J. Symb. Log. 50, 510–530 (1985)CrossRefGoogle Scholar
  3. R. Aumann, Interactive epistemology I: knowledge. Int. J. Game Theory 28, 263–300 (1999)CrossRefGoogle Scholar
  4. A. Baltag, S. Smets, Conditional doxastic models: a qualitative approach to dynamic belief revision, in Proceedings of WOLLIC 2006, Electronic Notes in Theoretical Computer Science, Stanford University, eds. by G. Mints, R. de Queiroz, 2006, Vol. 165, pp. 5–21Google Scholar
  5. A. Baltag, S. Smets, The logic of conditional doxastic actions, in New Perspectives on Games and Interaction, eds. by R. van Rooij, K. Apt. Texts in Logic and Games (Amsterdam University Press, Amsterdam, 2008a), pp. 9–31Google Scholar
  6. A. Baltag, S. Smets, A qualitative theory of dynamic interactive belief revision, in Logic and the Foundation of Game and Decision Theory (LOFT7), eds. by G. Bonanno, W. van der Hoek, M. Wooldridge. Texts in Logic and Games (Amsterdam University Press, Amsterdam, 2008b), pp. 13–60Google Scholar
  7. A. Baltag, S. Smets, ESSLLI 2009 course: dynamic logics for interactive belief revision (2009), Slides available online at:[[ESSLLI%2709%20Slides]]
  8. A. Baltag, L. Moss, S. Solecki, The logic of common knowledge, public announcements and private suspicions, in Proceedings of the 7th Conference on Theoretical Aspects of Rationality and Knowledge (TARK 98), Evanston, ed. by I. Gilboa, 1998, pp. 43–56Google Scholar
  9. P. Battigalli, M. Siniscalchi, Strong belief and forward induction reasoning. J. Econ. Theory 105, 356–391 (2002)CrossRefGoogle Scholar
  10. P. Blackburn, M. de Rijke, Y. Venema, Modal Logic (Cambridge University Press, Cambridge, 2002)Google Scholar
  11. O. Board, Dynamic interactive epistemology. Games Econ. Behav. 49, 49–80 (2004)CrossRefGoogle Scholar
  12. G. Bonanno, Axiomatic characterization of AGM belief revision in a temporal logic. Artif. Intell. 171, 144–160 (2007)CrossRefGoogle Scholar
  13. G. Bonanno, Belief change in branching time: AGM-consistency and iterated revision. J. Philos. Log. 41(1), 201–236 (2012). ManuscriptGoogle Scholar
  14. G. Bonanno, P. Battigalli, Recent results on belief, knowledge and the epistemic foundations of game theory. Res. Econ. 53(2), 149–225 (1999)CrossRefGoogle Scholar
  15. C. Boutilier, Conditional Logics for Default Reasoning and Belief Revision. PhD thesis, University of Toronto, 1992Google Scholar
  16. C. Boutilier, Iterated revision and minimal revision of conditional beliefs. J. Philos. Log. 25, 262–304 (1996)CrossRefGoogle Scholar
  17. A. Brandenburger, The power of paradox: some recent developments in interactive epistemology. Int. J. Game Theory 35, 465–492 (2007)CrossRefGoogle Scholar
  18. D. Christensen, Higher-order evidence. Philos. Phenomenol. Res. 81(1), 185–215 (2010)CrossRefGoogle Scholar
  19. C.B. Cross, ‘Can’ and the logic of ability. Philos. Stud. 50(1), 53–64 (1986)CrossRefGoogle Scholar
  20. A. Darwiche, J. Pearl, On the logic of iterated belief revision. Artif. Intell. 89, 1–29 (1997)CrossRefGoogle Scholar
  21. C. Dégremont, The Temporal Mind. Observations on the Logic of Belief Change in Interactive Systems. PhD thesis, Institute for Logic, Language and Computation. (DS-2010-03, 2010)Google Scholar
  22. P. Egré, B. Bonnay, Inexact knowledge with introspection. J. Philos. Log. 38(2), 179–228 (2009)CrossRefGoogle Scholar
  23. D. Elgesem, The modal logic of agency. Nord. J. Philos. Log. 2, 1–46 (1997)Google Scholar
  24. R. Fagin, J. Halpern, Y. Moses, M. Vardi, Reasoning about Knowledge (MIT, Cambridge, 1995)Google Scholar
  25. J. Gerbrandy, Bisimulations on Planet Kripke. PhD thesis, University of Amsterdam, 1999Google Scholar
  26. A. Grove, Two modellings for theory change. J. Philos. Log. 17, 157–170 (1988)CrossRefGoogle Scholar
  27. J. Halpern, Reasoning About Uncertainty (MIT, Cambridge, 2005)Google Scholar
  28. J. Halpern, Y. Moses, Knowledge and common knowledge in a distributed environment. J. ACM 37(3), 549–587 (1990)CrossRefGoogle Scholar
  29. J. Halpern, L. Rego, Reasoning about knowledge of unawareness revisited, in Proceedings of Theoretical Aspects of Rationality and Knowledge (TARK’09), Stanford, ed. by A. Heifetz, 2009Google Scholar
  30. V. Hendricks, Editor, special issue: “8 bridges between formal and mainstream epistemology”. Philos. Stud. 128(1), 1–227, 2006CrossRefGoogle Scholar
  31. V. Hendricks, Mainstream and Formal Epistemology (Cambridge University Press, Cambridge, 2006)Google Scholar
  32. J. Hintikka, Knowledge and Belief: An Introduction to the Logic of the Two Notions (Cornell University Press, Ithaca, 1962)Google Scholar
  33. J. Hintikka, Knowledge and Belief: An Introduction to the Logic of the Two Notions (with an Introduction by V. Hendricks and J. Symons) (King’s College Publications, London, 2005)Google Scholar
  34. J. Horty, Agency and Deontic Logic (Oxford University Press, Oxford/New York, 2001)CrossRefGoogle Scholar
  35. T. Hoshi, Epistemic Dynamics and Protocol Information. PhD thesis, Stanford University, 2009Google Scholar
  36. W. Jamroga, T. Ågotnes, Constructive knowledge: what agents can achieve under imperfect information. J. Appl. Non-class. Log. 17(4), 423–475 (2007)CrossRefGoogle Scholar
  37. P. Lamarre, Y. Shoham, Knowledge, certainty, belief and conditionalisation, in Proceedings of the International Conference on Knowledge Representation and Reasoning, Bonn, 1994, pp. 415–424Google Scholar
  38. D. Lewis, Counterfactuals (Blackwell, Oxford, 1973)Google Scholar
  39. F. Liu, Changing for the better: preference dynamics and agent diversity. PhD thesis, Institute for Logic, Language and Computation (ILLC), 2008Google Scholar
  40. A. Nayak, M. Pagnucco, P. Peppas, Dynamic belief revision operators. Artif. Intell. 146, 193–228 (2003)CrossRefGoogle Scholar
  41. E. Pacuit, S. Simon, Reasoning with protocols under imperfect information. Rev. Symb. Log. 4, 412–444 (2011)CrossRefGoogle Scholar
  42. E. Pacuit, R. Parikh, E. Cogan, The logic of knowledge based obligation. Synthese 149(2), 311–341 (2006)CrossRefGoogle Scholar
  43. R. Parikh, R. Ramanujam, A knowledge based semantics of messages. J. Log Lang. Inf. 12, 453–467 (2003)CrossRefGoogle Scholar
  44. J. Plaza, Logics of public communications, in Proceedings, 4th International Symposium on Methodologies for Intelligent Systems, Charlotte, ed. by M.L. Emrich, M.S. Pfeifer, M. Hadzikadic, Z. Ras, 1989, pp. 201–216. (republished as Plaza (2007))Google Scholar
  45. J. Plaza, Logics of public communications. Synthese 158(2), 165–179 (2007)CrossRefGoogle Scholar
  46. B. Rodenhäuser, A logic for extensional protocols, J. Appl. Non-class. Log. 21(3–4), 477–502 (2011)CrossRefGoogle Scholar
  47. H. Rott, Shifting priorities: simple representations for 27 itereated theory change operators, in Modality Matters: Twenty-Five Essays in Honour of Krister Segerberg, eds. by H. Lagerlund, S. Lindström, R. Sliwinski, Vol. 53. Uppsala Philosophical Studies, 2006, pp. 359–384Google Scholar
  48. Y. Shoham, K. Leyton-Brown, Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations (Cambridge University Press, Cambridge/New York, 2009)Google Scholar
  49. R. Stalnaker, The problem of logical omniscience I. Synthese 89, 425–440 (1991)CrossRefGoogle Scholar
  50. R. Stalnaker, On the evaluation of solution concepts. Theory Decis. 37(42), 49–73 (1994)CrossRefGoogle Scholar
  51. R. Stalnaker, Iterated belief revision. Erkentnis 70, 189–209 (2009)CrossRefGoogle Scholar
  52. J. van Benthem, Dynamic logic for belief revision. J. Appl. Non-class. Log. 17(2), 129–155 (2007)CrossRefGoogle Scholar
  53. J. van Benthem, The information in intuitionistic logic. Synthese 167, 329–348 (2009)CrossRefGoogle Scholar
  54. J. van Benthem, Logical Dynamics of Information and Interaction (Cambridge University Press, Cambridge, 2011)CrossRefGoogle Scholar
  55. J. van Benthem, J. van Eijck, B. Kooi, Logics of communication and change. Inf. Comput. 204(11), 1620–1662 (2006)CrossRefGoogle Scholar
  56. J. van Benthem, J. Gerbrandy, T. Hoshi, E. Pacuit, Merging frameworks for interaction. J. Philos. Log. 38(5), 491–526 (2009)CrossRefGoogle Scholar
  57. H. van Ditmarsch, Prolegomena to dynamic logic for belief revision. Synth. Knowl. Ration. Action 147, 229–275 (2005)Google Scholar
  58. H. van Ditmarsch, W. van der Hoek, B.P. Kooi, Dynamic Epistemic Logic, Synthese Library (Springer, Dordrecht, 2007)Google Scholar
  59. H. van Ditmarsch, S. Ghosh, R. Verbrugge, Y. Wang, Hidden protocols, in Proceedings of the 13th Conference on Theoretical Aspects of Rationality and Knowledge (TARK), Groningen, ed. by K. Apt (ACM Digital Library, 2011)Google Scholar
  60. Y. Wang, Epistemic Modelling and Protocol Dynamics. PhD thesis, CWI, 2010Google Scholar
  61. T. Williamson, Knowledge and Its Limits (Oxford University Press, Oxford, 2000)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Tilburg Institute for Logic and Philosophy of ScienceTilburg UniversityTilburgThe Netherlands

Personalised recommendations