Logical Dynamics of Evidence

  • Johan van Benthem
  • Eric Pacuit
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6953)


Evidence is the underpinning of beliefs and knowledge. Modeling evidence for an agent requires a more fine-grained semantics than possible worlds models. We do this in the form of “neighbourhood models”, originally proposed for weak modal logics. We show how these models support natural actions of “evidence management”, ranging from update with external new information to internal rearrangement. This perspective leads to richer languages for neighborhood semantics, including modalities for new kinds of conditional evidence and conditional belief. Using these, we indicate how one can obtain relative completeness theorems for the dynamic logic of evidence-changing actions.


Modal Logic Belief Revision Plausibility Model Belief Change Dynamic Logic 
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.


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  1. 1.
    Ågotnes, T., Alechina, N.: The dynamics of syntactic knowledge. Journal of Logic and Computation 17(1), 83–116 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Andreka, H., Ryan, M., Schobbens, P.Y.: Operators and laws for combining preference relations. Journal of Logic and Computation 12(1), 13–53 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Baltag, A., Smets, S.: Conditional doxastic models: A qualitative approach to dynamic belief revision. In: Mints, G., de Queiroz, R. (eds.) Proceedings of WOLLIC 2006. LNCS, vol. 165, pp. 5–21 (2006)Google Scholar
  4. 4.
    Baltag, A., Smets, S.: ESSLLI (2009) course: Dynamic logics for interactive belief revision (2009), Slides available at
  5. 5.
    Boutilier, C.: Conditional Logics for Default Reasoning and Belief Revision. Ph.D. thesis, University of Toronto (1992)Google Scholar
  6. 6.
    Chellas, B.: Modal Logic: An Introduction. Cambridge University Press, Cambridge (1980)CrossRefzbMATHGoogle Scholar
  7. 7.
    Demey, L.: Agreeing to Disagree in Probabilistic Dynamic Epistemic Logic. Master’s thesis, ILLC University of Amsterdam, LDC 2010-14 (2010)Google Scholar
  8. 8.
    Dempster, A.P.: Upper and lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics 38(2), 325–339 (1967)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Synthese Library. Springer, Heidelberg (2007)CrossRefzbMATHGoogle Scholar
  10. 10.
    Fagin, R., Halpern, J.: Belief, awareness and limited reasoning. Artificial Intelligence 34, 39–76 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Gerbrandy, J.: Bisimulations on Planet Kripke. Ph.D. thesis, Institute for Logic, Language and Computation, DS-1999-01 (1999)Google Scholar
  12. 12.
    Girard, P.: Modal Logic for Belief and Preference Change. Ph.D. thesis, ILLC University of Amsterdam Dissertation Series DS-2008-04 (2008)Google Scholar
  13. 13.
    Halpern, J., Pucella, R.: A logic for reasoning about evidence. Journal of AI Research 26, 1–34 (2006)MathSciNetzbMATHGoogle Scholar
  14. 14.
    Hansen, H.H.: Monotonic Modal Logic. Master’s thesis, Universiteit van Amsterdam (ILLC technical report: PP-2003-24) (2003)Google Scholar
  15. 15.
    Hansen, H.H., Kupke, C., Pacuit, E.: Neighbourhood structures: Bisimilarity and basic model theory. Logical Methods in Computer Science 5(2), 1–38 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Hansson, S.O.: A Textbook of Belief Dynamics. Theory Change and Database Updating. Kluwer, Dordrecht (1999)CrossRefzbMATHGoogle Scholar
  17. 17.
    Kratzer, A.: What must and can must and can mean. Linguistics and Philosophy 1, 337–355 (1977)CrossRefGoogle Scholar
  18. 18.
    Leitgeb, H., Segerberg, K.: Dynamic doxastic logic: why, how and where to? Synthese 155(2), 167–190 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Lewis, D.: Counterfactuals. Blackwell Publishers, Oxford (1973)zbMATHGoogle Scholar
  20. 20.
    Liu, F.: Reasoning about Preference Dynamics. Synthese Library, vol. 354. Springer, Heidelberg (2011)CrossRefzbMATHGoogle Scholar
  21. 21.
    Liu, F.: A two-level perspective on preference. Journal of Philosophical Logic (to appear, 2011)Google Scholar
  22. 22.
    Moss, L., Parikh, R.: Topological reasoning and the logic of knowledge. In: Moses, Y. (ed.) Proceedings of TARK IV. Morgan Kaufmann, San Francisco (1992)Google Scholar
  23. 23.
    Nicola, R.D.: Extensional equivalences for transition systems. Acta Informatica 24, 211–237 (1987), MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Pacuit, E.: Neighborhood semantics for modal logic: An introduction (2007), ESSLLI 2007 course notes,
  25. 25.
    Pauly, M.: Logic for Social Software. Ph.D. thesis, ILLC University of Amsterdam Dissertation Series DS 2001-10 (2001)Google Scholar
  26. 26.
    Plaza, J.: Logics of public communications. Synthese: Knowledge, Rationality, and Action 158(2), 165–179 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Rott, H.: Change, Choice and Inference: A Study in Belief Revision and Nonmonotonic Reasoning. Oxford University Press, Oxford (2001)zbMATHGoogle Scholar
  28. 28.
    Rott, H.: Shifting priorities: Simple representations for 27 iterated theory change operators. In: Lagerlund, H., Lindström, S., Sliwinski, R. (eds.) Modality Matters: Twenty-Five Essays in Honor of Krister Segerberg. Uppsala Philosophical Studies, vol. 53, pp. 359–384 (2006)Google Scholar
  29. 29.
    Segerberg, K.: Belief revision from the point of view of doxastic logic. Journal of the IGPL 3(4), 535–553 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)zbMATHGoogle Scholar
  31. 31.
    Shoham, Y., Leyton-Brown, K.: Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations. Cambridge University Press, Cambridge (2009)zbMATHGoogle Scholar
  32. 32.
    Stalnaker, R.: Knowledge, belief and counterfactual reasoning in games. Economics and Philosophy 12(02), 133–163 (1996)CrossRefGoogle Scholar
  33. 33.
    Su, K., Sattar, A., Governatori, G., Chen, Q.: A computationally grounded logic of knowledge, belief and certainty. In: Proceedings of the Fourth International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS 2005, pp. 149–156 (2005),
  34. 34.
    van Benthem, J.: Dynamic logic for belief revision. Journal of Applied Non-Classical Logics 14(2), 129–155 (2004)MathSciNetzbMATHGoogle Scholar
  35. 35.
    van Benthem, J.: A note on modeling theories. In: Festa, R., Aliseda, A., Peijnenburg, J. (eds.) Poznan Studies in the Philosophy of the Sciences and Humanities: Confirmation, Empirical Progress and Truth Approximation. Essays in Debate with Theo Kuipers, vol. 17, pp. 403–419 (2005)Google Scholar
  36. 36.
    van Benthem, J.: Merging observation and access in dynamic logic. Studies in Logic 1(1), 1–17 (2008)Google Scholar
  37. 37.
    van Benthem, J.: Logical Dynamics of Information Flow. Cambridge University Press, Cambridge (2011)CrossRefzbMATHGoogle Scholar
  38. 38.
    van Benthem, J., Minică, Ş.: Toward a dynamic logic of questions. In: He, X., Horty, J.F., Pacuit, E. (eds.) LORI 2009. LNCS, vol. 5834, pp. 27–41. Springer, Heidelberg (2009), CrossRefGoogle Scholar
  39. 39.
    Velazquez-Quesada, F.R.: Inference and update. Synthese (Knowledge, Rationality & Action) 169(2), 283–300 (2009)MathSciNetzbMATHGoogle Scholar
  40. 40.
    Veltman, F.: Prejudices, presuppositions and the theory of conditionals. In: Groenendijk, J., Stokhof, M. (eds.) Amsterdam Papers in Formal Grammar, vol. 1, pp. 248–281 (1976)Google Scholar
  41. 41.
    Zvesper, J.: Playing with Information. Ph.D. thesis, ILLC University of Amsterdam Dissertation Series DS-2010-02 (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Johan van Benthem
    • 1
  • Eric Pacuit
    • 2
  1. 1.ILLC, University of Amsterdam and Stanford UniversityNetherlands
  2. 2.Tilburg Institute for Logic and Philosophy of ScienceNetherlands

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