Studia Logica

, 99:61 | Cite as

Dynamic Logics of Evidence-Based Beliefs

  • J. van BenthemEmail author
  • E. Pacuit


This paper adds evidence structure to standard models of belief, in the form of families of sets of worlds. We show how these more fine-grained models support natural actions of “evidence management”, ranging from update with external new information to internal rearrangement. We show how this perspective leads to new richer languages for existing neighborhood semantics for modal logic. Our main results are relative completeness theorems for the resulting dynamic logic of evidence.


Dynamic Logics of Belief Revision Neighborhood Models for Modal Logic 


  1. 1.
    Andreka Hajnal, Mark Ryan, Pierre Yves Schobbens: ‘Operators and laws for combining preference relations’. Journal of Logic and Computation 12(1), 13–53 (2002)CrossRefGoogle Scholar
  2. 2.
    Baltag, A., and S. Smets, ‘Conditional doxastic models: A qualitative approach to dynamic belief revision’, in G. Mints, and R. de Queiroz, (eds.), Proceedings of WOLLIC 2006, LNCS, vol. 165, 2006, pp. 5–21.Google Scholar
  3. 3.
    Boutilier, Craig, Conditional Logics for Default Reasoning and Belief Revision, Ph.D. thesis, University of Toronto, 1992.Google Scholar
  4. 4.
    Chellas, Brian, Modal Logic: An Introduction, Cambridge University Press, 1980.Google Scholar
  5. 5.
    Demey, Lorenz, Agreeing to Disagree in Probabilistic Dynamic Epistemic Logic., Master’s thesis, ILLC University of Amsterdam (LDC 2010-14), 2010.Google Scholar
  6. 6.
    Dempster A.P.: ‘Upper and lower probabilities induced by a multivalued mapping’. Annals of Mathematical Statistics 38(2), 325–339 (1967)CrossRefGoogle Scholar
  7. 7.
    Gärdenfors, Peter, Knowledge in Flux: Modeling the Dynamics of Epistemic States, Bradford Books, MIT Press, 1988Google Scholar
  8. 8.
    Girard, Patrick, Modal Logic for Belief and Preference Change, Ph.D. thesis, ILLC University of Amsterdam Dissertation Series DS-2008-04, 2008.Google Scholar
  9. 9.
    Halpern Joe, Ricardo Pucella: ‘A logic for reasoning about evidence’. Journal of AI Research 26(1), 1–34 (2006)Google Scholar
  10. 10.
    Hansen Helle Hvid, Clemens Kupke, Eric Pacuit: ‘Neighbourhood structures: Bisimilarity and basic model theory’. Logical Methods in Computer Science 5(2), 1–38 (2009)Google Scholar
  11. 11.
    Hansson, Sven Ove, A Textbook of Belief Dynamics. Theory Change and Database Updating, Kluwer, 1999.Google Scholar
  12. 12.
    Kratzer Angelika: ‘What must and can must and can mean’. Linguistics and Philosophy 1, 337–355 (1977)CrossRefGoogle Scholar
  13. 13.
    Leitgeb Hannes, Krister Segerberg: ‘Dynamic doxastic logic: why, how and where to?’. Synthese 155(2), 167–190 (2007)CrossRefGoogle Scholar
  14. 14.
    Lewis David: Counterfactuals. Blackwell Publishers, Oxford (1973)Google Scholar
  15. 15.
    Liu, Fenrong, Reasoning about Preference Dynamics, vol. 354 of Synthese Library, Springer-Verlag, 2008.Google Scholar
  16. 16.
    Liu, Fenrong, ‘A two-level perspective on preference’, Journal of Philosophical Logic, 2011. To Appear.Google Scholar
  17. 17.
    Moss, Larry, and Rohit Parikh, ‘Topological reasoning and the logic of knowledge’, in Yoram Moses, (ed.), Proceedings of TARK IV, Morgan Kaufmann, 1992.Google Scholar
  18. 18.
    Pacuit, Eric, ‘Neighborhood semantics for modal logic: An introduction’, 2007. ESSLLI 2007 course notes (
  19. 19.
    Pauly, Marc, Logic for Social Software, Ph.D. thesis, ILLC University of Amsterdam Dissertation Series DS 2001-10, 2001.Google Scholar
  20. 20.
    Plaza J.: ‘Logics of public communications’. Synthese: Knowledge, Rationality, and Action 158(2), 165–179 (2007)Google Scholar
  21. 21.
    Rott, Hans, Change, Choice and Inference: A Study in Belief Revision and Nonmonotonic Reasoning, Oxford University Press, 2001.Google Scholar
  22. 22.
    Rott, Hans, ‘Shifting priorities: Simple representations for 27 iterated theory change operators’, in H. Lagerlund, S. Lindström, and R. Sliwinski, (eds.), Modality Matters: Twenty-Five Essays in Honor of Krister Segerberg, vol. 53 of Uppsala Philosophical Studies, 2006, pp. 359–384.Google Scholar
  23. 23.
    Segerberg Krister: ‘Belief revision from the point of view of doxastic logic’. Journal of the IGPL 3(4), 535–553 (1995)CrossRefGoogle Scholar
  24. 24.
    Shafer, Glen, A Mathematical Theory of Evidence, Princeton University Press, 1976.Google Scholar
  25. 25.
    Shoham, Yoav, and Kevin Leyton-Brown, Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations, Cambridge University Press, 2009.Google Scholar
  26. 26.
    Stalnaker Robert: ‘Knowledge, belief and counterfactual reasoning in games’. Economics and Philosophy 12(02), 133–163 (1996)CrossRefGoogle Scholar
  27. 27.
    Su, Kaile, Abdul Sattar, Guido Governatori, and Qingliang Chen, ‘A computationally grounded logic of knowledge, belief and certainty’, in Proceedings of the fourth international joint conference on autonomous agents and multiagent systems, AAMAS ’05, 2005, pp. 149–156.Google Scholar
  28. 28.
    van Benthem Johan: ‘Dynamic logic for belief revision’. Journal of Applied Non-Classical Logics 14(2), 129–155 (2004)Google Scholar
  29. 29.
    van Benthem, Johan, ‘A note on modeling theories’, in R. Festa, A. Aliseda, and J. Peijnenburg, (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, 2005, pp. 403–419.Google Scholar
  30. 30.
    van Benthem Johan: ‘Merging observation and access in dynamic logic’. Studies in Logic 1(1), 1–17 (2008)Google Scholar
  31. 31.
    van Benthem, Johan, Logical Dynamics of Information Flow, Cambridge University Press, 2011.Google Scholar
  32. 32.
    van Benthem, Johan, and Stefan Minica, ‘Toward a dynamic logic of questions’, in Xiangdong He, John F. Horty, and Eric Pacuit, (eds.), Logic, Rationality, and Interaction, vol. 5834 of LNCS, Springer, 2009, pp. 27–41.Google Scholar
  33. 33.
    van Benthem, Johan, and Eric Pacuit, ‘Dynamic logics of evidence-based belief’, Tech. rep., Institute for Logic, Language and Computation, 2011.Google Scholar
  34. 34.
    van Benthem Johan, Fernando Raymundo Velázquez-Quesada: ‘The dynamics of awareness’. Synthese 177, 5–27 (2010)CrossRefGoogle Scholar
  35. 35.
    van Ditmarsch, H., W. van der Hoek, and B. Kooi, Dynamic Epistemic Logic, Synthese Library, Springer, 2007Google Scholar
  36. 36.
    Velazquez-Quesada F.R.: ‘Inference and update’. Synthese (Knowledge, Rationality and Action) 169(2), 283–300 (2009)Google Scholar
  37. 37.
    Veltman, Frank, ‘Prejudices, presuppositions and the theory of conditionals’, in Jeroen Groenendijk, and Martin Stokhof, (eds.), Amsterdam Papers in Formal Grammar, vol. 1, 1976, pp. 248–281.Google Scholar
  38. 38.
    Zvesper, Jonathan, Playing with Information, Ph.D. thesis, ILLC University of Amsterdam Dissertation Series DS-2010-02, 2010.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Institute for Logic, Language and ComputationUniversity of AmsterdamAmsterdamThe Netherlands
  2. 2.Department of PhilosophyStanford UniversityStanfordUSA
  3. 3.Tilburg Center for Logic and Philosophy of ScienceTilburg UniversityTilburgThe Netherlands

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