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Dynamic Logics of Evidence-Based Beliefs

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Abstract

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.

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References

  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)

    Article  Google Scholar 

  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.

  3. Boutilier, Craig, Conditional Logics for Default Reasoning and Belief Revision, Ph.D. thesis, University of Toronto, 1992.

  4. Chellas, Brian, Modal Logic: An Introduction, Cambridge University Press, 1980.

  5. Demey, Lorenz, Agreeing to Disagree in Probabilistic Dynamic Epistemic Logic., Master’s thesis, ILLC University of Amsterdam (LDC 2010-14), 2010.

  6. Dempster A.P.: ‘Upper and lower probabilities induced by a multivalued mapping’. Annals of Mathematical Statistics 38(2), 325–339 (1967)

    Article  Google Scholar 

  7. Gärdenfors, Peter, Knowledge in Flux: Modeling the Dynamics of Epistemic States, Bradford Books, MIT Press, 1988

  8. Girard, Patrick, Modal Logic for Belief and Preference Change, Ph.D. thesis, ILLC University of Amsterdam Dissertation Series DS-2008-04, 2008.

  9. Halpern Joe, Ricardo Pucella: ‘A logic for reasoning about evidence’. Journal of AI Research 26(1), 1–34 (2006)

    Google Scholar 

  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. Hansson, Sven Ove, A Textbook of Belief Dynamics. Theory Change and Database Updating, Kluwer, 1999.

  12. Kratzer Angelika: ‘What must and can must and can mean’. Linguistics and Philosophy 1, 337–355 (1977)

    Article  Google Scholar 

  13. Leitgeb Hannes, Krister Segerberg: ‘Dynamic doxastic logic: why, how and where to?’. Synthese 155(2), 167–190 (2007)

    Article  Google Scholar 

  14. Lewis David: Counterfactuals. Blackwell Publishers, Oxford (1973)

    Google Scholar 

  15. Liu, Fenrong, Reasoning about Preference Dynamics, vol. 354 of Synthese Library, Springer-Verlag, 2008.

  16. Liu, Fenrong, ‘A two-level perspective on preference’, Journal of Philosophical Logic, 2011. To Appear.

  17. Moss, Larry, and Rohit Parikh, ‘Topological reasoning and the logic of knowledge’, in Yoram Moses, (ed.), Proceedings of TARK IV, Morgan Kaufmann, 1992.

  18. Pacuit, Eric, ‘Neighborhood semantics for modal logic: An introduction’, 2007. ESSLLI 2007 course notes (ai.stanford.edu/~epacuit/classes/).

  19. Pauly, Marc, Logic for Social Software, Ph.D. thesis, ILLC University of Amsterdam Dissertation Series DS 2001-10, 2001.

  20. Plaza J.: ‘Logics of public communications’. Synthese: Knowledge, Rationality, and Action 158(2), 165–179 (2007)

    Google Scholar 

  21. Rott, Hans, Change, Choice and Inference: A Study in Belief Revision and Nonmonotonic Reasoning, Oxford University Press, 2001.

  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.

  23. Segerberg Krister: ‘Belief revision from the point of view of doxastic logic’. Journal of the IGPL 3(4), 535–553 (1995)

    Article  Google Scholar 

  24. Shafer, Glen, A Mathematical Theory of Evidence, Princeton University Press, 1976.

  25. Shoham, Yoav, and Kevin Leyton-Brown, Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations, Cambridge University Press, 2009.

  26. Stalnaker Robert: ‘Knowledge, belief and counterfactual reasoning in games’. Economics and Philosophy 12(02), 133–163 (1996)

    Article  Google Scholar 

  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.

  28. van Benthem Johan: ‘Dynamic logic for belief revision’. Journal of Applied Non-Classical Logics 14(2), 129–155 (2004)

    Google Scholar 

  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.

  30. van Benthem Johan: ‘Merging observation and access in dynamic logic’. Studies in Logic 1(1), 1–17 (2008)

    Google Scholar 

  31. van Benthem, Johan, Logical Dynamics of Information Flow, Cambridge University Press, 2011.

  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.

  33. van Benthem, Johan, and Eric Pacuit, ‘Dynamic logics of evidence-based belief’, Tech. rep., Institute for Logic, Language and Computation, 2011.

  34. van Benthem Johan, Fernando Raymundo Velázquez-Quesada: ‘The dynamics of awareness’. Synthese 177, 5–27 (2010)

    Article  Google Scholar 

  35. van Ditmarsch, H., W. van der Hoek, and B. Kooi, Dynamic Epistemic Logic, Synthese Library, Springer, 2007

  36. Velazquez-Quesada F.R.: ‘Inference and update’. Synthese (Knowledge, Rationality and Action) 169(2), 283–300 (2009)

    Google Scholar 

  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.

  38. Zvesper, Jonathan, Playing with Information, Ph.D. thesis, ILLC University of Amsterdam Dissertation Series DS-2010-02, 2010.

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Authors and Affiliations

  1. Institute for Logic, Language and Computation, University of Amsterdam, 1090 GE, Amsterdam, The Netherlands

    J. van Benthem

  2. Department of Philosophy, Stanford University, Stanford, CA, 94305, USA

    J. van Benthem

  3. Tilburg Center for Logic and Philosophy of Science, Tilburg University, P.O. Box 90153, 5000 LE, Tilburg, The Netherlands

    E. Pacuit

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  1. J. van Benthem
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  2. E. Pacuit
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Correspondence to J. van Benthem.

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Dedicated to Professor Ryszard Wójcicki on the occasion of his 80th birthday

Ryszard has been an inspirational leader in logical research and a major force in the organization of the field for decades. His influence is felt in many circles in many countries. It is an honour to contribute to this special issue of Studia Logica our article to him.

Special issue in honor of Ryszard Wójcicki on the occasion of his 80th birthday

Edited by J. Czelakowski, W. Dziobiak, and J. Malinowski

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van Benthem, J., Pacuit, E. Dynamic Logics of Evidence-Based Beliefs. Stud Logica 99, 61 (2011). https://doi.org/10.1007/s11225-011-9347-x

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