Journal of Philosophical Logic

, Volume 41, Issue 4, pp 735–764 | Cite as

Agreement Theorems in Dynamic-Epistemic Logic

  • Cédric DégremontEmail author
  • Oliver RoyEmail author


This paper introduces Agreement Theorems to dynamic-epistemic logic. We show first that common belief of posteriors is sufficient for agreement in epistemic-plausibility models, under common and well-founded priors. We do not restrict ourselves to the finite case, showing that in countable structures the results hold if and only if the underlying plausibility ordering is well-founded. We then show that neither well-foundedness nor common priors are expressible in the language commonly used to describe and reason about epistemic-plausibility models. The static agreement result is, however, finitely derivable in an extended modal logic. We provide the full derivation. We finally consider dynamic agreement results. We show they have a counterpart in epistemic-plausibility models, and provide a new form of agreements via public announcements.


Agreement theorems Dynamic-epistemic logic Information Belief revision Fixed-point logic Hybrid logic 


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  1. 1.
    Aumann, R. J. (1976). Agreeing to disagree. Annals of Statistics, 4, 1236–1239.CrossRefGoogle Scholar
  2. 2.
    Bacharach, M. (1985). Some extensions of a claim of Aumann in an axiomatic model of knowledge. Journal of Economic Theory, 37(1), 167–190.CrossRefGoogle Scholar
  3. 3.
    Baltag, A., Moss, L. S., & Solecki, S. (1998). The logic of public announcements, common knowledge, and private suspicions. In TARK ’98: Proceedings of the 7th conference on theoretical aspects of rationality and knowledge (pp. 43–56). San Francisco: Morgan Kaufmann Publishers Inc.Google Scholar
  4. 4.
    Baltag, A., & Smets, S. (2006). Conditional doxastic models: A qualitative approach to dynamic belief revision. In G. Mints, & R. de Queiroz (Eds.), Proceedings of WOLLIC 2006, electronic notes in theoretical computer science (Vol. 165).Google Scholar
  5. 5.
    Baltag, A., & Smets, S. (2008). A qualitative theory of dynamic interactive belief revision. In G. Bonanno, W. van der Hoek, & M. Wooldridge (Eds.), Logic and the foundation of game and decision theory (LOFT7). Texts in logic and games (Vol. 3, pp. 13–60). Amsterdam University Press.Google Scholar
  6. 6.
    Baltag, A., & Smets, S. (2009). Group belief dynamics under iterated revision: fixed points and cycles of joint upgrades. In A. Heifetz (Ed.), TARK (pp. 41–50), New York: ACM.Google Scholar
  7. 7.
    Baltag, A., & Smets, S. (2009). Learning by questions and answers: From belief-revision cycles to doxastic fixed points. LNCS, 5514/2009, 124–139.Google Scholar
  8. 8.
    van Benthem, J. (2007). Dynamic logic for belief revision. Journal of Applied Non-classical Logics, 17(2), 129–155.CrossRefGoogle Scholar
  9. 9.
    van Benthem, J. (2007). Rational dynamics and epistemic logic in games. International Game Theory Review, 9(1), 377–409. Erratum reprint 9(2), 377–409.CrossRefGoogle Scholar
  10. 10.
    van Benthem, J. (2006). One is a lonely number. In Z. Chatzidakis, P. Koepke, & W. Pohlers (Eds.), Logic colloquium ’02. Wellesley: ASL & A.K. Peters.Google Scholar
  11. 11.
    Blackburn, P., de Rijke, M., & Venema, Y. (2001). Modal logic. In: Cambridge tracts in theoretical computer science (Vol. 53). UK: Cambridge University Press.Google Scholar
  12. 12.
    Board, O. (2004). Dynamic interactive epistemology. Games and Economic Behavior, 49, 49–80.CrossRefGoogle Scholar
  13. 13.
    Bonanno, G., & Nehring, K. (1997). Agreeing to disagree: A survey. Department of Economics 97-18, California Davis.Google Scholar
  14. 14.
    Bourbaki, N. (1949). Sur le théorème de Zorn. Archiv der Mathematik, 2, 434–437.CrossRefGoogle Scholar
  15. 15.
    Cate, B. t. (2005). Model theory for extended modal languages. Ph.D. thesis, University of Amsterdam. ILLC Dissertation Series DS-2005-01.Google Scholar
  16. 16.
    Cave, J. A. K. (1983). Learning to agree. Economics Letters, 12(2), 147–152.CrossRefGoogle Scholar
  17. 17.
    Dégremont, C. (2010). The temporal mind. PhD dissertation, ILLC, Amsterdam, DS-2010-03.Google Scholar
  18. 18.
    Degremont, C., & Roy, O. (2009). Agreement theorems in dynamic-epistemic logic. In A. Heifetz (Ed.), Proceedings of TARK’09 (theoretical aspects of rationality and knowledge) (pp. 91–98). ACM Digital Library.Google Scholar
  19. 19.
    Demey, L. (2010). Agreeing to disagree in probabilistic dynamic epistemic logic. Master’s thesis, Institute for Logic, Language and Computation, Amsterdam.Google Scholar
  20. 20.
    van Ditmarsch, H., van der Hoek, W., & Kooi, B. (2007). Dynamic epistemic logic. In: Synthese library series (Vol. 337). Springer.Google Scholar
  21. 21.
    Fagin, R., Halpern, J. Y., Moses, Y., & Vardi, M. Y. (1995). Reasoning about knowledge. Cambridge: MIT Press. ISBN 0262061627.Google Scholar
  22. 22.
    Geanakoplos, J. D., & Polemarchakis, H. M. (1982). We can’t disagree forever. Journal of Economic Theory, 28(1), 192–200.CrossRefGoogle Scholar
  23. 23.
    Gerbrandy, J. (1999). Bisimulations on planet Kripke. PhD thesis, ILLC, Amsterdam.Google Scholar
  24. 24.
    Monderer, D., & Samet, D. (1989). Approximating common knowledge with common beliefs. Games and Economic Behavior, 1(2), 170–190.CrossRefGoogle Scholar
  25. 25.
    Plaza, J. A. (1989). Logics of public communications. In M. L. Emrich, M. S. Pfeifer, M. Hadzikadic, & Z. W. Ras (Eds.), Proceedings of the 4th international symposium on methodologies for intelligent systems: Poster session program (pp. 201–216). Oak Ridge National Laboratory.Google Scholar
  26. 26.
    Samet, D. (2010) Agreeing to disagree: The non-probabilistic case. Games and Economic Behavior, 69(1), 169–174.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of Artificial IntelligenceUniversity of GroningenGroningenThe Netherlands
  2. 2.Munich Center for Mathematical PhilosophyLudwig-Maximilians-Universität MünchenMünchenGermany

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