Abstract
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.
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References
Aumann, R. J. (1976). Agreeing to disagree. Annals of Statistics, 4, 1236–1239.
Bacharach, M. (1985). Some extensions of a claim of Aumann in an axiomatic model of knowledge. Journal of Economic Theory, 37(1), 167–190.
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.
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).
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.
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.
Baltag, A., & Smets, S. (2009). Learning by questions and answers: From belief-revision cycles to doxastic fixed points. LNCS, 5514/2009, 124–139.
van Benthem, J. (2007). Dynamic logic for belief revision. Journal of Applied Non-classical Logics, 17(2), 129–155.
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.
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.
Blackburn, P., de Rijke, M., & Venema, Y. (2001). Modal logic. In: Cambridge tracts in theoretical computer science (Vol. 53). UK: Cambridge University Press.
Board, O. (2004). Dynamic interactive epistemology. Games and Economic Behavior, 49, 49–80.
Bonanno, G., & Nehring, K. (1997). Agreeing to disagree: A survey. Department of Economics 97-18, California Davis.
Bourbaki, N. (1949). Sur le théorème de Zorn. Archiv der Mathematik, 2, 434–437.
Cate, B. t. (2005). Model theory for extended modal languages. Ph.D. thesis, University of Amsterdam. ILLC Dissertation Series DS-2005-01.
Cave, J. A. K. (1983). Learning to agree. Economics Letters, 12(2), 147–152.
Dégremont, C. (2010). The temporal mind. PhD dissertation, ILLC, Amsterdam, DS-2010-03.
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.
Demey, L. (2010). Agreeing to disagree in probabilistic dynamic epistemic logic. Master’s thesis, Institute for Logic, Language and Computation, Amsterdam.
van Ditmarsch, H., van der Hoek, W., & Kooi, B. (2007). Dynamic epistemic logic. In: Synthese library series (Vol. 337). Springer.
Fagin, R., Halpern, J. Y., Moses, Y., & Vardi, M. Y. (1995). Reasoning about knowledge. Cambridge: MIT Press. ISBN 0262061627.
Geanakoplos, J. D., & Polemarchakis, H. M. (1982). We can’t disagree forever. Journal of Economic Theory, 28(1), 192–200.
Gerbrandy, J. (1999). Bisimulations on planet Kripke. PhD thesis, ILLC, Amsterdam.
Monderer, D., & Samet, D. (1989). Approximating common knowledge with common beliefs. Games and Economic Behavior, 1(2), 170–190.
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.
Samet, D. (2010) Agreeing to disagree: The non-probabilistic case. Games and Economic Behavior, 69(1), 169–174.
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Dégremont, C., Roy, O. Agreement Theorems in Dynamic-Epistemic Logic. J Philos Logic 41, 735–764 (2012). https://doi.org/10.1007/s10992-012-9236-4
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DOI: https://doi.org/10.1007/s10992-012-9236-4