Agreement theorems in dynamic-epistemic logic

  • Authors:

  • Cédric Dégremont;Olivier Roy

  • Affiliations:

  • Institute for Logic, Language and Computation, Universiteit van Amsterdam, The Netherlands;Faculty of Philosophy, University of Groningen, The Netherlands

  • Venue:
  • LORI'09 Proceedings of the 2nd international conference on Logic, rationality and interaction
  • Year:
  • 2009

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Abstract

In this paper we study Aumann's Agreement Theorem in dynamic-epistemic logic. We show that common belief of posteriors is sufficient for agreements in "epistemic-plausibility models", under common and well-founded priors, from which the usual form of agreement results follows, using common knowledge. We do not restrict ourselves to the finite case, and show that in countable structures such results hold if and only if the underlying "plausibility ordering" is well-founded. We look at these results from a syntactic point of view, showing that neither well-foundedness nor common priors are expressible in a commonly used language, but that the static agreement result is finitely derivable in an extended modal logic. We finally consider "dynamic" agreement results, show they have a counterpart in epistemic-plausibility models, and provide a new form of agreements via "public announcements". Comparison of the two types of dynamic agreement reveals that they can indeed be different.