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.
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Dégremont, C., Roy, O. (2009). Agreement Theorems in Dynamic-Epistemic Logic. In: He, X., Horty, J., Pacuit, E. (eds) Logic, Rationality, and Interaction. LORI 2009. Lecture Notes in Computer Science(), vol 5834. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04893-7_9
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DOI: https://doi.org/10.1007/978-3-642-04893-7_9
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