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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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