Agreement Theorems in Dynamic-Epistemic Logic |
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Authors: | Cédric Dégremont Oliver Roy |
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Affiliation: | 1.Department of Artificial Intelligence,University of Groningen,Groningen,The Netherlands;2.Munich Center for Mathematical Philosophy,Ludwig-Maximilians-Universit?t München,München,Germany |
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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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