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Dégremont, Cédric ; Roy, Olivier:
Agreement Theorems in Dynamic-Epistemic Logic.
In: Journal of Philosophical Logic.
Bd. 41
(2012)
Heft 4
.
- S. 735-764.
ISSN 1573-0433
DOI: https://doi.org/10.1007/s10992-012-9236-4
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.