Agreeing to disagree in probabilistic dynamic epistemic logic
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This paper studies Aumann’s agreeing to disagree theorem from the perspective of dynamic epistemic logic. This was first done by Dégremont and Roy (J Phil Log 41:735–764, 2012) in the qualitative framework of plausibility models. The current paper uses a probabilistic framework, and thus stays closer to Aumann’s original formulation. The paper first introduces enriched probabilistic Kripke frames and models, and various ways of updating them. This framework is then used to prove several agreement theorems, which are natural formalizations of Aumann’s original result. Furthermore, a sound and complete axiomatization of a dynamic agreement logic is provided, in which one of these agreement theorems can be derived syntactically. These technical results are used to show the importance of explicitly representing the dynamics behind the agreement theorem, and lead to a clarification of some conceptual issues surrounding the agreement theorem, in particular concerning the role of common knowledge. The formalization of the agreement theorem thus constitutes a concrete example of the so-called dynamic turn in logic.
KeywordsAumann’s agreement theorem Probabilistic dynamic epistemic logic Dynamic turn Common knowledge
Earlier versions of this paper were presented at local seminars in Tilburg (TiLPS), Amsterdam (ILLC) and Leuven (CLAW). I would like to thank the audiences of these talks for their helpful remarks and suggestions. Furthermore, I would like to thank Johan van Benthem, Cédric Dégremont, Dick de Jongh, Eric Pacuit, and two anonymous referees for their feedback on earlier versions of this paper. The early stages of this research were funded by the University of Leuven’s Formal Epistemology Project and the Huygens Scholarship Programme (NUFFIC); during the final stages I held a PhD fellowship from the Research Foundation—Flanders (FWO).
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