Title: Agreeing to Disagree in Probabilistic Dynamic Epistemic Logic
Authors: Demey, Lorenz # ×
Issue Date: 2014
Publisher: Springer
Series Title: Synthese: an International Journal for Epistemology, Methodology and Philosophy of Science vol:191 issue:3 pages:409-438
Abstract: 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.
ISSN: 0039-7857
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Centre for Logic and Analytical Philosophy
× corresponding author
# (joint) last author

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