Logic and Interactive Rationality Yearbook 2010 pages:1-26
LIRa Seminar location:Amsterdam
This paper studies Aumann's agreeing to disagree theorem from the perspective of probabilistic dynamic epistemic logic. We introduce 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, we provide a sound and complete axiomatization of a dynamic agreement logic, in which one of these agreement theorems can be derived syntactically. These technical results are then used to clarify some conceptual issues surrounding the agreement theorem, in particular the role of common knowledge and the importance of explicitly representing the dynamics.