Probabilistic Dynamic Epistemic Logic

In this paper I combine the dynamic epistemic logic of Gerbrandy (1999) with the probabilistic logic of Fagin and Halpern (1999). The result is a new probabilistic dynamic epistemic logic, a logic for reasoning about probability, information, and information change that takes higher order information into account. Probabilistic epistemic models are defined, and a way to build them for applications is given. Semantics and a proof system is presented and a number of examples are discussed, including the Monty Hall Dilemma