Extending probabilistic dynamic epistemic logic

This paper aims to extend in two directions the probabilistic dynamic epistemic logic provided in Kooi’s paper [7] and to relate these extensions to ones made in [10]. Kooi’s probabilistic dynamic epistemic logic adds to probabilistic epistemic logic sentences that express consequences of public announcements. The paper [10] extends [7] to using action models, but in both papers, the probabilities are discrete, and are defined on trivial σalgebras over finite sample spaces. The first extension offered in this paper is to add a previous-time operator to a probabilistic dynamic epistemic logic similar to Kooi’s in [7]. The other is to involve non-trivial σ-algebras and continuous probabilities in probabilistic dynamic epistemic logic.