The Relative Expressivity of Public and Private Communication in BMS Logic

Dynamic Epistemic Logic (DEL) is the study of formal logics that reason about knowledge change. In DEL research, events that cause changes in knowledge are called updates. One class of updates—the BMS updates due to Baltag, Moss, and Solecki—has received much attention in the DEL literature because of the joint expressive power of the various BMS Logics based on these updates. There is, however, very little known about the relative expressive power of the BMS Logics based on individual BMS updates. The purpose of the present paper is two-fold. First, we provide a succinct, self-contained exposition of the rather complicated syntax and semantics for the class of BMS Logics. Second, we study the relative expressivity of BMS Logics for public and private communication. The results we obtain are a first-step in a larger study whose aim is to characterize the relative expressive power of BMS Logics in general.