Public Announcement Logics with Constrained Protocols

Public announcement logic (PAL) is a paradigm case of dynamic epistemic logic, which models how agents’ epistemic states change when pieces of information are communicated publicly. PAL extends epistemic logic with the operator [A], where the intended reading of [A]φ is “After a public announcement that A, φ holds.” This logic has recently received two improvements. One improvement, studied in [1], is to extend PAL with a generalized public announcement operator that allows quantification over public announcements. The other, studied in [5, 6], is a semantic setting to model “announcement protocols” to restrict the announcable sequences of formulas, while whatever is true is assumed to be announcable in PAL itself. The purpose of the present paper is to merge these two kinds of improvements. We consider the extension of public announcement logic with the generalized public announcement operator in the semantic setting of restricted announcement protocols.