Realizing Public Announcements by Justifications

Modal public announcement logics study how public announcements affect changes in beliefs of the agents. What cannot be expressed in these logics, however, is the exact reasons for the updated beliefs. Justification Logic suggests a way of filling this gap by representing evidence and/or justifications for agents’ beliefs in the object language. We present two alternative justification counterparts of Gerbrandy-Groeneveld's logic of public introspective announcements over the basic modal logic K. In particular, we show that erasing justifications for belief in either of the two suggested counterparts yields a valid modal statement about announcements. For the opposite direction, we establish a constructive procedure for restoring justifications within modalities, a process called realization, for one of the suggested counterparts provided the modalities occur outside of announcements. We discuss how recording more information about announcements in our system of justifications in the other suggested counterpart creates difficulties for applying the method of “realization by reduction” we have developed.
(Joint work with Samuel Bucheli and Thomas Studer, University of Bern.)