Coalition announcements

Abstract

Coalition announcement logic is one of the family of logics of quantified announcements. It extends public announcement logic with formulas $\langle \! [ G ] \! \rangle \varphi$ that are read as `there is a truthful public announcement by agents from $G$ such that whatever agents from $A \setminus G$ announce at the same time, $\varphi$ holds after the joint announcement.' The logic has enjoyed comparatively less attention than its siblings --- arbitrary and group announcement logics. The reason for such a situation can be partially attributed to the inherent alternation of quantification in coalition announcements. To deal with the problem, we consider relativised group announcements that separate the coalition's announcement from the anti-coalition's response. We present coalition and relativised group announcement logic and show its completeness. Apart from that, we prove that the complexity of the model-checking problem for coalition announcement logic is PSPACE-complete in the general case, and in P in a special case of positive target formulas. We also study relative expressivity of logics of quantified announcements. In particular we show that arbitrary and coalition announcement logics are not at least as expressive as group announcement logic. Finally, we present a counter-example to the proposed definition of coalition announcements in terms of group announcements, and consider some other interesting properties