Groups Versus Coalitions: On the Relative Expressivity of GAL and CAL

Group Announcement Logic (GAL) and Coalition Announcement Logic (CAL) were proposed to study effects of public announcements by groups of agents on knowledge in multiagent systems. Both logics have operators that quantify over such announcements. In GAL, it is possible to express that 'a group of agents G has a (truthful) announcement such that after this announcement, some property A holds'; for example, A may involve some agents in G gaining additional knowledge, while agents outside G remain ignorant. In CAL, the meaning of the coalition announcement operator is subtly different: it says that 'G has an announcement such that, whatever else the agents outside G announce simultaneously, some property A is guaranteed to hold after the joint announcement'. It has been open for some time whether GAL and CAL are equally expressive. We show that this is not the case: there is a property expressible in GAL that is not expressible in CAL. It is still an open question whether CAL is subsumed by GAL, or whether the two logics have incomparable expressive power.