Arbitrary public announcement logic ) reasons about how the knowledge of a set of agents changes after true public announcements and after arbitrary announcements of true epistemic formulas. We consider a variant of arbitrary public announcement logic called positive arbitrary public announcement logic ), which restricts arbitrary public announcements to announcement of positive formulas. Positive formulas prohibit statements about the ignorance of agents. The positive formulas correspond to the universal fragment in first-order logic. As two successive announcements of positive formulas (...) need not correspond to the announcement of a positive formula, \ is rather different from \. We show that \ is more expressive than public announcement logic \, and that \ is incomparable with \. We also provide a sound and complete infinitary axiomatisation. (shrink)

There are several ways to quantify over public announcements. The most notable are reflected in arbitrary, group, and coalition announcement logics, with the latter being the least studied so far. In the present work, we consider coalition announcements through the lens of group announcements, and provide a complete axiomatisation of a logic with coalition announcements. To achieve this, we employ a generalisation of group announcements. Moreover, we study some logical properties of both coalition and group announcements that have not been (...) studied before. (shrink)

We introduce Arbitrary Public Announcement Logic with Memory (APALM), obtained by adding to the models a ‘memory’ of the initial states, representing the information before any communication took place (“the prior”), and adding to the syntax operators that can access this memory. We show that APALM is recursively axiomatizable (in contrast to the original Arbitrary Public Announcement Logic, for which the corresponding question is still open). We present a complete recursive axiomatization, that includes a natural finitary rule, and study this (...) logic’s expressivity and the appropriate notion of bisimulation. We then examine Group Announcement Logic with Memory (GALM), the extension of APALM obtained by adding to its syntax group announcement operators, and provide a complete finitary axiomatization (again in contrast to the original Group Announcement Logic, for which the only known axiomatization is infinitary). We also show that, in the memory-enhanced context, there is a natural reduction of the so-called coalition announcement modality to group announcements (in contrast to the memory-free case, where this natural translation was shown to be invalid). (shrink)