Positive Announcements

Arbitrary public announcement logic (APAL) 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 (APAL), 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, APAL is rather different from APAL. We show that APAL is more expressive than public announcement logic PAL, that it is incomparable with APAL, and we provide a sound and complete infinitary axiomatisation.