  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, and that APAL+ is incomparable with APAL. We also
provide a sound and complete infinitary axiomatisation.
