  Various extensions of public announcement logic have been proposed with
quantification over announcements. The best-known extension is called arbitrary
public announcement logic, APAL. It contains a primitive language construct Box
phi intuitively expressing that "after every public announcement of a formula,
formula phi is true". The logic APAL is undecidable and it has an infinitary
axiomatization. Now consider restricting the APAL quantification to public
announcements of Boolean formulas only, such that Box phi intuitively expresses
that "after every public announcement of a Boolean formula, formula phi is
true". This logic can therefore called Boolean arbitrary public announcement
logic, BAPAL. The logic BAPAL is the subject of this work. Unlike APAL it has a
finitary axiomatization. Also, BAPAL is not at least as expressive as APAL. A
further claim that BAPAL is decidable is deferred to a companion paper.
