  Dynamic epistemic logics consider formal representations of agents'
knowledge, and how the knowledge of agents changes in response to informative
events, such as public announcements. Quantifying over informative events
allows us to ask whether it is possible to achieve some state of knowledge, and
has important applications in synthesising secure communication protocols.
However, quantifying over quite simple informative events, public
announcements, is not computable: such an arbitrary public announcement logic,
APAL, has an undecidable satisfiability problem. Here we consider even simpler
informative events called Boolean announcements, where announcements are
restricted to be a Boolean combination of atomic propositions. The logic is
called Boolean arbitrary public announcement logic, BAPAL. A companion paper
provides a complete finitary axiomatization, and related expressivity results,
for BAPAL. In this work the satisfiability problem for BAPAL is shown to
decidable, and also that BAPAL does not have the finite model property.
