Quantifying over Boolean announcements

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