  We investigate the expressive power of the two main kinds of program logics
for complex, non-regular program properties found in the literature: those
extending propositional dynamic logic (PDL), and those extending the modal
mu-calculus. This is inspired by the recent discovery of a decidable program
logic called Visibly Pushdown Fixpoint Logic with Chop which extends both the
modal mu-calculus and PDL over visibly pushdown languages, which, so far,
constituted the ends of two pillars of decidable program logics.
  Here we show that this logic is not only more expressive than either of its
two fragments, but in fact even more expressive than their union. Hence, the
decidability border amongst program logics has been properly pushed up. We
complete the picture by providing results separating all the PDL-based and
modal fixpoint logics with regular, visibly pushdown and arbitrary context-free
constructions.
