  We define a general notion of transition system where states and action
labels can be from arbitrary nominal sets, actions may bind names, and state
predicates from an arbitrary logic define properties of states. A
Hennessy-Milner logic for these systems is introduced, and proved adequate and
expressively complete for bisimulation equivalence. A main technical novelty is
the use of finitely supported infinite conjunctions. We show how to treat
different bisimulation variants such as early, late, open and weak in a
systematic way, explore the folklore theorem that state predicates can be
replaced by actions, and make substantial comparisons with related work. The
main definitions and theorems have been formalised in Nominal Isabelle.
