Three logics for branching bisimulation

Three temporal logics are introduced which induce on labeled transition systems the same identifications as branching bisimulation. The first is an extension of Hennessy-Milner logic with a kind of unit operator. The second is another extension of Hennessy-Milner logic which exploits the power of backward modalities. The third is CTL with the next-time operator interpreted over all paths, not just over maximal ones. A relevant side effect of the last characterization is that it sets a bridge between the state- and event-based approaches to the semantics of concurrent systems.