Action versus state based logics for transition systems

A temporal logic based on actions rather than on states is presented and interpreted over labelled transition systems. It is proved that it has essentially the same power as CTL*, a temporal logic interpreted over Kripke structures. The relationship between the two logics is established by introducing two mappings from Kripke structures to labelled transition systems and viceversa and two transformation functions between the two logics which preserve truth. A branching time version of the action based logic is also introduced. This new logic for transition systems can play an important role as an intermediate between Hennessy-Milner Logic and the modal μ-calculus. It is sufficiently expressive to describe safety and liveness properties but permits model checking in linear time.