Propositional Temporal Logics and Equivalences

We compare propositional temporal logics by comparing the equivalences that they induce on models. Linear time, branching time and partial order temporal logics are considered. The logics are interpreted on occurrence transition systems, generated by labelled prime event structures without auto-concurrency. The induced equivalences are also compared to directly deened equivalences, e.g., history preserving bisimulation, pomset bisimulation, pom-set trace equivalence, and others. It is then shown which of the induced equivalences are and which are not preserved under action reenement. Rather unexpectedly, the addition of the backward next step operator to the weakest logic considered yields a logic stronger than all others. It is shown that weak history preserving bisimulation can be obtained as the equivalence induced by a slightly constrained version of that logic.