On the Weak Adequacy of Branching-Time Remporal Logic

We study the adequacy of branching-time temporal logic w.r.t. bisimulation semantics in the framework of non-deterministic programs without the finitely-branching restriction. The process equivalence generated by branching-time logic is compared with bisimulation and with two observational equivalences. It is found at best weakly adequate. This further illustrates the strength of the finitely-branching restriction. However, we argue that in connection with branching time temporal logic, one has no better choice than bisimulation as a semantic equivalence: in particular, the equivalence generated by temporal logic is not a congruence w.r.t. usual process operators.

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