The power of the future perfect in program logics

Abstract

The expressiveness of branching time tense (temporal) logics whose eventually operators are relativised to general paths into the future is investigated. These logics are interpreted in models obtained by generalising the usual notion of transition system to allow infinite transitions. It is shown that the presence of formulae expressing the future perfect enables one to prove that the expressiveness of the logic can be characterised by a notion of bisimulation on the generalised transition systems. The future perfect is obtained by adding a past tense operator to the language. Finally the power of various tense languages from the literature are investigated in this framework.