Differential Temporal Dynamic Logic dTL

Chapter

Synopsis

We combine first-order dynamic logic for reasoning about the possible behaviour of hybrid systems with temporal logic for reasoning about the temporal behaviour during their operation. Our logic supports verification of hybrid programs with first-order definable flows and provides a uniform treatment of discrete and continuous evolution. For our combined logic, we generalise the semantics of dynamic modalities to refer to hybrid traces instead of final states. Further, we prove that this gives a conservative extension of our dynamic logic for hybrid systems. On this basis, we provide a modular verification calculus that reduces correctness of temporal behaviour of hybrid systems to nontemporal reasoning, and prove that we obtain a complete axiomatisation relative to the nontemporal base logic. Using this calculus, we analyse safety invariants in a train control system and symbolically synthesise parametric safety constraints.

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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.School of Computer ScienceCarnegie Mellon UniversityPittsburghUSA

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