A Logic for Verifying Metric Temporal Properties in Distributed Hybrid Systems

We introduce a logic for specifying and verifying metric temporal properties of distributed hybrid systems that combines quantified differential dynamic logic (QdL) for reasoning about the possible behavior of distributed hybrid systems with metric temporal logic (MTL) for reasoning about the metric temporal behavior during their operation. For our combined logic, we generalize the semantics of dynamic modalities to refer to hybrid traces instead of final states. Further, we prove that this gives a conservative extension of QdL for distributed hybrid systems. On this basis, we provide a modular verification calculus that reduces correctness of metric temporal behavior of distributed hybrid systems to generic temporal reasoning and then non-temporal reasoning, and prove that we obtain a complete axiomatization relative to the non-temporal base logic QdL.