dTL: Differential Temporal Dynamic Logic with Nested Temporalities for Hybrid Systems

The differential temporal dynamic logic dTL is a logic to specify temporal properties of hybrid systems. It combines differential dynamic logic with temporal logic to reason about the intermediate states reached by a hybrid system. The logic dTL supports some linear time temporal properties of LTL. It extends differential temporal dynamic logic dTL with nested temporalities. We provide a semantics and a proof system for the logic dTL, and show its usefulness for nontrivial temporal properties of hybrid systems. We take particular care to handle the case of alternating universal dynamic and existential temporal modalities and its dual, solving an open problem formulated in previous work.