dTL2: 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. This material is based upon work supported by the National Science Foundation under NSF CAREER Award CNS-1054246, NSF EXPEDITION CNS-0926181 and under Grant No. CNS-0931985. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution or government. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of any sponsoring institution or government.