A Temporal Differential Dynamic Logic Formal Embedding

Differential temporal dynamic logic dTL2 is a logic to specify and verify temporal properties of hybrid systems. It extends differential dynamic logic (dL) with temporal operators that enable reasoning on intermediate states in both discrete and continuous dynamics. This paper presents an embedding of dTL2 in the Prototype Verification System (PVS). The embedding includes the formalization of a trace semantics as well as the logic and proof calculus of dTL, which have been enhanced to support the verification of universally quantified reachability properties. The embedding is fully functional and can be used to interactively verify hybrid programs in PVS using a combination of PVS proof commands and specialized proof strategies.