Non-deterministic temporal logics for general flow systems

In this paper, we use the constructs of branching temporal logic to formalize reasoning about a class of general flow systems, including discrete-time transition systems, continuous-time differential inclusions, and hybrid-time systems such as hybrid automata. We introduce Full General Flow Logic, GFL*, which has essentially the same syntax as the well-known Full Computation Tree Logic, CTL*, but generalizes the semantics to general flow systems over arbitrary time-lines. We propose an axiomatic proof system for GFL* and establish its soundness w.r.t. the general flow semantics.