Intuitionistic LTL and a New Characterization of Safety and Liveness

Classical linear-time temporal logic (LTL) is capable of specifying of and reasoning about infinite behaviors only. While this is appropriate for specifying non-terminating reactive systems, there are situations (e.g., assume-guarantee reasoning, run-time verification) when it is desirable to be able to reason about finite and infinite behaviors. We propose an interpretation of the operators of LTL on finite and infinite behaviors, which defines an intuitionistic temporal logic (ILTL). We compare the expressive power of LTL and ILTL. We demonstrate that ILTL is suitable for assume-guarantee reasoning and for expressing properties that relate finite and infinite behaviors. In particular, ILTL admits an elegant logical characterization of safety and liveness properties.