Abstract

Temporal logic has been extensively utilized in academia and industry to formally specify and verify behavioural properties of numerous kinds of hardware and software. We present a novel way to apply temporal logic to the study of a version of itself, namely, propositional linear-time temporal logic (PTL). This involves a hierarchical framework for obtaining standard results for PTL, including a small model property, decision procedures and axiomatic completeness. A large number of the steps involved are expressed in a propositional version of Interval Temporal Logic (ITL) which is referred to as PITL. It is a natural generalization of PTL and includes operators for reasoning about periods of time and sequential composition. Versions of PTL with finite time and infinite time are both considered and one benefit of the framework is the ability to systematically reduce infinitetime reasoning to finite-time reasoning. The treatment of PTL with the operator until and past time naturally reduces to that for PTL without either one. The interval-oriented methodology differs from other analyses of PTL which typically

Citations