Temporal Properties

Abstract

This chapter considers expanding modal logic by operators that allow one to express standard global and temporal properties of a process or labelled transition system. These include temporal operators for expressing when a property is always, possibly, or eventually true in the future. These operators are associated with fixed point equations over the modal logic, and it is shown how solutions for these equations can be obtained by evaluating these equations over a given labelled transition system. Next, the syntax and semantics of the modal mu-calculus are formally introduced and it is shown how, for the negation-free fragment, solutions for modal formulae can be computed. It is then discussed how recursive properties of processes can be encoded by using least and greatest fixed points and how these fixed points can be computed iteratively. As examples, it is shown how the standard temporal operators considered can be defined in the modal mu-calculus, as well as various other advanced properties.