Temporal Logic and the μ-Calculus

As we have briefly discussed in the previous chapter, modal logic is a powerful tool that allows us to check important behavioural properties of systems. In Section 11.6 the focus was on Hennessy-Milner logic, whose main limitation is due to its finitary structure: a formula can express properties of states up to a finite number of steps ahead and thus only local properties can be investigated. In this chapter we show some extensions of Hennessy-Milner logic that increase the expressiveness of the formulas by defining properties about finite and infinite computations. The most expressive language that we present is the μ-calculus, but we start by introducing some other well-known logics for program verification, called temporal logics.