Expressive Completeness of Duration Calculus

This paper compares the expressive power of first-order monadic logic of order, a fundamental formalism in mathematical logic and the theory of computation, with that of the Propositional version of Duration Calculus (PDC), a formalism for the specification of realtime systems. Our results show that the propositional duration calculus is expressively complete for first-order monadic logic of order. Our semantics for PDC conservatively extends the standard one to all positive (including infinite) length intervals. Hence, in view of the expressive completeness, liveness properties can be specified in PDC. This observation refutes a widely believed misconception that the Duration Calculus cannot specify liveness properties.