Succinctness Gap between Monadic Logic and Duration Calculus

In [8, 11] the expressive completeness of the Propositional fragment of Duration Calculus relative to monadic first-order logic of order was established. In this paper we show that there is at least an exponential blow-up in every meaning preserving translation from monadic logic to PDC. Hence, there exists an exponential gap between the succinctness of monadic logic and that of duration calculus.