Specifying various time models with temporal propositional variables in duration calculus

Many extensions of Duration Calculus (DC) have been proposed for handling different aspects of real-time systems. For each extension several different semantics are defined for different time structures which are suitable for different applications and achieve low complexity for the decidability of some properties. Hence, different proof systems have to be developed for reasoning in different calculi. We demonstrate that with temporal propositional letters, many useful time structures and operators can be completely described in the original DC with continuous time. Hence, we can use the proof system for original DC and the specification of the specific time structure to reason in that time structure without the need of introducing a new calculus.