Abstract

Duration Calculus was introduced in [1] as a notation to specify real-time systems, and as a calculus to verify theorems about such systems. Its distinctive feature is reasoning about durations of states within any time interval, without explicit mention of absolute time. Duration Calculus, which is an extension of Interval Temporal Logic, was originally designed to reason about real-time requirements for control systems; but it has been used at other levels of abstraction also: for example to give real-time semantics to communicating processes executed on a shared processor configuration and to reason about the correctness of a circuit transformation. The purpose of this paper is to introduce a formal syntax and semantics for Duration Calculus, and to prove its completeness — relative to the completeness of Interval Temporal Logic.

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