# Semantics and completeness of Duration Calculus

## 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.

## Keywords

Duration Calculus Interval Temporal Logic proof system real-time systems relative completeness specifications specification languages verification## Preview

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