The completeness of a natural system for reasoning with time intervals

Abstract

James Allen defined a calculus of time intervals by identifying time intervals as pairs of real numbers, and considering binary relations that can hold between such pairs [Alll83]. We call this the Interval Calculus. We consider the system of interval time units defined in [Lad86.2] (the TUS), which was intended for the natural representation of real clock time on any scale. We introduce the convex part of the TUS, and show that it may be regarded as a canonical model of the Interval Calculus. We discuss the consequences of this result.