Abstract:

Interval relations on a line form a familiar algebraic structure with 13 elements. For many purposes, however, it is convenient to think of time as a circle. Interval relations on a circle form a similar structure with 16 elements, which is much more symmetrical than the linear case, and can be generated from a four-element set (corresponding to four ways to place a point with respect to an interval) by applying three natural invertible mappings (two inversions and a reflection). The transitivity table of this larger structure exhibits the same regularities. The linear case can be obtained from the cyclic case by a projective transformation from a point chosen to be 'at infinity'. The resulting system of constraints seems to have several advantages over the traditional one used for temporal reasoning.