Title: Cyclic time intervals

Patrick J Hayes

University of West Florida

**
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.