A system for reasoning with nonconvex intervals

We describe a new system of relations for reasoning about general, i.e., both convex and nonconvex, intervals of time. This system is essentially an integration of Allen's theory (J.F. Allen, 1981; 1984) and a one-dimensional version of the Region Connection Calculus of A.G. Cohn et al. (1997) and D.A. Randall et al. (1992). When dealing solely with convex intervals, this system reduces to Allen's set of relations. Fundamental to the definition of our system is the concept of convexity with respect to an interval, an extension of the concept of convexity.