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