Representation of Non-Convex Time Intervals and Propagation of Non-Convex Relations

Therefore, we have developed a new calculus based on non-convex intervals and have defined a set of corresponding non-convex relations. The non-convex intervals are sets of convex intervals and contain temporal gaps. The non-convex relations are tripels: a first part for specifying the intended manner of the whole relation, a second part for defining relations between subintervals, and a third part for declaring relations of whole, convexified non-convex intervals. In the non-convex calculus the convex intervals and relations of Allen are also integrated as a special case.

Additionally, we have elaborated and fully implemented a constraint propagation algorithm for the non-convex relations. In comparison with the convex case we get a more expressive calculus with same time complexity for propagation and only different by a constant factor.