An interval-based temporal relational calculus for events with gaps

Abstract

Abstract Traditional interval-based representations of time assume interval convexity, i.e., that intervals are uninterrupted. This assumption makes it difficult to represent the common sense notion of a single event with ‘gaps’. Having a representation of this species of event contributes favorably to the ability of the human or machine to solve certain tasks, such as planning or database retrieval. This paper defines two kinds of discourse and knowledge object which comprise collections of convex intervals. Although other researchers have suggested the need for a relaxation of the assumption of convexity in event representation, there has been no attempt to offer a concise representation of gapped events. The formulation employed here to introduce gapped events is an extension of James Allen's interval-based approach to time representation. Allen's calculus of thirteen binary relations defined between two convex intervals is generalized to a matrix of binary relations between each pair of subintervals o...