Towards a formal characterization of temporal repetition with closed time

Proposes a novel approach to formally characterize temporal repetition. This differs from what has appeared so far in the AI/temporal reasoning literature, where time and particularly temporal repetition are represented within a linear structure. We propose to model temporal objects representing repetition with a closed time structure. Based on convex intervals and J.F. Allen's (1983) convex relations, we define a new temporal object: the time loop. Such an object captures in one cycle the core of what is repeated and which relations hold between each repetition. Hence, this formalism allows one, for example, to concisely represent the scheduling of regular meetings in a university, to specify calendars and to represent repetitive processes, such as those occurring in an assembly line.