Moments and Points in an Interval-Based Temporal Logic

The literature on the nature and representation of time is full of disputes and contradictory theories. This is surprising since the nature of time does not cause any worry for people in their everyday coping with the world. What this suggests is that there is some form of common sense knowledge about time that is rich enough to enable people to deal with the world, and that is universal enough to enable cooperation and communication between people. In this paper, we propose such a theory and defend it in two different ways. We axiomatize a theory of time in terms of intervals and the single relation MEET. We then show that this axiomatization subsumes Allen's interval-based theory. We then extend the theory by formally defining the beginnings and endings of intervals and show that these have properties we normally would associate with points. We distinguish between these point-like objects and the concept of moment as hypothesized in discrete time models. Finally, we examine the theory in terms of each of several different models. This research was supported in part by the National Science Foundation under Grant DCR-8502481 and the Air Force Systems Command, Rome Air Development Center and the Air Force Office of Scientific Research under Contract F30602-85-C­ 0008, which supports the Northeast Artificial Intelligence Consortium (NAIC). *P.J. Hayes's current address is Xerox Palo Alto Research Center, 3333 Coyote Hill Road, Palo Alto, CA, 94304.