A common-sense theory of time

TLDR: This paper proposes an axiomatic a theory of time in terms of intervals and the single relation MEET and shows that this axiomatization subsumes Allen's interval-based theory.

Abstract: 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 which 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 axiomatic 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 the 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