A common-sense theory of time

TLDR

The literature on time is marked by disputes, yet everyday life proceeds smoothly, implying a universal common‑sense understanding of time. The authors propose a common‑sense theory of time and defend it through two distinct arguments. The theory is axiomatized using intervals and the MEET relation, extended with formal definitions of interval endpoints and point‑like objects distinct from discrete moments, and then evaluated across several models. The axiomatization subsumes Allen’s interval theory, demonstrating its broader applicability.

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.