Addressing time intervals

One of the fundamental questions regarding the temporal ontology is what is time composed of. While the traditional time structure is based on a set of points, a notion that has been prevalently adopted in classical physics and mathematics, it has also been noticed that intervals have been widely adopted for expre~sion of common sense temporal knowledge, especially in the domain of artificial intelligence. However, there has been a longstanding debate on how intervals should be addressed, leading to two different approaches to the treatment of intervals. In the first, intervals are addressed as derived objects constructed from points, e.g., as sets of points, or as pairs of points. In the second, intervals are taken as primitive themselves. This article provides a critical examination of these two approaches. By means of proposing a definition of intervals in terms of points and types, we shall demonstrate that, while the two different approaches have been viewed as rivals in the literature, they are actually reducible to logically equivalent expressions under some requisite interpretations, and therefore they can also be viewed as allies.