Time Domain

In its full generality, a time domain can be defined as a set of temporal individuals connected by a set of temporal relations. Different choices for the temporal individuals and/or the temporal relations give rise to different temporal ontologies. In the database context, the most common temporal ontology takes time instants (equivalently, points or moments) as the temporal individuals and a linear order over them as the (unique) temporal relation [5]. In addition, one may distinguish between discrete and dense, possibly continuous, time domains and between bounded and unbounded time domains. In the discrete case, one may further consider whether the time domain is finite or infinite and, in the case of unbounded domains, one can differentiate between left-bounded, rightbounded, and totally unbounded domains. Moreover, besides linear time, one may consider branching time, where the linear order is replaced with a partial one (a tree or even a directed acyclic graph), or circular time, which can be used to represent temporal periodicity. As for temporal individuals, time instants can be replaced with time intervals (equivalently, periods or anchored stretches of time) connected by (a subset of) Allen’s relations before, meets, overlaps, starts, during, equal, and finishes, and their inverses or suitable combinations [7]. As in the case of instant-based domains, one may distinguish between discrete and dense domains, bounded and unbounded domains, linear, branching, and circular domains, and so on.