This article proposes a crisp-based approach for representing and reasoning about concepts evolving in time and of their properties in terms of qualitative relations (e.g., “before”) in addition to quantitative ones, time intervals and points. It is not only suitable to handle precise time intervals and points, but also imprecise ones. It extends the 4D-fluents approach with crisp components to represent handed data. It also extends the Allen's interval algebra. This extension allows reasoning about imprecise time intervals. Compared to related work, it is based on crisp set theory. These relations preserve many properties of the original algebra. Their definitions are adapted to allow relating a time interval and a time point, and two time points. All relations can be used for temporal reasoning by means of transitivity tables. Finally, it proposes a crisp ontology that based on the extended Allen's algebra instantiates the 4D-fluents-based representation.
