In the Semantic Web field, representing and reasoning on imprecise temporal data is a common requirement. Several works exist to represent and reason on crisp temporal data in ontology; however, to the best of our knowledge, there is no work devoted to handle imprecise temporal data. Representing and reasoning on imprecise time intervals in OWL 2, is the problem this work is dealing with. Our approach is based only on crisp environment. First, we extend the 4D-fluents approach to represent imprecise time intervals and crisp temporal interval relations. Second, we extend the Allen’s interval algebra to propose crisp temporal relations between imprecise time intervals. We show that, unlike most related work, our temporal interval relations preserve many of the properties of the Allen’s interval algebra. Furthermore, we show how they can be used for temporal reasoning by means of a transitivity table. We experimentally infer the resulting temporal relations from the introduced imprecise time intervals via a set of SWRL rules. Finally, we illustrate the usefulness of our work in the context of the Captain Memo memory prosthesis.