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In the last years the representation and management of temporal information has become crucial for several computer applications. In the temporal database literature, every fact stored into a database may be equipped with two temporal dimensions: the valid time, that describes the time when the fact is true in the modeled reality, and the transaction time, that describes the time when the fact is current in the database and it can be retrieved. Temporal functional dependencies (TFDs) add (transaction) valid time to classical functional dependencies (FDs) in order to express database integrity constraints over the flow of time. Currently, proposals dealing with TFDs adopt a point-based approach, where tuples hold at specific time points. Moreover, TFDs may involve the use of different granularities (i.e., partitions of the time domain), to express integrity constraints as "for each month, the salary of an employee depends only on his role". At the best of our knowledge, there are no proposals dealing with interval-based temporal functional dependencies (ITFDs for short) where the associated valid time is represented by an interval. In this paper, we propose a set of ITFDs based on the Allen's interval relations, we analyze their expressive power with respect to other TFDs proposed in the literature and we propose an algorithm for verifying ITFDs in a database system.