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The analysis of the semantics of temporal data and queries plays a central role in the area of temporal databases. Although many different algebrae and models have been proposed, almost all of them are based on a point-based (snapshot) semantics for data. On the other hand, in the areas of linguistics, philosophy, and recently, artificial intelligence, an oft-debated issue concerns the use of an interval-based versus a point-based semantics. In this paper, we first show some problems inherent in the adoption of a point-based semantics for data, then argue that these problems arise because there is no distinction drawn in the data between telic and atelic facts. We then introduce a three-sorted temporal model and algebra including coercion functions for transforming relations of one sort into relations of the other at query time which properly copes with these issues.