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We argue that certain familiar ontology design problems are profitably addressed by treating ontologies as theories and by defining a set of operations that create new on-tologies, including their constraints, out of other ontologies. Such operations extend the idea of namespaces to take into account constraints. Consider first the problem of designing an ontology to publish data on the Web. If the designer follows the Linked Data principles (Bernes-Lee, 2006; Bizer et al., 2007), he must select known ontologies, as much as possible, to organize the data so that applications “can dereference the URIs that identify vocabulary terms in order to find their definition”. We argue that the designer should go further and analyze the constraints of the ontologies from which he is drawing the terms to construct his vo-cabulary. Furthermore, he should publish the data in such a way that the original se-mantics of the terms is preserved. To facilitate ontology design from this perspective, we introduce three operations on ontologies, called projection, union and deprecation. Consider now the problem of comparing the expressive power of two ontologies, O1=(V1,Σ1) and O2=(V2,Σ2). If the designer wants to know what they have in common