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An increasing number of applications rely on RDF, OWL 2, and SPARQL for storing and querying data. SPARQL, however, is not targeted towards end-users, and suitable query interfaces are needed. Faceted search is a prominent approach for end-user data access, and several RDF-based faceted search systems have been developed. There is, however, a lack of rigorous theoretical underpinning for faceted search in the context of RDF and OWL 2. In this paper, we provide such solid foundations. We formalise faceted interfaces for this context, identify a fragment of first-order logic capturing the underlying queries, and study the complexity of answering such queries for RDF and OWL 2 profiles. We then study interface generation and update, and devise efficiently implementable algorithms. Finally, we have implemented and tested our faceted search algorithms for scalability, with encouraging results.