A faceted ontology consists of a set of facets, where each facet consists of a predefined set of terms structured by a subsumption relation. We propose two extensions of faceted ontologies, which allow inferring conjunctions of terms that are valid in the underlying domain. We give a model-theoretic interpretation to these extended faceted ontologies and we provide mechanisms for inferring the valid conjunctions of terms. This inference service can be exploited for preventing errors during the indexing process and for deriving navigation trees that are suitable for browsing. The proposed scheme has several advantages by comparison to the hierarchical classification schemes that are currently used, namely: conceptual clarity: it is easier to understand, compactness: it takes less space, and scalability: the update operations can be formulated easier and be performed more efficiently.