The success of the use of ontology-based systems depends on efficient and user-friendly methods of formulating queries against the ontology. We propose a method to query a class of ontologies, called facet ontologies (fac-ontologies), using a faceted human-oriented approach. A fac-ontology has two important features: (a) a hierarchical view of it can be defined as a nested facet over this ontology and the view can be used as a faceted interface to create queries and to explore the ontology; (b) the ontology can be converted into an ontological database, the ABox of which is stored in a database, and the faceted queries are evaluated against this database. We show that the proposed faceted interface makes it possible to formulate queries that are semantically equivalent to $${\mathcal {SROIQ}}^{Fac}$$
SROIQ
Fac
, a limited version of the $${\mathcal {SROIQ}}$$
SROIQ
description logic. The TBox of a fac-ontology is divided into a set of rules defining intensional predicates and a set of constraint rules to be satisfied by the database. We identify a class of so-called reflexive weak cycles in a set of constraint rules and propose a method to deal with them in the chase procedure. The considerations are illustrated with solutions implemented in the DAFO system (data access based on faceted queries over ontologies).