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We propose a method to query a class of ontologies, called <jats:italic>facet ontologies<\/jats:italic> (<jats:italic>fac-ontologies<\/jats:italic>), 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 <jats:italic>ontological database<\/jats:italic>, 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 <jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathcal {SROIQ}}^{Fac}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mrow>\n                      <mml:mi>SROIQ<\/mml:mi>\n                    <\/mml:mrow>\n                    <mml:mrow>\n                      <mml:mi>Fac<\/mml:mi>\n                    <\/mml:mrow>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, a limited version of the <jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathcal {SROIQ}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>SROIQ<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> 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 <jats:italic>reflexive weak cycles<\/jats:italic> 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 (<jats:italic>data access based on faceted queries over ontologies<\/jats:italic>).<\/jats:p>","DOI":"10.1007\/s00778-022-00735-3","type":"journal-article","created":{"date-parts":[[2022,3,15]],"date-time":"2022-03-15T18:23:13Z","timestamp":1647368593000},"page":"103-121","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Ontological databases with faceted queries"],"prefix":"10.1007","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8168-4365","authenticated-orcid":false,"given":"Tadeusz","family":"Pankowski","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,3,15]]},"reference":[{"key":"735_CR1","volume-title":"Foundations of Databases","author":"S Abiteboul","year":"1995","unstructured":"Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. 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