Eliminating Nonmonotonic DL-Atoms in Description Logic Programs

Abstract

Nonmonotonic description logic programs (dl-programs) are a well-known formalism for combining rules and ontologies, where rules interact with an underlying ontology via dl-atoms that allow queries to the ontology under a possible update of its assertional part. It is known that dl-atoms may be nonmonotonic and dl-programs without nonmonotonic dl-atoms have many desirable properties. In this paper, we show that it is possible to remove nonmonotonic dl-atoms from a dl-program while preserving its strong/weak answer set semantics. Though the translation is faithful, it relies on the knowledge about monotonicity of dl-atoms. We then thoroughly investigate the complexity of deciding whether a dl-atom is monotonic under the description logics DL-Lite$_{\mathcal R}$, ${\mathcal{EL}}^{++}$, ${\mathcal{SHIF}}$ and ${\mathcal{SHOIN}}$, which is of independent interest for computing strong answer sets. We show that the problem is intractable in general, but tractable for dl-atoms with bounded queries in DL-Lite$_{\mathcal R}$.