A Set-Theoretic Approach to ABox Reasoning Services

In this paper we consider the most common ABox reasoning services for the description logic \(\mathcal {DL}\langle \mathsf {4LQS}^{\mathsf{R},\!\times }\rangle (\mathbf {D})\) (\(\mathcal {DL}_{\mathbf {D}}^{4,\!\times }\), for short) and prove their decidability via a reduction to the satisfiability problem for the set-theoretic fragment \(\mathsf {4LQS^R}\). The description logic \(\mathcal {DL}_{\mathbf {D}}^{4,\!\times }\) is very expressive, as it admits various concept and role constructs and data types that allow one to represent rule-based languages such as SWRL.