Finding Data Tractable Description Logics for Computing a Minimum Cost Diagnosis Based on ABox Decomposition

Ontology diagnosis, a well-known approach for handling inconsistencies in a description logic (DL) based ontology, computes a diagnosis of the ontology, i.e., a minimal subset of axioms in the ontology whose removal restores consistency. However, ontology diagnosis is computationally hard, especially computing a minimum cost diagnosis (MCD) which is a diagnosis such that the sum of the removal costs attached to its axioms is minimized. This paper addresses this problem by finding data tractable DLs for computing an MCD which allow computing an MCD in time polynomial in the size of the ABox of a given ontology. ABox decomposition is used to find a sufficient and necessary condition to identify data tractable DLs for computing an MCD under the unique name assumption (UNA) among all fragments of $\mathcal{S}\mathcal{H}\mathcal{I}\mathcal{N}$ that are at least as expressive as ${\mathrm{D}\mathrm{L}-\mathrm{L}\mathrm{i}\mathrm{t}\mathrm{e}}_{\text{core}}$ without inverse roles. The most expressive, data tractable DL identified is $\mathcal{S}\mathcal{H}\mathcal{I}\mathcal{N}$ without inverse roles or qualified existential restrictions.