Ontologies based on Description Logic (DL) represent general background knowledge in a terminology (TBox) and the actual data in an ABox. DL systems can then be used to compute consequences (such as answers to certain queries) from an ontology consisting of a TBox and an ABox. Since both human-made and machine-learned data sets may contain errors, which manifest themselves as unintuitive or obviously incorrect consequences, repairing DL-based ontologies in the sense of removing such unwanted consequences is an important topic in DL research. Most of the repair approaches described in the literature produce repairs that are not optimal, in the sense that they do not guarantee that only a minimal set of consequences is removed. In a series of papers, we have developed an approach for computing optimal repairs, starting with the restricted setting of an 𝓔𝓛 instance store, extending this to the more general setting of a quantified ABox (where some individuals may be anonymous), and then adding a static 𝓔𝓛 TBox.

Here, we extend the expressivity of the underlying DL considerably, by adding nominals, inverse roles, regular role inclusions and the bottom concept to 𝓔𝓛, which yields a fragment of the well-known DL Horn-𝓢𝓡𝓞𝓘𝓠. The ideas underlying our repair approach still apply to this DL, though several non-trivial extensions are needed to deal with the new constructors and axioms. The developed repair approach can also be used to treat unwanted consequences expressed by certain conjunctive queries or regular path queries, and to handle Horn-𝓐𝓛𝓒𝓞𝓘 TBoxes with regular role inclusions.