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In ontology-mediated query answering, access to incomplete data sources ismediated by a conceptual layer constituted by an ontology, which can beformulated in a description logic (DL) or using existential rules. In theliterature, there exists a multitude of complex techniques for incorporatingontological knowledge into queries. However, few of these approaches weredesigned for explainability of the query answers. We tackle this challenge byadapting an existing proof framework toward conjunctive query answering, basedon the notion of universal models. We investigate the data and combinedcomplexity of determining the existence of a proof below a given qualitythreshold, which can be measured in different ways. By distinguishing variousparameters such as the shape of the query, we obtain an overview of thecomplexity of this problem for several Horn DLs.

Explaining Ontology-Mediated Query Answers using Proofs over Universal Models (Technical Report)