Query-Based Entailment and Inseparability for ALC Ontologies (Full Version)

Abstract: We investigate the problem whether two ALC knowledge bases are indistinguishable by queries over a given vocabulary. We give model-theoretic criteria in terms of (partial) homomorphisms and products and prove that this problem is undecidable for conjunctive queries (CQs) but 2EXPTIME-complete for UCQs (unions of CQs). The same results hold if CQs are replaced by rooted CQs. We also consider the problem whether two ALC TBoxes give the same answers to any query in a given vocabulary over all ABoxes, and show that for CQs this problem is undecidable, too, but becomes decidable and 2EXPTIME-complete in Horn-ALC, and even EXPTIME-complete in Horn-ALC when restricted to (unions of) rooted CQs.