Query Inseparability for ALC Ontologies
This addresses a fundamental issue in ontology engineering for tasks like versioning and modularisation, but it is incremental as it builds on existing decidability and complexity results in description logics.
The paper tackles the problem of determining whether two ALC ontologies are indistinguishable by queries, showing that for conjunctive queries (CQs), this problem is undecidable, but for unions of CQs (UCQs), it is 2ExpTime-complete, and for Horn-ALC TBoxes, it becomes decidable with 2ExpTime-completeness or ExpTime-completeness for rooted queries.
We investigate the problem whether two ALC ontologies are indistinguishable (or inseparable) by means of queries in a given signature, which is fundamental for ontology engineering tasks such as ontology versioning, modularisation, update, and forgetting. We consider both knowledge base (KB) and TBox inseparability. For KBs, we give model-theoretic criteria in terms of (finite partial) homomorphisms and products and prove that this problem is undecidable for conjunctive queries (CQs), but 2ExpTime-complete for unions of CQs (UCQs). The same results hold if (U)CQs are replaced by rooted (U)CQs, where every variable is connected to an answer variable. We also show that inseparability by CQs is still undecidable if one KB is given in the lightweight DL EL and if no restrictions are imposed on the signature of the CQs. We also consider the problem whether two ALC TBoxes give the same answers to any query over any ABox in a given signature and show that, for CQs, this problem is undecidable, too. We then develop model-theoretic criteria for Horn-ALC TBoxes and show using tree automata that, in contrast, inseparability becomes decidable and 2ExpTime-complete, even ExpTime-complete when restricted to (unions of) rooted CQs.