Query Inseparability for ALC Ontologies
  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.
