Learning Query Inseparable ELH Ontologies

We investigate the complexity of learning query inseparable ELH ontologies in a variant of Angluin's exact learning model. Given a fixed data instance A* and a query language Q, we are interested in computing an ontology H that entails the same queries as a target ontology T on A*, that is, H and T are inseparable w.r.t. A* and Q. The learner is allowed to pose two kinds of questions. The first is `Does (T,A)\models q?', with A an arbitrary data instance and q and query in Q. An oracle replies this question with `yes' or `no'. In the second, the learner asks `Are H and T inseparable w.r.t. A* and Q?'. If so, the learning process finishes, otherwise, the learner receives (A*,q) with q in Q, (T,A*)\models q and (H,A*)\not\models q (or vice-versa). Then, we analyse conditions in which query inseparability is preserved if A* changes. Finally, we consider the PAC learning model and a setting where the algorithms learn from a batch of classified data, limiting interactions with the oracles.