A Journey into Ontology Approximation: From Non-Horn to Horn

We study complete approximations of an ontology formulated in a non-Horn description logic (DL) such as ALC in a Horn DL such as~EL. We provide concrete approximation schemes that are necessarily infinite and observe that in the ELU-to-EL case finite approximations tend to exist in practice and are guaranteed to exist when the original ontology is acyclic. In contrast, neither of this is the case for ELU_bot-to-EL_bot and for ALC-to-EL_bot approximations. We also define a notion of approximation tailored towards ontology-mediated querying, connect it to subsumption-based approximations, and identify a case where finite approximations are guaranteed to exist.