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

TL;DR

This paper investigates methods for approximating complex non-Horn ontologies with simpler Horn ontologies, providing schemes, existence guarantees, and applications to ontology-mediated querying.

Contribution

It introduces concrete approximation schemes for non-Horn to Horn ontologies, analyzes their properties, and connects these to ontology-mediated querying.

Findings

Finite approximations often exist in practice for certain cases.

Acyclic ontologies guarantee finite approximations in some scenarios.

Certain approximation schemes are necessarily infinite for some ontology classes.

Abstract

We study complete approximations of an ontology formulated in a non-Horn description logic (DL) such as $\mathcal{ALC}$ in a Horn DL such as~$\mathcal{EL}$. We provide concrete approximation schemes that are necessarily infinite and observe that in the $\mathcal{ELU}$-to-$\mathcal{EL}$ 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 $\mathcal{ELU}_\bot$-to-$\mathcal{EL}_\bot$ and for $\mathcal{ALC}$-to-$\mathcal{EL}_\bot$ 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.