Effective Computation of Maximal Sound Approximations of Description Logic Ontologies

Abstract

We study the problem of approximating Description Logic (DL) ontologies specified in a source language LS in terms of a less expressive target language LT . This problem is getting very relevant in practice: e.g., approximation is often needed in ontology-based data access systems, which are able to deal with ontology languages of a limited expressiveness. We first provide a general, parametric, and semantically well-founded definition of maximal sound approximation of a DL ontology. Then, we present an algorithm that is able to effectively compute two different notions of maximal sound approximation according to the above parametric semantics when the source ontology language is OWL 2 and the target ontology language is OWL 2 QL. Finally, we experiment the above algorithm by computing the two OWL 2 QL approximations of a large set of existing OWL 2 ontologies. The experimental results allow us both to evaluate the effectiveness of the proposed notions of approximation and to compare the two different notions of approximation in real cases.

Experiencing OptiqueVQS: a multi-paradigm and ontology-based visual query system for end users

“…Figure 6), which transform the ontology into one that is as expressive as possible, while still falling within the required profile (cf. [65,22,21]). …”

“…Thus an OWL 2 QL approximator is provided [22,21] to approximate or remove such axioms. However, although this information is not used in the rewriting process, it does have an important role in the OptiqueVQS.…”

Ontology-Mediated Queries

“…Ideally, one would show that the simpler ontology is equivalent to the original with regards to query answering [17], and thus provides the exact set of answers. Alternatively, one can use a simpler ontology to approximate the answers for the full one [17,28] (possibly employing a more costly complete algorithm to decide the status of the remaining candidate answers [89]). Theorem 3.9.…”

“…We show that α satisfies the disjunct of f ▽ Q that corresponds to Θ; cf. (28). Observe that, since all zeros are covered by E ′ , the following variables are evaluated to 1 by α :…”

“…If p t is part of the label, then there is z ∈ λ(N i ) with w k [z] = P t . By the definition of τ (N i ), we obtain t ∈ Θ, whence, by (28), α (p t ) = 1. Therefore, E ′ s is independent and covers all zeros under α , which means that P s (α ) = 1.…”