How to Approximate Ontology-Mediated Queries

TL;DR

This paper explores approximation techniques for ontology-mediated queries in description logics, aiming to improve computational efficiency by replacing ontologies or databases with simpler, tractable versions.

Contribution

It introduces and analyzes two types of approximations for ontology-mediated queries, detailing their complexity and effectiveness in reducing computational costs.

Findings

Data complexity often reduced from coNP-complete to PTime.

Some approximations achieve fixed-parameter tractability and linear time.

Combined complexity may increase or not improve with certain approximations.

Abstract

We introduce and study several notions of approximation for ontology-mediated queries based on the description logics ALC and ALCI. Our approximations are of two kinds: we may (1) replace the ontology with one formulated in a tractable ontology language such as ELI or certain TGDs and (2) replace the database with one from a tractable class such as the class of databases whose treewidth is bounded by a constant. We determine the computational complexity and the relative completeness of the resulting approximations. (Almost) all of them reduce the data complexity from coNP-complete to PTime, in some cases even to fixed-parameter tractable and to linear time. While approximations of kind (1) also reduce the combined complexity, this tends to not be the case for approximations of kind (2). In some cases, the combined complexity even increases.