Ontology-Mediated Querying on Databases of Bounded Cliquewidth

TL;DR

This paper analyzes the complexity of evaluating ontology-mediated queries on databases with bounded cliquewidth, showing fixed-parameter linearity for various description logics and query types.

Contribution

It provides a detailed parameterized complexity analysis of OMQ evaluation on bounded cliquewidth databases, highlighting the fixed-parameter linearity and dependence on the ontology and query size.

Findings

All studied OMQ problems are fixed-parameter linear.

The analysis reveals how running time depends on the size of the ontology and query.

The results apply to multiple description logics and query types.

Abstract

We study the evaluation of ontology-mediated queries (OMQs) on databases of bounded cliquewidth from the viewpoint of parameterized complexity theory. As the ontology language, we consider the description logics $\mathcal{ALC}$ and $\mathcal{ALCI}$ as well as the guarded two-variable fragment GF$_2$ of first-order logic. Queries are atomic queries (AQs), conjunctive queries (CQs), and unions of CQs. All studied OMQ problems are fixed-parameter linear (FPL) when the parameter is the size of the OMQ plus the cliquewidth. Our main contribution is a detailed analysis of the dependence of the running time on the parameter, exhibiting several interesting effects.