The Data Complexity of Ontology-Mediated Queries with Closed Predicates

TL;DR

This paper analyzes the data complexity of ontology-mediated queries with closed predicates across different description logics, providing classifications of tractability and linking complexity to surjective CSPs.

Contribution

It offers a detailed complexity classification for OMQCs with closed predicates in lightweight and expressive DLs, including a dichotomy and connections to CSP complexity.

Findings

Dichotomy between FO-rewritable and coNP-complete for DL-Lite ontologies.

Complexity classification for EL ontologies as PTime or coNP-complete.

Identification of tractable OMQC classes based on DL-Lite that are FO-rewritable.

Abstract

In the context of ontology-mediated querying with description logics (DLs), we study the data complexity of queries in which selected predicates can be closed (OMQCs). We provide a non-uniform analysis, aiming at a classification of the complexity into tractable and non-tractable for ontologies in the lightweight DLs DL-Lite and EL, and the expressive DL ALCHI. At the level of ontologies, we prove a dichotomy between FO-rewritable and coNP-complete for DL-Lite and between PTime and coNP-complete for EL. The meta problem of deciding tractability is proved to be in PTime. At the level of OMQCs, we show that there is no dichotomy (unless NP equals PTime) if both concept and role names can be closed. If only concept names can be closed, we tightly link the complexity of query evaluation to the complexity of surjective CSPs. We also identify a class of OMQCs based on ontologies formulated in DL-Lite that are guaranteed to be tractable and even FO-rewritable.