On Finite Entailment of Non-Local Queries in Description Logics

TL;DR

This paper investigates the computational complexity of finite entailment for non-local queries with transitive closure in certain description logics, establishing tight bounds for these problems.

Contribution

It extends the analysis of finite entailment to non-local queries with transitive closure in ALCOI and ALCOQ, providing tight complexity bounds.

Findings

Finite entailment in ALCOI and ALCOQ is 2EXPTIME upper bound.

Finite entailment of conjunctive queries with transitive closure in ALC is 2EXPTIME-hard.

The paper establishes tight bounds for these entailment problems.

Abstract

We study the problem of finite entailment of ontology-mediated queries. Going beyond local queries, we allow transitive closure over roles. We focus on ontologies formulated in the description logics ALCOI and ALCOQ, extended with transitive closure. For both logics, we show 2EXPTIME upper bounds for finite entailment of unions of conjunctive queries with transitive closure. We also provide a matching lower bound by showing that finite entailment of conjunctive queries with transitive closure in ALC is 2EXPTIME-hard.