On Finite and Unrestricted Query Entailment beyond SQ with Number Restrictions on Transitive Roles

TL;DR

This paper investigates the computational complexity of query entailment in extended description logics with transitive roles, nominals, and inverse roles, providing tight bounds for various query types.

Contribution

It establishes tight 2EXPTIME bounds for unrestricted and finite entailment in these extended description logics, advancing understanding of their computational properties.

Findings

2EXPTIME upper bounds for regular path query entailment

2EXPTIME-completeness for instance query entailment with inverses

Finite entailment results for nominals and inverse roles

Abstract

We study the description logic SQ with number restrictions applicable to transitive roles, extended with either nominals or inverse roles. We show tight 2EXPTIME upper bounds for unrestricted entailment of regular path queries for both extensions and finite entailment of positive existential queries for nominals. For inverses, we establish 2EXPTIME-completeness for unrestricted and finite entailment of instance queries (the latter under restriction to a single, transitive role).