On Finite and Unrestricted Query Entailment beyond SQ with Number
Restrictions on Transitive 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 fi-
nite entailment of instance queries (the latter under
restriction to a single, transitive role).