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We study the description logic SQ with number restrictions applicable totransitive roles, extended with either nominals or inverse roles. We show tight2EXPTIME upper bounds for unrestricted entailment of regular path queries forboth extensions and finite entailment of positive existential queries fornominals. For inverses, we establish 2EXPTIME-completeness for unrestricted andfinite entailment of instance queries (the latter under restriction to asingle, transitive role).

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