Regular Path Queries in Expressive Description Logics with Nominals

Reasoning over complex queries in the DLs underlying OWL 2 is of  importance in several application domains.  We provide decidability and (tight) upper bounds for the problem of checking entailment and containment of positive regular path queries under various combinations of constructs used in such expressive DLs; specifically: regular expressions and (safe) Booleans over roles, and allowing for the combination of any two constructs among inverse roles, qualified number restrictions, and nominals.  Our results carry over also to the DLs of the SR family, and thus have a direct impact on OWL 2.