Conjunctive Query Answering for Description Logics with Transitive Roles

An important reasoning task, in addition to the standard DL reasoning services, is conjunctive query answering. In this paper, we present algorithms for conjunctive query answering in the expressive Description Logics SHQ and SHOQ. In particular, we allow for transitive (or nonsimple) roles in the query body, which is a feature that is not supported by other existing conjunctive query answering algorithms. For SHQ, we achieve this by extending the logic with a restricted form of ↓ binders and state variables as known from Hybrid Logics. We also highlight, why the addition of inverse roles makes the task of finding a decision procedure for conjunctive query answering more complicated.