Applications of semantic technologies often require the representation of and reasoning with structured objects--that is, objects composed of parts connected in complex ways. Although OWL is a general and powerful language, its class descriptions and axioms cannot be used to describe arbitrarily connected structures. An OWL representation of structured objects can thus be underconstrained, which reduces the inferences that can be drawn and causes performance problems in reasoning. To address these problems, we extend OWL with description graphs, which allow for the description of structured objects in a simple and precise way. To represent conditional aspects of the domain, we also allow for SWRLlike rules over description graphs. Based on an observation about the nature of structured objects, we ensure decidability of our formalism. We also present a hypertableau-based decision procedure, which we implemented in the HermiT reasoner. To evaluate its performance, we have extracted desc...