Description Logics, and in particular the web ontology language OWL has been proposed as an appropriate basis for computing matches between structured objects for the sake of information integration and service discovery. A drawback of the direct use of subsumption as a matching criterion is the inability to compute partial matches and qualify the degree of mismatch. In this paper, we describe a method for overcoming these problems that is based on approximate logical reasoning. In particular, we approximate the subsumption relation by defining the notion of subsumption with respect to a certain subset of the concept and relation names. We present the formal semantics of this relation, describe a sound and complete algorithm for computing approximate subsumption and discuss its application to matching tasks.