This paper formalizes UML class diagrams and structural patterns as mathematical objects and provides a precise notion of conformance of a structural model specified as a class diagram to a structural pattern. We also present a conformance verification method which represents a class diagram as a logic program and a structural pattern as a query. The conformance of the class diagram to the structural pattern is verified by computing all the answers to the query by the logic program and checking the satisfaction of realization multiplicity constraints imposed by the pattern.