This article presents a general framework for integrating reasoning about object structure and concept taxonomies. The structural relations in the domain of objects discussed are mereological relations (part, overlap, etc.). Relations defining the concept taxonomies are taken from the standard relations of subsumption hierarchies. A small set of (homogeneous) predicators is introduced to relate the two areas. Predicators can be used to distinguish different modes of predication, corresponding to different types of associated inference patterns. Reasoning about different modes of predication depends both on the theory of objects and the theory of concepts. The theories of objects, concepts, and predicators are formulated in an axiomatic manner. Composition tables can be formally derived from the theories. Consequently, constraint propagation approaches can be easily extended to handle reasoning in the interface of conceptual knowledge and object structure.