Progress was made in the understanding of object-oriented (O-O) architectures through the introduction of patterns of design and architecture. Few works, however, offer methods of precise specification for O-O architectures. This article provides a well-defined ontology and an underlying framework for the formal specification of O-O architectures: We observe key regularities and elementary design motifs in O-O design and architectures; define “architectural model” in logic; and formulate relations between specifications. We demonstrate how to declare and reason with the representations. Finally, we use our conceptual toolkit to compare and evaluate proposed formalisms.