Recent research in design theory has sought to formalize the engineering design process without particular concern for the paradigm used to model design information. The authors propose that no correct formalization of the design process can be achieved without first formalizing the semantics of the information used in the process. To this end, the authors present a new formal theory of design information. The theory, called the Hybrid Model, is an extended form of axiomatic set theory, and relies on it for consistency and logical rigor. The theory is stated as a collection of axioms, using a standard logic notation. Design entities are modeled by formal units called objects. Generalized functions and relations are used to formalize important ordering schemes and abstraction mechanisms relevant to design, including classification by structure and by function, aggregation, specialization and generalization. The hybrid model is meant not only to aid in the study of the design process itself, but also to improve communications between designers, assist standardization of design specifications, and develop new, powerful software tools to aid the designer in his work.