It is shown how a theoretical underlying model for object-oriented knowledge-based systems can enhance the precise understanding of its modeling power and consequently simplify the sharing of system components by the developers of the systems. This is one of the major problems encountered in large knowledge-based systems, leading to loss of modularity and extensibility. Since a formal model for all approaches is impossible, emphasis is placed on a typed, extensible object-oriented data model. It is pointed out that theoretical underlying models for other object-oriented knowledge-based systems can be obtained in a similar way. The integration of different knowledge-based systems will be much easier when the theoretical underlying model for each one of them is well defined. Special emphasis is placed on defining and cleanly separating the structural and semantic parts of object-oriented definitions (here, structural refers to the organization of the data and the operations on the data whereas semantic refers to the connections of these concepts to the real world). All parts of the proposed dual model are shown to be well defined, both from the aspect of their structural or semantic nature and from the mathematical aspect.