Expressiveness in Conceptual Data Modelling

Conceptual data modelling techniques aim at the representation of data at a high level of abstraction. The Conceptualisation Principle states that only those aspects are to be represented that deal with the meaning of the Universe of Discourse. Conventional conceptual data modelling techniques, as e.g. ER or NIAM, have to violate the Conceptualisation Principle when dealing with objects with a complex structure. In order to represent these objects conceptually irrelevant choices have to made. It is even worse: sometimes the Universe of Discourse has to be adapted to suit the modelling technique. These objects typically occur in domains as meta-modelling, hypermedia and CAD/CAM. In this paper extensions to an existing data modelling technique (NIAM) will be discussed and formally deened, that make it possible to naturally represent objects with complex structures without having to violate the Conceptualisation Principle. These extensions will be motivated from a practical point of view by examples and from a theoretical point of view by a comparison with the expressive power of formal set theory and grammar theory.