Modelling is typically supported by languages that are well-founded and easy to apply for the description of the application domain, the requirements and the system solution. It is thus based on a theory of modelling constructs. At the same time, modelling incorporates a description of the application domain and a prescription of requirements for supporting systems. It is thus based on methods of application domain gathering. Modelling is also an engineering activity with engineering steps and engineering results. It is thus engineering. The first facet of modelling has led to a huge body of knowledge. The second facet is considered from time to time in the scientific literature. The third facet is underexposed in the scientific literature.

This paper aims in developing principles of conceptual modelling. They cover modelling constructs as well as modelling activities as well as modelling properties. We first clarify the notion of conceptual modelling. Principles of modelling may be applied and accepted or not by the modeler. Based on these principles we can derive a theory of conceptual modelling that combines foundations of modelling constructs, application capture and engineering.

A general theory of conceptual modelling is far too comprehensive and far too complex. It is not yet visible how such a theory can be developed. This paper therefore aims in introducing a framework and an approach to a general theory of conceptual modelling. We are however in urgent need of such a theory. We are sure that this theory can be developed and use this paper for the introduction of the main ingredients of this theory.