Conceptual modelling is one of the central activities in Computer Science. Conceptual models are mainly used as intermediate artifact for system construction. They are schematic descriptions of a system, a theory, or a phenomenon of an origin thus forming a model. A conceptual model is a model enhanced by concepts. The process of conceptual modelling is ruled by the purpose of modelling and the models. It is based on a number of modelling acts, on a number of correctness conditions, on modelling principles and postulates, and on paradigms of the background or substance theories. Purposes determine the (surplus) value of a model. Conceptual modelling is performed by a modeller that directs the process based on his/her experience, education, understanding, intention and attitude.

Conceptual models are products that are used by other stakeholders such as programmers, learners, business users, and evaluators. Conceptual models use a language as a carrier for the modelling artifact and are restricted by the expressiveness of this carrier. This language is often also used for the description of the concepts that are incorporated into a modelling result. Concepts can be explicitly defined or can be implicitly assumed based on some common sense within an application domain, a Computer Science sub-culture and within a community of practice.

A theory of conceptual models and a theory of modelling acts have been developed in [26,27]. This paper aims at a development of a general theory of modelling as an art in the sense of [9]. A general theory of modelling also considers modelling as an apprenticeship and as a technology. We distinguish between the art of modelling within a creation and production process, the art of modelling within an explanation and exploration process, the art of modelling within an optimisation and variation process, and the art of modelling within a verification process. This distinction allows to relate the specific purpose with macro-steps of modelling and with criteria for approval or refusal of modelling results.