# Model

A model may be described as an abstract representation of reality constructed to fulfil a certain purpose for research or implementation activities. According to an early definition by Apostel (1960), any subject using a system A to obtain information about a system B, with A being neither directly nor indirectly interacting with B, is using A as a model for B.

According to Dietz (2006), there are three system categories: concrete, symbolic and conceptual systems. Their relationships are represented in the figure below. Referring to this figure:

- A concrete model of a concrete system is called an
*imitation*(e.g. a scale model of an airplane or a ship or any other concrete thing). - A conceptual model of a concrete system is called a
*conceptualization*(e.g. the geometrical sphere as a model for celestial bodies; the Process Model as the conceptualization of the business processes in an enterprise). - A concrete model of a conceptual system is called an
*implementation*(e.g. the pyramids of Giza are an implementation of the geometric concept of pyramid; a business process as an implementation of the Process Model). - A conceptual model of a conceptual system is called a
*conversion*(e.g. the algebraic concept of a circle (*x*2 +*y*2 =*r*2) is a conversion of its geometric concept). - A symbolic model of a conceptual system is called a
*formulation*(e.g. the notion of the algebraic concept of a circle mentioned previously as a conversion model, is also a formulation model when referring to its notation). - A conceptual model of a symbolic system is called an
*interpretation*, which is actually the reverse of formulation (e.g. the deciphering of the Stone of Rosetta). - A symbolic model of a symbolic system is called a
*transformation*(e.g. from Morse to the Roman notation of letters).

The term model can be equated to some graphical diagram. This is because in many fields (e.g. information systems, business processes management) most models used are graphical models. Models, however, do not necessarily have to be graphical (Op ’t Land et al, 2009). A model that is graphically displayed typically consists of three elements: (i) a collection of symbol structure types, (ii) a collection of operations that can be applied to any valid symbol structure, and (iii) a collection of inherent constraints that define the set of consistent symbol structure states, or valid changes of states (Mylopoulos and Borgida, 2009).

References:

Apostel, L. (1960) Towards the formal study of models in the non-formal sciences. Synthese, 12(2-3), pp.125–161, pdf

Dietz, J.L.G. (2006) Enterprise Ontology: Theory and Methodology. Springer, Heidelberg.

Mylopoulos, J. & Borgida, A. (2009) A Sophisticate’s Guide to Information Modeling. In: Metamodeling for Method Engineering, Jeusfeld, M.A., Jarke, M. & Mylopoulos, J. (eds.), MIT Press, Cambridge, Massachusetts, pdf

Op ’t Land, M., Proper, E., Waage, M., Cloo, J. & Steghuis, C. (2009) Enterprise Architecture: Creating Value by Informed Governance. Springer, Heidelberg.