What is a model?

My previous post got me thinking about what a model is and why we model. I think everybody agrees that a text specification written in Word is not a model, while something in UML is.

The Cambridge Advanced Learner's Dictionary defines a model as

A representation of something, either as a physical object which is usually smaller than the real object, or as a simple description of the object which might be used in calculations.

I like the informal definition I heard from Jon Whittle last week: A model is an abstraction of the real thing for a specific purpose. However with this definition even a specification document written in Word will be a model and I don't think that makes sense.
Mellor et al. defines a model (Ludewig defines even more formal criteria):

A model is a coherent set of formal elements describing something (for example, a system, bank, phone, or train) built for some purpose that is amenable to a particular form of analysis, such as...

With this definition it is quite easy to exclude a Word document as a model, since it isn't composed of formal elements. It can incorporate diagrams based on a model, e.g. a class diagram from an UML model, but not the model itself.

In addition to this there should be a purpose with the model. John Daniels identifies three different types of models, each with a different purpose:

• Conceptual model
• Specification model
• Implementation model

When reading the article it is obvious that just by stating one has a UML model or a Simulink model really does not say anything about the purpose. What I am curios about is if one is using the same model for different purposes? Is it possible to use a model for completely different purposes with any degree of efficiency and quality? I am not talking about a transformation from one model to another, for example code generation or MDA. Do you use the same Simulink model for both conceptually understand the problem, specify properties of the solution and describe the implementation?

I had great help from my colleague Niklas Mellegård in his licentiate thesis Method and Tool Support for Automotive Software Engineering, which is defended on Thursday 30 September at 13:00 in room Torg 2, Patricia building, Lindholmen. Discussion leader will be Prof. Martin Törngren, Dept of Machine Design, Royal Institute of Technology.