The word model get used in a number of different ways in ordinary and technical language. There are scientific models, economic models, supermodels, model cars, and semantic models.
There are at least three distinct ways that the term model is used which are important to distinguish. One way to make understand the differences is to compare a ‘model citizen’ with a ‘model train’ with a ‘make and model’. A model citizen is someone who is close to perfect (as a citizen) and exemplifies the core characteristics of a citizen. A model train on the other hand is a replica of the real thing that is smaller or more manageable in some way. When we talk about the make and model of something, we are referring to a particular version or type of a generic category. In the first meaning, a ‘model’ is better than we would expect from real life. On the second meaning, a ‘model’ is a limited version of real life. On the third meaning, a ‘model’ is one of various alternatives that all have different characteristics but belong to some large category.
Supermodels, for example, clearly draw on the first meaning of ‘model’ – models are human being whose looks are considered to be close to perfect.
Scientific and economic models, on the other hand, draw on the second meaning. They are limited forms of reality which rely on simplifying assumptions to make then understandable or computable. Thus Neil Bohr’s model of the atom was a useful way of understanding it, but that has since been shown to be incomplete.
In the way they are normally understood, semantic models draw on the first meaning not the second. A semantic model is normally the mathematical structure that defines the semantic values of a formal logic and which establishes the link between truth and formal provability. Semantic models are clearly not intended to be limited forms of reality, but exemplify the core characteristics of formal logic.
Of the two different concepts of ‘model’ supermodels and semantic models belong in the same company.