*Let’s recapture some modelling basics:*

**What does a diagram like (Some Dia) say, in terms of logic?**

Lets call the “->” relation R, obviously there are two elements where one is R-related to the other, we express this with two variables x and y, as shown in figure (a), by

(1) x R y

Next, we want to assume that the diagram shows all R-relationships of its contained elements, and thus we must exclude cases like (b) by

(2) ¬yRx ∧ ¬xRx ∧ ¬yRy

Moreover, we want to express that we have at least two elements by

(3) x ≠ y

Finally we assume the diagram to cover the whole model, i.e. there are no other elements, by

(4) ∀_{z} x=z ∨ y=z

Thus, all together we get

(5) ∃_{x, y} (1) ∧ (2) ∧ (3) ∧ (4)

**(5) describes (some Dia) structurally, i.e. up to isomorphism.** Additionally, we could give the elements a material meaning, say a certain Person (x) drives (R) a certain Car (y). (see Unambiguous Models)

So long

|=

**PS**

Describing single structures is usually not enough in modelling. What we want is to model sets of structures like every Person drives at least one car.

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Modeling Theory and Abstraction Awareness in strive for scientific rigour and relevance to information systems engineering.