A simple relational Model

Let’s recapture some modelling basics:

Some Dia

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

Relations a b c dLets 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.

About modelpractice

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