Modelling Theory and Practice/Overview and Trivial Cases

The Notion of a Property of something

Property: separate sheep from goats -> look for property.

We write R(x) for an element x having property R.

Properties can be used to define sets. (intensional definition)

Set can also be defined by specifying every of its objects. (extensional definition)

Overview of Relations

'Relation' among objects, e.g. person drives car, formally written: Drives(person, car), Drives(Walter, Mini)

Notations: table, matrix, graph, ...

Binary relation: R(x, y), e.g. ...

N-ary relation: R(x₁, x₂, x₃, ..., x_n), e.g. ...

Property = unary relation R(x).

Structure of this chapter:

• Trivial Cases: R(x)
• Modelling with Concepts: R(x), S(y), T(z)
• Modelling with Modules: R(x, y, z)

Where concepts and modules are the basic approaches to handle complexity in the two directions.

Moreover, the directions of course can be combined. This is analysed in the next chapter.

Not covered: Soft relations, ...