Entity Modelling

www.entitymodelling.org - entity modelling introduced from first principles - relational database design theory and practice - dependent type theory

Composition Relationships

An entity model is a system of entity types and relationships and for a reader of a model the most important relationships — those to understand first — are those that represent associations between entities and their parts. These relationships are called composition relationships and the term composition structure is used to refer to the subsystem consisting solely of entity types and compositions relationships.

Composition relationships are shown top-down, which is to say that they are drawn leaving the lower edge of the box representing the type of the whole and entering the upper edge of the type representing the part, as here: (a) . This fragment signifies that there are one or more entities of type part type within the whole.

Looking at composition relationships the other way around — bottom up — then they are seen to relate entities with the contexts in which they exist and it is because of this that these are the most important relationships in an entity model — they provide context to entities.

The presence of the crows foot is representative of multiplicity — if the crows foot is present the notation asserts that there may be many parts of type part type within each entity of type whole type.

If the crows foot is absent, as here: (b) then the assertion is that there is exactly one entity of type part type within the whole.

A further distinction is made by use of a half-dashed line to represent the possibility of zero; this gives us

(c) there may be zero, one or more entities of part type within the whole:

and (d) there may be zero or one entities of type part type : .

If there are parts of different types, then the structure is shown branching as for example here: (e) or here: (f) .

Figures 1, 2 and 3 gives basic examples using the notation. More examples follow as more features of the notation are introduced. If you find yourself disagreeing with these examples — thinking that what they express is contrary to your understanding — then good! — It is reasonable to suppose that I will have achieved my aim of showing how the notation works — that it can be used to express precise models which it is then possible to disagree with, or, better, to refine.

  • a nucleus is composed of one or more protons and zero, one or more neutrons
Figure 1
The atomic nucleus
  • a complex sentence is composed of exactly one main clause and one or more subordinate clauses
Figure 2
From grammar
  • ‘Well I've often seen a cat without a grin,’ thought Alice; ‘but a grin without a cat! It's the most curious thing I ever saw in my life!’
Figure 3
From Alice's dream.

When the parts of a whole have a particular order amongst them then an ‘S’ shaped symbol (S for sequence) may be added to the relationship. In this way we can represent a sentence as a sequence of words: (a) and a word as a sequence of letters: (b)

Famously, we can represent a DNA molecule (a chromosome) as a sequence of nucleotides: