Entity Modelling

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

Context Composition Duality

In entity modelling we shall see that two seeming different aspects of representing what is:

  • the representation of entities as wholes or composite entities having parts of which they are composed
  • the modelling of context for which entities depend for their logical existence
are in fact two ways of looking at the same distinction and that in this way there is a duality between composition and context. For example we can say that the uses of the term ‘intra’ in contrast to ‘inter’ in the adjective ‘intranational’ and like constructions, derive applicability from context dependent entities having relationships within (intra) and across (inter) contexts. Equally we can say that these uses depend on existence of recognised composite entities (‘nations’) and relationships between parts of the same composites (‘intra’) and between parts of different composites (‘inter’).

Modelling wholes and parts is equivalent to modelling context in which things exist. It is achieved by distinguishing composition relationships to be described in section composition relationships— those between wholes and parts — from other relationships; for these others we use the term reference relationship as will be described in section reference relationships. It makes sense to ask of a reference relationship whether it is intra- or inter- any of the contexts in which its participating entities are defined to exist; answering this question is said to be scoping the relationship and the answer itself is said to be the scope of the relationship. We will describe a distiction between composition relationships and reference relationships and see that composition relationships do not have defined scopes, rather that they serve to define contexts and therefore scopes in the first place. In summary, reference relationships have defined scopes and composition relationships do not.

Entity models enable representation of the contexts within which things exist and it would be hard not to agree with Gilbert Ryle that context is most important to the meaning of things both said and written:

A given word will, in different sorts of context, express ideas of an indefinite range of differing logical types and, therefore, with different logical powers. And what is true of single words is also true of complex expressions and of grammatical constructions. (1945, 206)

If you are familiar with computer programming you will be aware that computer instructions require context for their execution and of the fact that they perform according to data within the contexts of their execution. Likewise, if we were to note the inferences that we make in reading a novel, say, to construct an opening scene and its characters and to place the narrator, then, focusing in this way on these mental steps, it would seem that novelists ask a lot of us the readers to construct a novel's opening context — that they make us work. Give it some thought, for a moment, or consider the opening lines from James Joyce's ‘Portrait of the Artist as a Young Man’.

Once upon a time and a very good time it was there was a moocow coming down the road met a nicens little boy named baby tuckoo... His father told him that story: his father looked at him through a glass: he had a hairy face.

When computer programs are written then context is represented explicitly — variables, i.e. individuals, are introduced explicitly — the moocow and the nicens little boy named tuckoo — and must be used consistently otherwise the software doesn't work. So computer programs are long and heavy on detail and they are in a style which is the antithesis of literary.

Contexts contain individual persons, and times (once upon a time) and places (the road) and they are modelled and represented as data in both computer programs and in novels. In both storytelling and programming, individuals from one context become inaccessible from others — they become ‘out of scope’ to use a programming term — so by the second paragraph quoted above the individuals of the first paragraph, in and by themselves, are ‘out of scope’— to be replaced by the first paragraph itself, which, in its totality, is ‘in scope’ as a story.

To introduce a real number as an unknown into a mathematical discussion is no different in principle to introducing a moocow or a tiny baby into a discourse. In both cases an individual is introduced into a context and becomes part of the context for the remaining discussion — until that is — that storyline is escaped, becomes embedded, or otherwise goes out of scope — in the mathematical book of exercises, by convention, unless otherwise stated, the x of question 1 is out of scope in question 2.

So contexts, computational, mathematical and discursive, are populated by individuals. ‘Moocow’, ‘baby’ and ‘Real number’ are types of individual. Man, ox, animal, tree, plant — large proportions of our vocabularies comprise words for types of things. Entity modelling is a tool enabling the expression of types (of entity) but also dependencies between individuals, types and contexts.