Entity Modelling

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

## Generalisation

Previously we gave this example model of an atomic nucleus:

This model can be expressed in a different way using the generalisation nucleon of the individual terms proton and neutron by stating: an atomic nucleus is composed of one or more nucleons; every nucleon is either a proton or a neutron. In an entity model diagram the generalisation type is shown as a box containing the specific types; so the model may be expressed thus:

Be aware that there is a minor difference between this way of expressing the situation and the first form: when expressed in this latter form the model is consistent with a nucleus with one neutron and zero protons — physics teaches us that such nuclei will not occur in the real world.

The same generalisation can be used to express that both protons and neutrons are combinations of quarks:

.

### Examples from Biology

As a further illustration of the notations described so far figures 17 and 18 give examples representing descriptions given in Biology.

• the characteristics of phylum arthropoda are (i) exoskeleton, (ii) body segments grouped into specialized regions (= tagmata) (iii) jointed appendages variously specialized for feeding, locomotion, sensing
Figure 17
An elementary description of phylum arthropoda.
Figure 18
You should know: animal cells have a nucleus, cytoplasm and a cell membrane. Plant cells also have a cell wall, a vacuole and chloroplasts.

### Fundamental Levels of Matter

• every molecule is composed of one or more nuclei and one or more electrons
• every nucleus is composed of one or more nucleons
• every nucleon is either a neutron or a proton
• every nucleon is composed of one or more quarks
Figure 19
Modelled from a description given by physicist Harald Fritzsch.

A variation in the use of the exclusion arc is illustrated in the next example, figure 20, in which the model formally describes a certain part of the structure of English as given in many books of grammar by describing the possible appearances of degree words, adverbs and adjectives in adjectival phrases. In this example the ordering of composition relationships as they leave an entity from its lower edge corresponds to the relative positions of such consituents within an adjectival phrase.

Adjectives, wherever they appear in sentences — as predicates or as qualifiers of nouns — may be themselves be qualified by degree words or by adverbs; adverbs themselves may in turn be qualified by degree words.

Figure 20
Description of an adjectival phrase — an arrangement of degree words, adverbs and an adjective said to be the head of the phrase.

Adjectival phrases may appear as the predicates of sentences or as the qualifiers of nouns. Examples of adjectival phrases and the types of the constitent words are given in table 1. The table uses abbreviations for the different word types as were introduced earlier in table 1 of section types of things.

Table 1
fierce A
very fierce Deg A
very fiercely barking Deg Adv A

The reason for the inclusion of a type adverbial phrase is illustrated by the example very fiercely barking in which the degree word ‘very’ is understood as qualifying the word ‘fiercely’ which as a combination (an entity) ‘very fiercely’ then qualifies the word ‘barking’. The phrase ‘very fiercely’ is an example of an adverbial phrase as represented in the model in figure 20.

A further extended example of the modelling of sentence structure in presented in section english sentence structure.

### Gilbert Ryle

When Gilbert Ryle introduced the phrase category mistake he gave a number of examples. The first example is of a visitor to Oxford. The visitor, upon viewing the colleges and library, reportedly inquired "But where is the University?" . The visitor's mistake, explains Ryle, is presuming that a University is part of the category "units of physical infrastructure" or some such thing, rather than the category "institution" , say, which are far more abstract and complex conglomerations of buildings, people, procedures, and so on.

Figure 21
A university as an abstract conglomeration of buildings, people and procedures.
• The march-past was not a parade of battalions, batteries, squadrons and a division; it was a parade of the battalions, batteries and squadrons of a division..
Figure 22
The March Past — Ryle's second example is of a child witnessing the march—past of a division of soldiers. After having had battalions, batteries, squadrons, etc. pointed out, the child asks when is the division going to appear.