www.entitymodelling.org - entity modelling introduced from first principles - relational database design theory and practice - dependent type theory
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:
The same generalisation can be used to express that both protons and neutrons are combinations of quarks:
As a further illustration of the notations described so far figures 17 and 18 give examples representing descriptions given in Biology.
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.
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.
|adjectival phrase||type sequence|
|very fierce||Deg A|
|fiercely barking||Adv 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.
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.