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disciplines or subject fields, e.g., theology, informatics;
units of measurement, e.g., hertz, volt, meter.
The classification above is accompanied by recommendations for how to con-
struct the associated terminology, e.g., rules for when to use plural and singular
forms, and rules for relating terms to each other, which may depend on the kind of
concepts designated by the terms.
4.2.2 Conceptual Modeling of Discrete Phenomena
The most successful modeling approach for the UoD is found in science, where
distinctions are made among individual concepts, class concepts, relation concepts,
and magnitudes (quantitative concepts) [ 5] . These general concept types are tools
for distinguishing among items and for grouping them. Individual concepts help us
to discriminate among individuals. Class concepts are used to establish classifica-
tions. Ordering and comparison are made possible by relation concepts. Distinctions
are made between specific (definite) concepts and generic (indefinite) concepts, e.g.,
“Obama” is a specific concept, but “x” is a generic concept and denotes an arbitrary
referent.
The concept classification of science is independent of the concept classification
made for thesauri purposes, and may be used for concept modeling within each
group in the thesaurus classification as well as for building models to relate concepts
that belong to different groups in the thesaurus classification.
Quantitative concepts apply to properties that reflect magnitudes associated with
individuals and/or sets, e.g., the temperature of a body, the number of elements of
a set. No distinct object is associated with a quantitative concept. Functions are
the structure of quantitative concepts, e.g., weight, mass, heat, acceleration. For
example, weight is a function W that maps the set of bodies (each of which has
a weight) into the set of real numbers. Quantitative concepts are the conceptual core
of measurement [5] .
Let “b” be a generic individual concept that represents some physical body (the
object variable) and let “w” be a generic individual concept that represents a numer-
ical value (the numerical variable). Then “W (b)
=
w” reflects the functional nature
of W, and is to be read “the weight of b equals w”. The numerical variable w occur-
ring in the weight function is equal to the number of weight units on a given scale,
e.g., kilogram or pound. If scale and unit system is not fixed by the context we need
to indicate it by a special symbol, say “s”. In short, “W(b,s)
=
w” is to be read “the
weight of b equals w measured in the scale s”.
Domain models are structures of individual concepts, class concepts, relation
concepts, and quantitative concepts. Class concepts apply to collections of individ-
uals, e.g., “PERSON” refers to all possible persons, and “NORWEGIAN” refers
to all Norwegians. That Norwegians are persons is stated in the domain model as
NORWEGIAN is a subset of PERSON.
Relation concepts and class concepts are closely related. For example,
“MARRIAGE” may be seen as a relation concept, where (it used to be that) each
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