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6.1.4 Concepts
Concepts constitute the basic elements of the agreed terminology for a problem
domain. From a high-level perspective, a concept - described by a concept
definition - provides attributes with names and types. Specified more formally
in MOF, a concept is made up of the following elements:
Class concept
hasNonFunctionalProperties type nonFunctionalProperties
hasSuperConcept type concept
hasAttribute type attribute
hasDefinition type logicalExpression multiplicity = single valued
Furthermore, a concept can be a subconcept of several (or possibly none)
direct superconcepts, as specified by an “is-a” relation. In the WSMO model,
each concept can have a finite number of concepts that serve as a superconcept
for some other concept. Being a subconcept of some other concept means, in
particular, that a concept inherits the signature of this superconcept and the
corresponding constraints.
A concept provides a (possibly empty) set of attributes that represent
named slots for the data values of instances. An attribute specifies a slot of a
concept by fixing the name of the slot and a logical constraint on the possible
values filling that slot, which, in a simple case, can be another concept. Hence,
this logical expression can be interpreted as a typing constraint.
Additionally, a concept is defined by a logical expression. This means that
axioms can be asserted about a concept that refine its meaning, for example
with nuances that are not expressible by attributes or an “is-a” hierarchy. A
logical expression can be used to refine the semantics of the concept. More
precisely, the logical expression defines (or restricts) the extension (i.e. the set
of instances) of the concept. More details of the concrete language in which
this is done are given in Chapter 7.
6.1.5 Relations
Relations are used in order to model interdependencies between several con-
cepts (or instances of these concepts). The arity of relations is not limited.
Specified more formally in MOF, a relation is made up of the following ele-
ments:
Class relation
hasNonFunctionalProperties type nonFunctionalProperties
hasSuperRelation type relation
hasParameter type parameter
hasDefinition type logicalExpression multiplicity = single valued
Every relation can have a finite set of relations , of which a defined relation
is declared as being a subrelation. Being a subrelation of some other relation
means, in particular, that a relation inherits the signature of this superrelation
and the corresponding constraints. Furthermore, the set of tuples belonging
to the relation (and the extension of the relation) is a subset of each of the
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