UMLR — Section: Classes

In Classes, Association, Semantics says: "Subsetting represents the familiar set-theoretic concept. It is applicable to the collections represented by association ends, not the association itself." and "Specialization is, in contrast to subsetting, a relationship in the domain of intensional semantics, which is to say it characterized the criteria whereby membership in the collection is defined, not by the membership. One classifier may specialize another by adding or redefining features; a set cannot specialize another set. A naive but popular and useful view has it that as the classifier becomes more specialized, the extent of the collection(s) of classified objects narrows. In the case of associations, subsetting ends, according to this view, correlates positively with specializing the association. This view falls down because it ignores the case of classifiers which, for whatever reason, denote the empty set. Adding new criteria for membership does not narrow the extent if the classifier already has a null denotation." ISSUE: It is the semantics of Generalization in UML is that all the instances of the subtype are instances of the supertype, so subtyping in UML implies subsetting. It is not necessarily proper subsetting, however, as the example above shows. Subsetting in UML can be achieved by subtyping (adding attributes, etc), but can only be done by adding constraints to the subtype. Also, for association classes, the user should be able to specialize an association class with another association class with the same semantics as subsetting ends.