UML14 — Generalization should be meta-metamodel element

Summary: UML 1.3 Metamodel Semantics

Generalization should be meta-metamodel element

It is a generally accepted fact that generalization is a second order
relation, ie, a relation whose elements (instances) are pairs of
types (classifiers, or whatever). Associations, by contrast, are
first order: their elements are tuples of objects (individuals,
etc.).

UML is based on a four-layer metamodel structure, including metamodel
and meta-metamodel layers. Why, then, do Generalization and
Association appear on the same layer, namely the metamodel? Much more
troublesome: How can they be specializations of the same
generalization, namely Relationship? Together with the defined
implication of generalization: "The more specific element is fully
consistent with the more general element (it has all of its
properties, members, and relationships) ..." [UML 1.3, sect. 2.5.2]
this leads to a paradox, because generalization itself would be
inherited. The paradox would be avoided, however, if generalization
were a relation of the meta-metalayer.

declined