The Whole-Part Relationship in the Unified Modeling Language: A New Approach

Abstract

This study of the semantics of the Whole-Part relationship in OO modeling is based upon, extends and, specifically, formalizes earlier analyses of the semantics of UML’s Aggregation and Composition (white and black diamonds, also called shared aggregation and composite aggregation). Although UML is nowadays regarded as a standard and is widely used as an OO modeling language, the way the Whole-Part relationship is formalized is unsatisfactory. Here, we provide a rigorous specification of various forms of the Whole-Part relationship using OCL (Object Constraint Language). The first part of the specification is based on the differentiation between primary characteristics (applicable to all Whole-Part relationships) assigned to a new Whole-Part metatype in the UML and secondary features, which are possessed by subtypes of this metatype and permit the representation of several “flavors” of the Whole-Part relationship. This UML-compliant style of specification, based on the use of OCL as well as metamodeling, allows us to directly incorporate our results into the UML metamodel, in particular revising UML’s definition of Composition.