An enterprise service system is large and complex and manages big and complicated data. A large set of partial data models is used in designing an enterprise service system because each service application consisting of an enterprise service system uses only a part of big and complicated data in most cases. These partial data models provide several complementary views on the system to be developed. This however leads to a need for compositional models that are able to produce a single integrated model. These data models are often described by a class diagram of Unified Modeling Language because it is a very popular modeling language and describing a static view of a system. In this paper, we propose syntactical foundation of algebra on a family of well-formed class diagrams with composition operations — merge, difference, complement and intersection operations. We then show that the algebraic properties as associativity, commutativity and involutivity of this foundation are desired for model management to develop an enterprise service system.
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