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Design pattern is a way of solution building on the common or recurring problems in software design, which can be combined with Unified Modeling Language (UML) to create a system framework. The UML is a semi-formal language which semantic part is described by natural language. So it will produce semantic inconsistency problem in the modeling process. Therefore, this paper proposes an object called refinement Calculus of Object Systems based on design pattern, for describing the UML using design patterns in class diagram and sequence diagram of the formal semantics and accurate system modeling. [ABSTRACT FROM PUBLISHER]