cuối cùng nhà nước (xây dựng nhà). Quá trình này có thể được tinh chế thành nhiều quá trình khác nhau, tất cả đều có ban đầu và cuối cùng các quốc gia và tập hợp con của các tương tác (các bên liên quan, chính quyền, vật liệu xây dựng) là trừu tượng. Tuy nhiên, trong khi tất cả các tương đương với các mô hình trừu tượng, các quá trình này tinh chế không tương đương nhau. | Matching Models of Different Abstraction Levels 101 final state a house built . This process can be refined into many different processes all having the same initial and final states and subset of interactions stakeholders authorities building materials as the abstract one. Yet while being all equivalent to the abstract model these refined processes are not equivalent to one another. As a detailed example consider the abstract process of Supplying Customer Order in Figure 4a which can be refined into the two different processes in Figure 4b and c. These two refined processes have identical initial and final states Open Customer Order and Delivered Customer Order respectively as does the abstract process. However while Figure 4. An abstract model and two possible refinements Customer Order b a c Copyright 2007 IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. 102 Soffer Reinhartz-Berger Sturm both processes can be considered equivalent to the abstract model they are not equivalent to one another in their internal division into subprocesses additional inputs and outputs etc. . It is therefore easier to formulate a necessary condition rather than a necessary and sufficient condition for refinement equivalence of processes. Observation 3 Let m1 be a model portion in which process A transforms an initial state S1 into a final state s Let E1 be the set of entities directly linked to A in ml. Let m2 be a model portion that refines ml. Then m2 consists of a path P and a set E2 of entities that are directly linked to the entities of P so that P is from an initial state S1 to a final state s2 and E1 G E2. Note that the initial and final states are not necessarily explicitly represented in an abstract model in which case the inputs and outputs of the process should be considered in a similar manner to the states. Observation 3 provides a necessary condition that might not be sufficient for the .
