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Each agent manages a graph grammar and a database of facts concerning the subtask for which it is responsible. The course of designing is determined by the interaction between cooperating specialized agents. The design context is expressed by the environment in which agents act and predicates describing design criteria. The organization, design methodology, and a semantic model of a grammar-based multiagent design system are presented. The notions of a valid design solution and a design solution consistent with the design criteria are also introduced. 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