Formal semantics provide precise specifications of the expected behavior of organizational model based on multi-agent system, allowing users to understand them and also modelers to reason about them and to prove their correctness. A first step was described to provide a formal specification framework among organization-centered multi-agent system by using an existing rewriting logic language called Maude to translate organizational models, which allows addressing these issues. Such formalization provides additional benefits, such as enabling the simulation of the specifications or giving access to the Maude toolkit to reason about them. In this paper, Maude was used to formally describe Agent-Group-Role-based-organization specifications. The proposed framework could, in fact, be used as is or with some extensions to describe other agent organization models. Actually, the results of precedent works [31, 32] were synthesized with additional extensions related to the formal description of the Agent-Group-Role model. This approach is illustrated using the supply chain management (SCM) case study.
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