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Multi-agent organizational modeling frameworks can be considered as an efficient solution regarding the distributed applications' problems such as task bundle mechanisms, supply chain management, as well as air traffic control. The main objective of this paper is to provide a solution based on a solid mathematical theory for the modeling, the analysis and the verification of artificial organizations properties, and particularly those of Multi-Agent Systems (MASs). Category theory is a mathematical formalism used to categorically study the logics of organizations in different societies. Therefore, it can be projected on artificial organizations in a categorical way. Our work is revolved around the idea of modeling Multi-Agents organization using category theory. In other words, it consists on the transformation of Agent-Group-Role (AGR) organizational model in a categorical way in order to obtain a formal semantics model describing the MAS organization. This formal model allows the analysis, the verification and also the validation of the main concepts of an organization at a high level of abstraction.Povzetek: Predstavljena je matematična formulacija agentnih sistemov na osnovi kategorij.

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