A Formal Composition of Multi-Agent Organization based on Category Theory

The application of organizational multi-agent systems (MAS) provides the possibility of solving complex distributed problems such as, task grouping mechanisms, supply chain management, and air traffic control. The composition of MAS organizational models can be considered as an effective solution to group different organizational multi-agent systems into a single organizational multi-agent system. The main objective of this paper is to provide a MAS organizational model based on the composition of two organizational models, Agent Group Role (AGR), and Yet Another Multi Agent Model (YAMAM), with the aim of providing a new MAS model combining the concepts of the composed organizational models. Category theory represents the mathematical formalism for studying and modeling different organizations in a categorical way. This paper is mainly based on the idea of modeling the multi-agent organization AGR and YAMAM in a categorical way in order to obtain formal semantic models describing these organizations of MAS, then compose them using also the theory of categories which represents a very sophisticated mathematical toolbox based on composition.