A Formal Framework for Reasoning about Agents' Independence in Self-organizing Multi-agent Systems

Self-organization is a process where a stable pattern is formed by the cooperative behavior between parts of an initially disordered system without external control or influence. It has been introduced to multi-agent systems as an internal control process or mechanism to solve difficult problems spontaneously. However, because a self-organizing multi-agent system has autonomous agents and local interactions between them, it is difficult to predict the behavior of the system from the behavior of the local agents we design. This paper proposes a logic-based framework of self-organizing multi-agent systems, where agents interact with each other by following their prescribed local rules. The dependence relation between coalitions of agents regarding their contributions to the global behavior of the system is reasoned about from the structural and semantic perspectives. We show that the computational complexity of verifying such a self-organizing multi-agent system is in exponential time. We then combine our framework with graph theory to decompose a system into different coalitions located in different layers, which allows us to verify agents' full contributions more efficiently. The resulting information about agents' full contributions allows us to understand the complex link between local agent behavior and system level behavior in a self-organizing multi-agent system. Finally, we show how we can use our framework to model a constraint satisfaction problem.