  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.
