Differentiable Modal Logic for Multi-Agent Diagnosis, Orchestration and Communication

ABSTRACT

As multi-agent systems evolve into autonomous swarms, debugging failures requires reasoning about knowledge, belief, and obligation. We present Differentiable Modal Logic (DML), implemented via Modal Logical Neural Networks (MLNNs). This framework enables systems to learn trust networks, causal chains, and regulatory boundaries from behavioral data alone. We demonstrate neurosymbolic debugging through four modalities: epistemic, temporal, deontic, and doxastic. MLNNs allow discovering hidden semantic structures (e.g., deceptive alliances) by minimizing logical contradictions. Key advantages include interpretable learned structures where trust is an explicit parameter and the ability to inject domain axioms to guide learning with sparse data.