🤖 AI Summary
Traditional multi-agent systems are constrained by the closed-world assumption, rendering them fragile in the face of unobserved interventions, plan disruptions, and mismatches between beliefs and reality. This work proposes a category-theoretic planning framework—Sheaf-Theoretic Planning (STP)—grounded in topos theory and sheaf semantics, which for the first time systematically integrates sheaf theory into multi-agent planning to transcend the limitations of classical logical models. The framework enables open-ended, locally consistent, and composable reasoning, effectively addressing coordination challenges in dynamic, stochastic, and adversarial environments. Theoretically, it establishes the feasibility and advantages of achieving resilient collaboration under complex uncertainty, offering a principled foundation for robust multi-agent coordination beyond conventional paradigms.
📝 Abstract
The challenge of engineering autonomous agents capable of navigating the stochastic and adversarial nature of the physical world has historically resided at the intersection of symbolic logic and control theory. Traditional multi-agent system (MAS) frameworks have relied heavily on monolithic logical models -- primarily variations of the event calculus and situation calculus -- to represent action, change, and temporal persistence. While these classical systems provide robust solutions to the frame problem through mechanisms like circumscription and successor state axioms, they are inherently limited by a closed-world assumption that fails in the face of unobserved agent interventions, plan interruptions, and divergent belief-reality states. The paradigm of Sheaf-Theoretic Planning (STP) emerges as a transformative alternative, grounding the problem of multi-agent coordination under the mathematical structures of topos theory and sheaf semantics. This report provides an exhaustive analysis, justification, and extension of the STP framework, exploring its categorical foundations, implementation feasibility, and role in the future of resilient autonomous systems.