Sheaf-Theoretic Planning: A Categorical Foundation for Resilient Multi-Agent Autonomous Systems
For researchers in multi-agent systems and autonomous robotics, this work proposes a new paradigm to address the closed-world assumption and belief-reality divergence, but the abstract lacks concrete results or comparisons.
The paper introduces Sheaf-Theoretic Planning (STP) as a new foundation for multi-agent coordination that overcomes limitations of classical logical models in handling stochastic and adversarial environments. It claims STP provides a transformative alternative grounded in topos theory and sheaf semantics, enabling resilient autonomous systems.
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.