Sheaf-Theoretic Planning: A Categorical Foundation for Resilient Multi-Agent Autonomous Systems

• URL: http://arxiv.org/abs/2605.01879v1
• Date: Sun, 03 May 2026 13:50:24 GMT
• Title: Sheaf-Theoretic Planning: A Categorical Foundation for Resilient Multi-Agent Autonomous Systems
• Abstract summary: Sheaf-Theoretic Planning (STP) is a transformative alternative to traditional multi-agent system (MAS)<n>STP emerges as a transformative alternative, grounding the problem of multi-agent coordination under the mathematical structures of topos theory and sheaf semantics.<n>This report provides an exhaustive analysis, justification, and extension of the resilient framework, exploring its categorical foundations, implementation feasibility, and role in the future of autonomous systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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