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

TL;DR

Sheaf-Theoretic Planning (STP) offers a novel categorical framework for resilient multi-agent autonomous systems, addressing limitations of classical logical models in dynamic, uncertain environments.

Contribution

This paper develops and extends the Sheaf-Theoretic Planning framework, grounding multi-agent coordination in topos theory and sheaf semantics for improved resilience.

Findings

STP provides a categorical foundation for multi-agent planning.

Sheaf semantics enable modeling of unobserved interventions and plan interruptions.

The framework demonstrates potential for implementation in resilient autonomous systems.

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.