用拓扑与层论构建抗干扰多智能体系统,突破传统逻辑框架局限。
Sheaf-Theoretic Planning: A Categorical Foundation for Resilient Multi-Agent Autonomous Systems
- 基于层论与范畴论重构多智能体规划模型
- 在非封闭世界下实现信念与现实的自洽协调
- 适合研究高鲁棒性自主系统架构的学者
构建能够应对物理世界随机性和对抗性的自主智能体,长期处于符号逻辑与控制理论的交汇处。传统多智能体系统(MAS)框架依赖于单体逻辑模型(如事件演算和情景演算)来表征动作、变化与时间持久性。尽管这些经典系统通过循环约束和后继状态公理等机制解决了框架问题,但其固有的闭世界假设在面对未观测到的代理干预、计划中断及信念-现实差异时失效。层论规划(Sheaf-Theoretic Planning, STP)作为一种变革性替代方案,将多智能体协调问题建立在拓扑范畴论与层语义的数学结构之上。本报告对STP框架进行了全面分析、论证与拓展,深入探讨其范畴基础、实现可行性及其在弹性自主系统未来中的作用。
原文摘要 · Abstract (English)
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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