多智能体系统的几何方面
Geometric Aspects of Multiagent Systems
摘要：
多智能体系统（MAS）和分布式系统理论中的认知逻辑的最新进展已经使用了各种组合结构，这些组合结构对系统的几何结构和逻辑模型的Kripke模型结构进行建模。考察这些模型的一个较简单的版本，解释系统，以及逻辑$S5_n$（一种具有$n$ -代理的认知逻辑）的相关Kripke语义，与群胚地图集的几何/同伦理论结构的相似性是惊人的。这些后者的对象出现在代数K-理论，一个领域的代数与研究分解和范式定理在线性代数的问题。它们有一个自然的结构良好的路径概念和路径对象的结构，等等，产生了丰富的同伦理论。
英文摘要：
Recent advances in Multiagent Systems (MAS) and Epistemic Logic within Distributed Systems Theory, have used various combinatorial structures that model both the geometry of the systems and the Kripke model structure of models for the logic. Examining one of the simpler versions of these models, interpreted systems, and the related Kripke semantics of the logic $S5_n$ (an epistemic logic with $n$-agents), the similarities with the geometric / homotopy theoretic structure of groupoid atlases is striking. These latter objects arise in problems within algebraic K-theory, an area of algebra linked to the study of decomposition and normal form theorems in linear algebra. They have a natural well structured notion of path and constructions of path objects, etc., that yield a rich homotopy theory.
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