用于分布式知识的半单纯集模型
Semi-simplicial Set Models for Distributed Knowledge
AI总结：
本文将单纯复形模型推广为半单纯集模型，以表达群体可区分而个体不可区分的分布式知识，并给出与伪模型对应的语义、子类划分及可靠完备公理化。
摘要：
近年来，出现了一类基于单纯复形的多智能体认知逻辑新模型。此后，人们研究了这些单纯模型的许多变体，产生了不同的逻辑和公理化。在本文中，我们提出了进一步的推广，即一组智能体可以区分两个世界，即使该组中的每个个体智能体都无法区分它们。为此，我们在单纯复形之外进行推广，转而考虑单纯集。通过这样做，我们为带有分布式知识的认知逻辑定义了一种新语义。事实证明，这些模型是 Kripke 模型的一种推广（称为“伪模型”）的几何对应物。我们识别了这些模型的各种有趣子类，涵盖了先前研究过的所有单纯模型变体；并为其中每一个给出了可靠且完备的公理化。
英文摘要：
In recent years, a new class of models for multi-agent epistemic logic has emerged, based on simplicial complexes. Since then, many variants of these simplicial models have been investigated, giving rise to different logics and axiomatizations. In this paper, we present a further generalization, where a group of agents may distinguish two worlds, even though each individual agent in the group is unable to distinguish them. For that purpose, we generalize beyond simplicial complexes and consider instead simplicial sets. By doing so, we define a new semantics for epistemic logic with distributed knowledge. As it turns out, these models are the geometric counterpart of a generalization of Kripke models, called "pseudo-models". We identify various interesting sub-classes of these models, encompassing all previously studied variants of simplicial models; and give a sound and complete axiomatization for each of them.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
