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.

翻译：近年来，基于单纯复形的多主体认知逻辑新模型类别逐渐兴起。此后，这些单纯模型的多种变体得到研究，催生了不同的逻辑体系与公理化系统。本文提出进一步泛化方案：即使群体中每个个体主体无法区分两个世界，群体整体仍可能区分它们。为此，我们超越单纯复形，转而考虑单纯集。通过这一方法，我们为具有分布式知识的认知逻辑定义了新的语义学。这些模型恰好是克里普克模型泛化形式（即"伪模型"）的几何对应物。我们识别了这些模型的多个有趣子类，涵盖了此前所有单纯模型变体，并为每个子类给出了可靠且完备的公理化系统。