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模型类应运而生。此后，这些单纯模型的多种变体被广泛研究，衍生出不同的逻辑体系与公理化系统。本文提出进一步的推广：当群体中每个个体主体均无法区分两个世界时，该群体仍可能区分它们。为此，我们将单纯复形推广至单纯集，从而定义了带有分布式知识的认知逻辑新语义。研究表明，此类模型恰是克里普克模型推广形式——“伪模型”——的几何对应物。我们识别出这些模型的若干有趣子类，涵盖了所有先前研究的单纯模型变体，并为每个子类给出了完备可靠的公理化系统。