We propose a many-sorted modal logic for reasoning about knowledge in multi-agent systems. Our logic introduces a clear distinction between participating agents and the environment. This allows to express local properties of agents and global properties of worlds in a uniform way, as well as to talk about the presence or absence of agents in a world. The logic subsumes the standard epistemic logic and is a conservative extension of it. The semantics is given in chromatic hypergraphs, a generalization of chromatic simplicial complexes, which were recently used to model knowledge in distributed systems. We show that the logic is sound and complete with respect to the intended semantics. We also show a further connection of chromatic hypergraphs with neighborhood frames.

翻译：我们提出了一种用于多智能体系统中知识推理的多类模态逻辑。该逻辑在参与智能体与所处环境之间建立了清晰区分，从而能够以统一方式表达智能体的局部属性与世界的全局属性，同时可讨论智能体在世界中的存在或缺失。该逻辑涵盖了标准认知逻辑，并是其保守扩展。其语义定义在色超图上——这是最近用于建模分布式系统中知识的色单纯复形的泛化形式。我们证明了该逻辑在目标语义下具有可靠性与完备性，并揭示了色超图与邻域框架之间的进一步关联。