$KB4_n$的一个简单模型：具有可能死亡主体的认知逻辑
A Simplicial Model for $KB4_n$: Epistemic Logic with Agents that May Die
摘要：
多智能体认知逻辑S5的标准语义是基于Kripke模型，其可达性关系是自反的，对称的和传递的。这个一维结构包含了超越成对相互作用的隐式高维信息，我们在以前的工作中将其形式化为纯单纯模型（信息与计算，2021）。在这里，我们将理论扩展到包含不一定是纯的单纯模型。Kripke模型的对应类是那些可达性关系是对称和传递的，但可能不是自反的。这些模型对应于认知逻辑KB4。不纯单纯模型出现在两个可能的世界可能没有相同的代理集的情况下。我们用同步系统中进程可能崩溃的分布式计算例子来说明它。
英文摘要：
The standard semantics of multi-agent epistemic logic S5 is based on Kripke models whose accessibility relations are reflexive, symmetric and transitive. This one dimensional structure contains implicit higher-dimensional information beyond pairwise interactions, that we formalized as pure simplicial models in a previous work (Information and Computation, 2021). Here we extend the theory to encompass simplicial models that are not necessarily pure. The corresponding class of Kripke models are those where the accessibility relation is symmetric and transitive, but might not be reflexive. Such models correspond to the epistemic logic KB4 . Impure simplicial models arise in situations where two possible worlds may not have the same set of agents. We illustrate it with distributed computing examples of synchronous systems where processes may crash.
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。
