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.
翻译:多试剂缩进逻辑S5的标准语义依据的Kripke模型,其无障碍关系是反反射、对称和中转的。这一维结构包含超越对称互动的隐性高维信息,我们在先前的工作(信息与计算,2021年)中正式确定为纯粹的简化模型。我们在此扩展理论,以包括不一定纯化的简化模型。Kripke模型的相应类别是,无障碍关系是对称和中转的,但可能不是反射的。这些模型与缩进逻辑 KB4 相对应。在两种可能的世界可能没有相同物剂的情况下产生不纯简化模型。我们用分布式的同步系统模型示例加以说明,在其中,过程可能会崩溃。