The paper investigates an evidence-based semantics for epistemic logics. It is shown that the properties of knowledge obtained from a potentially infinite body of evidence are described by modal logic S5. At the same time, the properties of knowledge obtained from only a finite subset of this body are described by modal logic S4. The main technical result is a sound and complete bi-modal logical system that describes properties of these two modalities and their interplay.

翻译：文件调查了一种基于证据的缩略语逻辑的语义,表明从可能无穷无尽的一组证据中获得的知识的特性由模式逻辑S5描述。 同时,仅从本机构一个有限子集获得的知识的特性由模式逻辑S4描述。主要的技术结果是健全和完整的双模式逻辑系统,描述这两种模式的特性及其相互作用。