This paper discusses the representation of ontologies in the first-order logical environment {\ttfamily FOLE}. An ontology defines the primitives with which to model the knowledge resources for a community of discourse. These primitives consist of classes, relationships and properties. An ontology uses formal axioms to constrain the interpretation of these primitives. In short, an ontology specifies a logical theory. This paper continues the discussion of the representation and interpretation of ontologies in the first-order logical environment {\ttfamily FOLE}. The formalism and semantics of (many-sorted) first-order logic can be developed in both a \emph{classification form} and an \emph{interpretation form}. Two papers, ``The {\ttfamily ERA} of {\ttfamily FOLE}: Foundation'', defining the concept of a structure, and the current paper, defining the concept of a sound logic, represent the \emph{classification form}, corresponding to ideas discussed in the ``Information Flow Framework''. Two papers, ``The {\ttfamily FOLE} Table'', defining the concept of a relational table, and ``The {\ttfamily FOLE} Database'', defining the concept of a relational database, represent the \emph{interpretation form}, expanding on material found in the paper ``Database Semantics''. Although the classification form follows the entity-relationship-attribute data model of Chen, the interpretation form incorporates the relational data model of Codd. A fifth paper ``{\ttfamily FOLE} Equivalence'' proves that the classification form is equivalent to the interpretation form. In general, the {\ttfamily FOLE} representation uses a conceptual structures approach, that is completely compatible with the theory of institutions, formal concept analysis and information flow.

翻译：本文探讨了一阶逻辑环境FOLE中的本体表示。本体定义了用于为话语社区建模知识资源的原语，这些原语包括类、关系和属性。本体通过形式化公理约束对这些原语的解释。简言之，本体指定了一个逻辑理论。本文延续了对一阶逻辑环境FOLE中本体的表示与解释的讨论。（多类）一阶逻辑的形式化与语义既可基于分类形式发展，也可基于解释形式发展。两篇论文——定义结构概念的《ERA of FOLE：基础》与本文（定义健全逻辑概念）——代表了分类形式，对应“信息流框架”中讨论的思想；另两篇论文——定义关系表概念的《FOLE表》与定义关系数据库概念的《FOLE数据库》——则代表了解释形式，拓展了《数据库语义学》一文的内容。尽管分类形式遵循Chen的实体-关系-属性数据模型，解释形式则融合了Codd的关系数据模型。第五篇论文《FOLE等价性》证明了分类形式与解释形式是等价的。总体而言，FOLE表示采用概念结构方法，该方法与机构理论、形式概念分析和信息流完全兼容。