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 current paper, defining the concept of a structure, and ``The {\ttfamily ERA} of {\ttfamily FOLE}: Superstructure'', 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：本文讨论了一阶逻辑环境FOLE中本体的表示方法。本体定义了对某个话语社群的知识资源进行建模的原始构件。这些原始构件包括类、关系和属性。本体通过形式化公理约束对这些原始构件的解释。简言之，本体指定了一个逻辑理论。本文延续了一阶逻辑环境FOLE中本体表示与解释的讨论。（多类）一阶逻辑的形式体系与语义可采用**分类形式**和**解释形式**两种方式发展。两篇论文——当前论文定义了结构的概念，以及《FOLE的ERA：上层结构》定义了合理逻辑的概念——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——《FOLE表》定义了关系表的概念，以及《FOLE数据库》定义了关系数据库的概念——代表了**解释形式**，扩展了《数据库语义学》论文中的内容。尽管分类形式遵循陈氏实体-关系-属性数据模型，但解释形式融合了科德的关系数据模型。第五篇论文《FOLE等价性》证明了分类形式与解释形式之间的等价性。总体而言，FOLE表示采用概念结构方法，该方法与制度理论、形式概念分析和信息流完全兼容。