This paper continues the discussion of the representation of ontologies in the first-order logical environment FOLE. According to Gruber, an ontology defines the primitives with which to model the knowledge resources for a community of discourse. These primitives, consisting of classes, relationships and properties, are represented by the entity-relationship-attribute ERA data model of Chen. An ontology uses formal axioms to constrain the interpretation of these primitives. In short, an ontology specifies a logical theory. A series of three papers by the author provide a rigorous mathematical representation for the ERA data model in particular, and ontologies in general, within FOLE. The first two papers, which provide a foundation and superstructure for FOLE, represent the formalism and semantics of (many-sorted) first-order logic in a classification form corresponding to ideas discussed in the Information Flow Framework (IFF). The third paper will define an interpretation of FOLE in terms of the transformational passage, first described in (Kent, 2013), from the classification form of first-order logic to an equivalent interpretation form, thereby defining the formalism and semantics of first-order logical/relational database systems. Two papers will provide a precise mathematical basis for FOLE interpretation: the current paper develops the notion of a FOLE relational table following the relational model of Codd, and a follow-up paper will develop the notion of a FOLE relational database. Both of these papers expand on material found in the paper (Kent, 2011). Although the classification form follows the entity-relationship-attribute data model of Chen, the interpretation form follows the relational data model of Codd. In general, the FOLE representation uses a conceptual structures approach, that is completely compatible with formal concept analysis and information flow.

翻译：本文继续论述一阶逻辑环境FOLE中本体表示的议题。根据Gruber的定义，本体规定了建模话语社群知识资源所需的基本要素。这些基本要素由陈品山提出的实体-关系-属性ERA数据模型表示，包括类、关系和属性。本体通过形式化公理约束对这些基本要素的解释。简言之，本体界定了逻辑理论。作者系列三篇论文为FOLE框架下的ERA数据模型（特别是本体）提供了严格的数学表示。前两篇论文为FOLE构建基础与上层结构，采用分类形式呈现（多类）一阶逻辑的形式体系与语义，其思想与信息流框架（IFF）相呼应。第三篇论文将定义从一阶逻辑的分类形式到等价解释形式的变换通道（最初见于Kent, 2013），从而界定一阶逻辑/关系数据库系统的形式体系与语义。两篇论文将为FOLE解释提供精确数学基础：本文遵循Codd关系模型发展FOLE关系表的概念，后续论文将发展FOLE关系数据库的概念。这两篇论文均扩展了文献（Kent, 2011）中的内容。尽管分类形式遵循陈品山的实体-关系-属性数据模型，但解释形式遵循Codd的关系数据模型。总体而言，FOLE表示采用概念结构方法，这与形式概念分析与信息流完全兼容。