This paper discusses the representation of ontologies in the first-order logical environment FOLE (Kent 2013). An ontology defines the primitives with which to model the knowledge resources for a community of discourse (Gruber 2009). These primitives, consisting of classes, relationships and properties, are represented by the entity-relationship-attribute ERA data model (Chen 1976). An ontology uses formal axioms to constrain the interpretation of these primitives. In short, an ontology specifies a logical theory. This paper is the first in a series of three papers that provide a rigorous mathematical representation for the ERA data model in particular, and ontologies in general, within the first-order logical environment FOLE. The first two papers show how FOLE represents the formalism and semantics of (many-sorted) first-order logic in a classification form corresponding to ideas discussed in the Information Flow Framework (IFF). In particular, this first paper provides a foundation that connects elements of the ERA data model with components of the first-order logical environment FOLE, and the second paper provides a superstructure that extends FOLE to the formalisms of first-order logic. The third paper defines 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 (Kent 2011). The FOLE representation follows a conceptual structures approach, that is completely compatible with formal concept analysis (Ganter and Wille 1999) and information flow (Barwise and Seligman 1997).

翻译：本文讨论了一阶逻辑环境FOLE（Kent 2013）中的本体表示问题。本体定义了用于建模某个话语社群知识资源的原语（Gruber 2009）。这些由类、关系和属性构成的元语，通过实体-关系-属性ERA数据模型（Chen 1976）进行表示。本体使用形式公理约束这些元语的解释。简言之，本体规定了一个逻辑理论。本文是系列三篇论文中的第一篇，旨在一阶逻辑环境FOLE中为ERA数据模型（特别是本体）提供严格的数学表示。前两篇论文展示了FOLE如何以分类形式表示（多类）一阶逻辑的形式体系与语义，该分类形式对应于信息流框架（IFF）中的相关思想。具体而言，本篇论文建立了连接ERA数据模型元素与一阶逻辑环境FOLE组件的基础；第二篇论文则构建了将FOLE扩展至一阶逻辑形式体系的上层结构。第三篇论文通过最初在（Kent 2013）中描述的转换通道，将FOLE解释为一阶逻辑分类形式到等价解释形式的转换，从而定义了一阶逻辑/关系数据库系统（Kent 2011）的形式体系与语义。FOLE表示遵循概念结构方法，该方法与形式概念分析（Ganter和Wille 1999）及信息流（Barwise和Seligman 1997）完全兼容。