The ERA of FOLE: Superstructure

This paper discusses the representation of ontologies in the first-order logical environment FOLE (Kent [10]). An ontology defines the primitives with which to model the knowledge resources for a community of discourse (Gruber [6]). These primitives, consisting of classes, relationships and properties, are represented by the entity-relationshipattribute ERA data model (Chen [2]). An ontology uses formal axioms to constrain the interpretation of these primitives. In short, an ontology specifies a logical theory. This paper is the second 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 [16]). In particular, the first paper (Kent [11]) provided a foundation that connected elements of the ERA data model with components of the first-order logical environment FOLE, and this second paper provides a superstructure that extends FOLE to the formalisms of first-order logic. The third paper (Kent [12]) will define an interpretation of FOLE in terms of the transformational passage, first described in Kent [10], 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 [9]). The FOLE representation follows a conceptual structures approach, that is completely compatible with formal concept analysis (Ganter and Wille [3]) and information flow (Barwise and Seligman [1]).