The ERA of FOLE: Foundation

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).