The ERA of FOLE: Foundation

TL;DR

This paper explores the formal representation of ontologies within the FOLE framework, integrating classification and interpretation forms to align with entity-relationship and relational data models, and proves their equivalence.

Contribution

It introduces a formalism for representing ontologies in FOLE, connecting classification and interpretation forms, and demonstrates their equivalence, advancing formal ontology modeling.

Findings

Classification form aligns with Chen's data model

Interpretation form incorporates Codd's relational model

Proves equivalence between classification and interpretation forms

Abstract

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.