The FOLE Database

TL;DR

This paper elaborates on the FOLE framework for representing and interpreting ontologies in first-order logic, integrating data models like ER and relational models within a formal, mathematically rigorous environment.

Contribution

It introduces a formalism for FOLE that unifies classification and interpretation forms, aligning with ER and relational models, and demonstrates their informational equivalence.

Findings

Classification form of FOLE is equivalent to interpretation form.

FOLE formalism aligns with ER and relational data models.

Provides a rigorous mathematical foundation for ontologies in first-order logic.

Abstract

This paper continues the discussion of the representation and interpretation of ontologies in the first-order logical environment {\ttfamily FOLE} (Kent). Ontologies are represented and interpreted in (many-sorted) first-order logic. Five papers provide a rigorous mathematical representation for the {\ttfamily ERA} (entity-relationship-attribute) data model (Chen) in particular, and ontologies in general, within the first-order logical environment {\ttfamily FOLE}. Two papers (Kent and another paper) represent the formalism and semantics of (many-sorted) first-order logic in a \emph{classification form} corresponding to ideas discussed in the Information Flow Framework (IFF). Two papers (Kent and the current paper) represent (many-sorted) first-order logic in an \emph{interpretation form} expanding on material found in the paper (Kent). A fifth paper (Kent) demonstrates that the classification form of {\ttfamily FOLE} is "informationally equivalent" to the interpretation form of {\ttfamily FOLE}, thereby defining the formalism and semantics of first-order logical/relational database systems. Although the classification form follows the entity-relationship-attribute data model of Chen, the interpretation form incorporates the relational data model of Codd. Two further papers discuss the "relational algebra" (Kent) and the "relational calculus". In general, the {\ttfamily FOLE} representation uses a conceptual structures approach, that is completely compatible with the theory of institutions (Goguen and Burstall), formal concept analysis (Ganter and Wille), and information flow (Barwise and Seligman).