The FOLE Table

TL;DR

This paper develops a formal mathematical framework for representing ontologies within the FOLE environment, connecting first-order logic, entity-relationship models, and relational databases.

Contribution

It introduces a rigorous mathematical basis for FOLE, including the notion of a FOLE relational table aligned with Codd's relational model.

Findings

Develops the concept of a FOLE relational table.

Provides a formal semantics for first-order logic in FOLE.

Connects FOLE with relational database interpretation.

Abstract

This paper continues the discussion of the representation of ontologies in the first-order logical environment FOLE. According to Gruber, an ontology defines the primitives with which to model the knowledge resources for a community of discourse. These primitives, consisting of classes, relationships and properties, are represented by the entity-relationship-attribute ERA data model of Chen. An ontology uses formal axioms to constrain the interpretation of these primitives. In short, an ontology specifies a logical theory. A series of three papers by the author provide a rigorous mathematical representation for the ERA data model in particular, and ontologies in general, within FOLE. The first two papers, which provide a foundation and superstructure for FOLE, represent the formalism and semantics of (many-sorted) first-order logic in a classification form corresponding to ideas discussed in the Information Flow Framework (IFF). The third paper will define 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. Two papers will provide a precise mathematical basis for FOLE interpretation: the current paper develops the notion of a FOLE relational table following the relational model of Codd, and a follow-up paper will develop the notion of a FOLE relational database. Both of these papers expand on material found in the paper (Kent, 2011). Although the classification form follows the entity-relationship-attribute data model of Chen, the interpretation form follows the relational data model of Codd. In general, the FOLE representation uses a conceptual structures approach, that is completely compatible with formal concept analysis and information flow.