FOLE Equivalence

TL;DR

This paper demonstrates the informational equivalence between the classification and interpretation forms of FOLE, a logical environment for distributed first-order information systems, integrating relational calculus and formal concept analysis.

Contribution

It establishes the formal equivalence between FOLE's classification and interpretation forms, unifying different representations of first-order logical environments.

Findings

Classification and interpretation forms of FOLE are informationally equivalent.

All relational algebra operations are rigorously developed within FOLE.

FOLE's approach is compatible with formal concept analysis and information flow.

Abstract

The first-order logical environment FOLE [5] provides a rigorous and principled approach to distributed interoperable first-order information systems. FOLE has been developed in two forms: a classification form and an interpretation form. Two papers represent FOLE in a classification form corresponding to ideas of the Information Flow Framework [11],[12],[13]: the first paper [6] provides a foundation that connects elements of the ERA data model [2] with components of the first-order logical environment FOLE; the second paper [7] provides a superstructure that extends FOLE to the formalisms of first-order logic. The formalisms in the classification form of FOLE provide an appropriate framework for developing the relational calculus. Two other papers represent FOLE in an interpretation form: the first paper [8] develops the notion of the FOLE table following the relational model [3]; the second paper [9] discusses the notion of a FOLE relational database. All the operations of the relational algebra have been rigorously developed [10] using the interpretation form of FOLE. The present study demonstrates that the classification form of FOLE is informationally equivalent to the interpretation form of FOLE. In general, the FOLE representation uses a conceptual structures approach, that is completely compatible with formal concept analysis [4] and information flow [1].