The ERA of FOLE: Foundation
- URL: http://arxiv.org/abs/1512.07430v4
- Date: Fri, 21 Apr 2023 18:13:22 GMT
- Title: The ERA of FOLE: Foundation
- Authors: Robert E. Kent
- Abstract summary: This paper continues the discussion of the representation and interpretation of the first-order logical environment ttfamily FOLE.
The formalism and semantics of (many-sorted) first-order logic can be developed in both a emphclassification form and an emphinterpretation form.
In general, the ttfamily FOLE representation uses a conceptual approach, that is completely compatible with the theory of institutions, formal concept analysis and information flow.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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