2016/02/13 by Kent, Robert E.
#Databases (cs.DB) #FOS: Computer and information sciences #Logic in Computer Science (cs.LO)
paper · doi:10.48550/arxiv.1602.04268
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 classification form and an interpretation form. Two papers, ``The \ttfamily ERA of \ttfamily FOLE: Foundation'', defining the concept of a structure, and the current paper, defining the concept of a sound logic, represent the 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 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.