The FOLE Database
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This paper continues the discussion of the representation and interpretation of ontologies in the first-order logical environment FOLE (Kent). Ontologies are represented and interpreted in (many-sorted) first-order logic. Five papers provide a rigorous mathematical representation for the ERA (entity-relationship-attribute) data model (Chen) in particular, and ontologies in general, within the first-order logical environment FOLE. Two papers (Kent and another paper) 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). Two papers (Kent and the current paper) represent (many-sorted) first-order logic in an interpretation form expanding on material found in the paper (Kent). A fifth paper (Kent) demonstrates that the classification form of FOLE is "informationally equivalent" to the interpretation form of 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 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).
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