Representing Knowledge and Querying Data using Double-Functorial Semantics

Category theory offers a mathematical foundation for knowledge representation and database systems. Popular existing approaches model a database instance as a functor into the category of sets and functions, or as a 2-functor into the 2-category of sets, relations, and implications. The functional a...

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Bibliographic Details
Published in:arXiv.org 2024-06
Main Authors: Lambert, Michael, Patterson, Evan
Format: Article
Language:English
Subjects:
Knowledge representation
Relational algebra
Semantics
Online Access:Get full text
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Summary:Category theory offers a mathematical foundation for knowledge representation and database systems. Popular existing approaches model a database instance as a functor into the category of sets and functions, or as a 2-functor into the 2-category of sets, relations, and implications. The functional and relational models are unified by double functors into the double category of sets, functions, relations, and implications. In an accessible, example-driven style, we show that the abstract structure of a 'double category of relations' is a flexible and expressive language in which to represent knowledge, and we show how queries on data in the spirit of Codd's relational algebra are captured by double-functorial semantics.
ISSN:2331-8422