A Categorical Unification for Multi-Model Data: Part I Categorical Model and Normal Forms

TL;DR

This paper introduces a categorical framework that unifies relation, XML, and graph data models, providing a formal abstraction and normal forms to reduce redundancy across diverse data types.

Contribution

It presents the first unified categorical model and normal form theory applicable to multiple data models, enhancing data consistency and management.

Findings

Unified categorical framework for multi-model data

Normal forms applicable to relation, XML, and graph data

Connections established with existing normal forms like BCNF and 4NF

Abstract

Modern database systems face a significant challenge in effectively handling the Variety of data. The primary objective of this paper is to establish a unified data model and theoretical framework for multi-model data management. To achieve this, we present a categorical framework to unify three types of structured or semi-structured data: relation, XML, and graph-structured data. Utilizing the language of category theory, our framework offers a sound formal abstraction for representing these diverse data types. We extend the Entity-Relationship (ER) diagram with enriched semantic constraints, incorporating categorical ingredients such as pullback, pushout and limit. Furthermore, we develop a categorical normal form theory which is applied to category data to reduce redundancy and facilitate data maintenance. Those normal forms are applicable to relation, XML and graph data simultaneously, thereby eliminating the need for ad-hoc, model-specific definitions as found in separated normal form theories before. Finally, we discuss the connections between this new normal form framework and Boyce-Codd normal form, fourth normal form, and XML normal form.