An algebraic theory for data linkage

TL;DR

This paper develops an algebraic framework using partial ordered monoids and Grothendieck constructions to model data linkage and information transfer across multiple sources, with applications in database theory and reasoning.

Contribution

It introduces a novel algebraic model for data linkage using partial ordered monoids and morphisms, unifying data combination and transfer in a formal structure.

Findings

Provides a formal algebraic foundation for data linkage.

Models information transfer between sources with morphisms.

Applies the framework to database theory and approximate reasoning.

Abstract

There are countless sources of data available to governments, companies, and citizens, which can be combined for good or evil. We analyse the concepts of combining data from common sources and linking data from different sources. We model the data and its information content to be found in a single source by a partial ordered monoid, and the transfer of information between sources by different types of morphisms. To capture the linkage between a family of sources, we use a form of Grothendieck construction to create a partial ordered monoid that brings together the global data of the family in a single structure. We apply our approach to database theory and axiomatic structures in approximate reasoning. Thus, partial ordered monoids provide a foundation for the algebraic study for information gathering in its most primitive form.