Reduction of Database Independence to Dividing in Atomless Boolean Algebras

TL;DR

This paper demonstrates that database independence can be reduced to dividing in atomless Boolean algebras, linking it to stochastic independence and providing a new logical perspective.

Contribution

It establishes a reduction of database independence to dividing calculus in atomless Boolean algebras, connecting database theory with model-theoretic independence.

Findings

Database independence is reducible to dividing in atomless Boolean algebras.

Links between database independence and stochastic independence are established.

Provides a logical framework connecting database theory and model theory.

Abstract

We prove that the form of conditional independence at play in database theory and independence logic is reducible to the first-order dividing calculus in the theory of atomless Boolean algebras. This establishes interesting connections between independence in database theory and stochastic independence. As indeed, in light of the aforementioned reduction and recent work of Ben-Yaacov [4], the former case of independence can be seen as the discrete version of the latter.