A finite axiomatization of conditional independence and inclusion dependencies

TL;DR

This paper provides a complete finite set of axioms for reasoning about inclusion and conditional independence dependencies, advancing the theoretical understanding of database dependencies and their logical implications.

Contribution

It introduces the first finite axiomatization for the implication problem of inclusion and conditional independence atoms in dependence logic.

Findings

Finite axiomatization for inclusion and conditional independence atoms

Implication problem for database dependencies is finitely axiomatizable in the unirelational case

Advances theoretical foundations of database dependency reasoning

Abstract

We present a complete finite axiomatization of the unrestricted implication problem for inclusion and conditional independence atoms in the context of dependence logic. For databases, our result implies a finite axiomatization of the unrestricted implication problem for inclusion, functional, and embedded multivalued dependencies in the unirelational case.