Testing Implication of Probabilistic Dependencies

TL;DR

This paper introduces a non-axiomatic chase method for testing probabilistic dependencies, offering a powerful tool for theoretical analysis and revealing connections between databases and probabilistic reasoning.

Contribution

It proposes a chase-based approach for probabilistic dependency implication testing, expanding beyond traditional axiomatic methods.

Findings

Chase method can determine if a dependency follows from others.

The approach offers new insights into database and probabilistic reasoning connections.

The computation may be exponential in some cases.

Abstract

Axiomatization has been widely used for testing logical implications. This paper suggests a non-axiomatic method, the chase, to test if a new dependency follows from a given set of probabilistic dependencies. Although the chase computation may require exponential time in some cases, this technique is a powerful tool for establishing nontrivial theoretical results. More importantly, this approach provides valuable insight into the intriguing connection between relational databases and probabilistic reasoning systems.