On Axiomatization of Probabilistic Conditional Independencies

TL;DR

This paper explores the relationship between probabilistic conditional independence and data dependency, providing an alternative proof to refute the conjecture that such independencies have a complete axiomatization.

Contribution

It establishes a connection between probabilistic conditional independence and data dependency, and offers a new proof refuting the completeness conjecture.

Findings

Probabilistic conditional independencies are not fully axiomatizable.

A new proof refutes the conjecture of completeness.

Links between probabilistic reasoning and database theory are demonstrated.

Abstract

This paper studies the connection between probabilistic conditional independence in uncertain reasoning and data dependency in relational databases. As a demonstration of the usefulness of this preliminary investigation, an alternate proof is presented for refuting the conjecture suggested by Pearl and Paz that probabilistic conditional independencies have a complete axiomatization.