Semigraphoids Are Two-Antecedental Approximations of Stochastic Conditional Independence Models

TL;DR

This paper demonstrates that semigraphoids serve as effective two-antecedental approximations for stochastic conditional independence models, providing a theoretical foundation for their use in probabilistic reasoning.

Contribution

It proves that the semigraphoid closure of any two CI-statements forms a stochastic CI-model and shows that all sound inference rules with up to two antecedents are derivable from semigraphoid rules.

Findings

Semigraphoid closure of two CI-statements is a stochastic CI-model.

All probabilistically sound two-antecedent inference rules are derivable from semigraphoids.

List of 19 potential dominant elements of the semigraphoid closure provided.

Abstract

The semigraphoid closure of every couple of CI-statements (GI=conditional independence) is a stochastic CI-model. As a consequence of this result it is shown that every probabilistically sound inference rule for CI-model, having at most two antecedents, is derivable from the semigraphoid inference rules. This justifies the use of semigraphoids as approximations of stochastic CI-models in probabilistic reasoning. The list of all 19 potential dominant elements of the mentioned semigraphoid closure is given as a byproduct.