Semigraphoids Are Two-Antecedental Approximations of Stochastic Conditional Independence Models
This work provides a theoretical justification for using semigraphoids in probabilistic reasoning, addressing foundational issues in AI and statistics, but it appears incremental as it builds on existing semigraphoid theory.
The paper tackled the problem of approximating stochastic conditional independence models using semigraphoids, showing that every probabilistically sound inference rule with at most two antecedents is derivable from semigraphoid rules, and provided a list of 19 potential dominant elements as a byproduct.
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.