Patterns of conjunctive forks

Abstract

Three events in a probability space form a conjunctive fork if they satisfy specific constraints on conditional independence and covariances. Patterns of conjunctive forks within collections of events are characterized by means of systems of linear equations that have positive solutions. This characterization allows patterns of conjunctive forks to be recognized in polynomial time. Relations to previous work on causal betweenness and on patterns of conditional independence among random variables are discussed.

The mathematical content of this paper is nearly identical with that of its version 1, but the two versions differ in their ways of presenting this content. Chvátal and Zwols disapprove of the presentation in version 1