On Patterns of Conditional Independences and Covariance Signs among Binary Variables

Given finitely many events in a probability space, conditional independences among the indicators of events are considered simultaneously with the signs of covariances. Resulting discrete structures are studied restricting attention mostly to all couples and triples of events. Necessary and sufficient conditions for such structures to be represented by events are found. Consequences of the results for the patterns of conjunctive forks are discussed.