Conditional Independences among Four Random Variables Ii

Numerous new properties of stochastic conditional independence are introduced. They are aimed, together with two surprisingly trivial examples, at a further reduction of the problem of probabilistic representability for four{element sets, i.e. of the problem which conditional independences within a system of four random variables can occur simultaneously. Proofs are based on fundamental properties of conditional independence and, in discrete case, on use of I{divergence and algebraic manipulations with marginal probabilities. A duality question is answered in negative. 3