Attempts at axiomatic description of conditional independence

This paper concerns the problem of characterization of conditional-independence relations (the abbreviation CIR) which arises in connection with probabilistic expert systems. The first two sections contain some lately found properties (axioms) of CIRs; the rest of the paper is a proposal for a proper generalization of the concept of CIR. Since it is defined by means of the concept of multiinformation it is called the M-relation. Some advantages of the M-relations are discussed. Some questions are still open, we express our hypotheses through the paper. The paper is a survey only, the extended version with proofs will be published later.