The role of coherence for handling probabilistic evaluations and conditional independence

This paper deals with coherent conditional probability able to manage uncertainty, partial knowledge and conditional independence, overcoming the critical situations presented by the classic independence definition. When a probability is not complete (i.e. it is defined on an arbitrary set of conditional events) the conditional independence statements are not necessarily automatically induced by the values of the assessment, so given a set of independence statements its compatibility with the numerical values (conditional probability) need to be checked. This problem related to the compatibility of independence statements and conditional probability assessment is studied and a procedure for checking the compatibility is proposed.