Qualitative combination of independence models

We deal with the problem of combining sets of independence statements coming from different experts. It is known that the independence model induced by a strictly positive probability distribution has a graphoid structure, but the explicit computation and storage of the closure (w.r.t. graphoid properties) of a set of independence statements is a computational hard problem. For this, we rely on a compact symbolic representation of the closure called fast closure and study three different combination strategies of two sets of independence statements, working on fast closures. We investigate when the complete DAG representability of the given models is preserved in the combined one.