Chain graphs: semantics and expressiveness

A chain graph (CG) is a graph admitting both directed and undirected edges with forbidden directed cycles. It generalizes both the concept of undirected graph (UG) and the concept of directed acyclic graph (DAG). CGs can be used eeciently to store graphoids, that is, independency knowledge of the form \X is independent of Y given Z" obeying a set of ve properties (axioms). Two equivalent criteria for reading independencies from a CG are formulated , namely the moralization criterion and the separation criterion. These criteria give exactly the graphoid closure of the input list for the CG. Moreover, a construction of a CG from a graphoid (through an input list), which produces a minimal I-map of that graphoid, is given.