  Several types of graphs with different conditional independence
interpretations --- also known as Markov properties --- have been proposed and
used in graphical models. In this paper we unify these Markov properties by
introducing a class of graphs with four types of edges --- lines, arrows, arcs,
and dotted lines --- and a single separation criterion. We show that
independence structures defined by this class specialize to each of the
previously defined cases, when suitable subclasses of graphs are considered. In
addition, we define a pairwise Markov property for the subclass of chain mixed
graphs which includes chain graphs with the LWF interpretation, as well as
summary graphs (and consequently ancestral graphs). We prove the equivalence of
this pairwise Markov property to the global Markov property for compositional
graphoid independence models.
