  We study the problem of restricting Markov equivalence classes of maximal
ancestral graphs (MAGs) containing certain edge marks, which we refer to as
expert knowledge. MAGs forming a Markov equivalence class can be uniquely
represented by an essential ancestral graph. We seek to learn the restriction
of the essential ancestral graph containing the proposed expert knowledge. Our
contributions are several-fold. First, we prove certain properties for the
entire Markov equivalence class including a conjecture from Ali et al. (2009).
Second, we present three sound graphical orientation rules, two of which
generalize previously known rules, for adding expert knowledge to an essential
graph. We also show that some orientation rules of Zhang (2008) are not needed
for restricting the Markov equivalence class with expert knowledge. We provide
an algorithm for including this expert knowledge and show that our algorithm is
complete in certain settings i.e., in these settings, the output of our
algorithm is a restricted essential ancestral graph. We conjecture this
algorithm is complete generally. Outside of our specified settings, we provide
an algorithm for checking whether a graph is a restricted essential graph and
discuss its runtime. This work can be seen as a generalization of Meek (1995).
