  Maier et al. (2010) introduced the relational causal model (RCM) for
representing and inferring causal relationships in relational data. A lifted
representation, called abstract ground graph (AGG), plays a central role in
reasoning with and learning of RCM. The correctness of the algorithm proposed
by Maier et al. (2013a) for learning RCM from data relies on the soundness and
completeness of AGG for relational d-separation to reduce the learning of an
RCM to learning of an AGG. We revisit the definition of AGG and show that AGG,
as defined in Maier et al. (2013b), does not correctly abstract all ground
graphs. We revise the definition of AGG to ensure that it correctly abstracts
all ground graphs. We further show that AGG representation is not complete for
relational d-separation, that is, there can exist conditional independence
relations in an RCM that are not entailed by AGG. A careful examination of the
relationship between the lack of completeness of AGG for relational
d-separation and faithfulness conditions suggests that weaker notions of
completeness, namely adjacency faithfulness and orientation faithfulness
between an RCM and its AGG, can be used to learn an RCM from data.
