  We revisit the problem of general identifiability originally introduced in
[Lee et al., 2019] for causal inference and note that it is necessary to add
positivity assumption of observational distribution to the original definition
of the problem. We show that without such an assumption the rules of
do-calculus and consequently the proposed algorithm in [Lee et al., 2019] are
not sound. Moreover, adding the assumption will cause the completeness proof in
[Lee et al., 2019] to fail. Under positivity assumption, we present a new
algorithm that is provably both sound and complete. A nice property of this new
algorithm is that it establishes a connection between general identifiability
and classical identifiability by Pearl [1995] through decomposing the general
identifiability problem into a series of classical identifiability
sub-problems.
