  Identifying effects of actions (treatments) on outcome variables from
observational data and causal assumptions is a fundamental problem in causal
inference. This identification is made difficult by the presence of confounders
which can be related to both treatment and outcome variables. Confounders are
often handled, both in theory and in practice, by adjusting for covariates, in
other words considering outcomes conditioned on treatment and covariate values,
weighed by probability of observing those covariate values. In this paper, we
give a complete graphical criterion for covariate adjustment, which we term the
adjustment criterion, and derive some interesting corollaries of the
completeness of this criterion.
