  Causal models have proven extremely useful in offering formal representations
of causal relationships between a set of variables. Yet in many situations,
there are non-causal relationships among variables. For example, we may want
variables $LDL$, $HDL$, and $TOT$ that represent the level of low-density
lipoprotein cholesterol, the level of lipoprotein high-density lipoprotein
cholesterol, and total cholesterol level, with the relation $LDL+HDL=TOT$. This
cannot be done in standard causal models, because we can intervene
simultaneously on all three variables. The goal of this paper is to extend
standard causal models to allow for constraints on settings of variables.
Although the extension is relatively straightforward, to make it useful we have
to define a new intervention operation that $disconnects$ a variable from a
causal equation. We give examples showing the usefulness of this extension, and
provide a sound and complete axiomatization for causal models with constraints.
