Why does Judea Pearl call his causal graphs Markovian?

Question

In his texts on causality, Judea Pearl always refers to the simplest graphs he uses, i.e. the acyclic graphs with independent confounders, as Markovian. I don't see why these graphs contain anything like a Markov-property.

Answer 1

He is referring to the Parental Markov Condition (see theorems 1.2.7 and 1.4.1 of Causality). Given a graph $G$, we say a distribution $P$ is Markov relative to $G$ if every variable is independent of all its non descendants conditional on its parents. An acyclic causal model $M$ with jointly independent error terms induce a probability distribution over the observed variables which is Markovian relative to $G(M)$.

Answer 2

These graphs do satisfy the Markov property - once you condition on the parent node, from which the causal arrow comes, the variable is independent of earlier ancestors that causally affect that parent (unless there is a separate arrow directly from the ancestor node to the present node).