A Graph-Based Inference Method for Conditional Independence
  The graphoid axioms for conditional independence, originally described by
Dawid [1979], are fundamental to probabilistic reasoning [Pearl, 19881. Such
axioms provide a mechanism for manipulating conditional independence assertions
without resorting to their numerical definition. This paper explores a
representation for independence statements using multiple undirected graphs and
some simple graphical transformations. The independence statements derivable in
this system are equivalent to those obtainable by the graphoid axioms.
Therefore, this is a purely graphical proof technique for conditional
independence.
