Intercausal Reasoning with Uninstantiated Ancestor Nodes
  Intercausal reasoning is a common inference pattern involving probabilistic
dependence of causes of an observed common effect. The sign of this dependence
is captured by a qualitative property called product synergy. The current
definition of product synergy is insufficient for intercausal reasoning where
there are additional uninstantiated causes of the common effect. We propose a
new definition of product synergy and prove its adequacy for intercausal
reasoning with direct and indirect evidence for the common effect. The new
definition is based on a new property matrix half positive semi-definiteness, a
weakened form of matrix positive semi-definiteness.
