On the Properties of Conditional Independence

As the paper explains, it is crucial to epistemology in general and to the theory of causation in particular to investigate the properties of conditional independence as completely as possible. The paper summarizes the most important results concerning conditional independence with respect to two important representations of epistemic states, namely (strictly positive) probability measures and natural conditional (or disbelief or ranking) functions. It finally adds some new observations. In 1978, I submitted my manuscript "Stochastic Independence, Causal Independence, and Shieldability" to the Journal of Philosophical Logic. Having realized that the laws of conditional probabilistic independence are the basis of any theory of probabilistic causality and trying to explain how in my view that theory should be built upon this basis I started the manuscript by proving as many of the laws of conditional and also of unconditional probabilistic independence as I knew and conjectured that the two lists were indeed complete; these conjectures looked very plausible to me after half a year of unsuccessful attempts to prove them. The editor responded that I should rewrite the paper in the light of the referee's comments and attached an utmost valuable report which was four pages long; I have not received so long and careful a review since then. My first guess turned out to be right later on; Pat Suppes was the referee.