Stochastic independence, causal independence, and shieldability

“Stochastic Independence, Causal Independence, and Shieldability”: The aim of the paper is to explicate causal independence and Reichenbach's screening-off relation, or equivalently, causal dependence and direct causal dependence (always taken as relations between sets of factors or variables) in probabilistic terms along the lines of Suppes' probabilistic theory of causality, which is amended by the observation that there are not only spurious and indirect, but also hidden causes. The notion central to the explication is that of conditional stochastic or probabilistic independence, for which the graphoid axioms, as they have been called later on, are proved to hold. The adequacy of the explication is supported by proving some intuitively expected theorems, such as that unions of sets of factors causally independent from some other set are causally independent from that set as well, or that partitions into probabilistic independent parts are equivalent with partitions into causally independent parts. (Much of the paper is contained already in my Ph.D. thesis of 1976, published as Grundlagen der Entscheidungstheorie, 1978. However, the theory of indirect causal dependence developed in the paper is essentially revised in my paper “Direct and Indirect Causes”.