Axioms of Causal Relevance

This paper develops a set of graphoid-like axioms for causal relevance, that is, statements of the form: "Changing X will not affect Y if we hold Z constant". Both a probabilistic and deterministic definition of causal irrelevance are proposed. The probabilistic definition allows for only two axioms, unless stability is assumed. Under the stability assumption, probabilistic causal irrelevance is equivalent to path interception in cyclic graphs. The deterministic definition allows for all of the axioms of path interception in cyclic graphs, with the exception of transitivity. Introduction In (Geiger, Verma, & Pearl 1990), a set of axioms was developed for a class of relations called graphoids. These axioms characterize informational relevance among observed events based on the semantics of conditional independence in probability calculus. This paper develops a parallel set of axioms for causal relevance, that is, the tendency of certain events to affect the occurrence of other events..