Axioms of causal relevance

This paper develops axioms and formal semantics for statements of the form “X is causally irrelevant to Y in context Z”, which is interpreted to mean “Changing X will not affect Y once Z is held constant”.

Abstract

This paper develops axioms and formal semantics for statements of the form "X is causally irrelevant to Y in context Z", which we interpret to mean "Changing X will not affect Y once Z is held constant". The axiomization of causal irrelevance is contrasted with the axiomization of informational irrelevance, as in "Finding X will not alter our belief in Y, once we know Z". Two versions of causal irrelevance are analyzed: probabilistic and deterministic. We show that, unless stability is assumed, the probabilistic definition yields a very loose structure that is governed by just two trivial axioms. Under the stability assumption, probabilistic causal irrelevance is isomorphic to path interception in cyclic graphs. Under the deterministic definition, causal irrelevance complies with all of the axioms of path interception in cyclic graphs except transitivity. We compare our formalism to that of Lewis (1973) and offer a graphical method of proving theorems about causal relevance.