A Calculus for Causal Relevance

We present a sound and complete calculus for causal relevance that uses Pearl’s functional causal models as semantics. The calculus consists of axioms and rules of inference for reasoning about causal relevance relationships. We extend the set of known axioms for causal relevance with new axioms and rules of inference. The axioms are then divided into different sets for reasoning about specific subclasses of models. These subclasses make up a new decomposition of the class of causal models. At the end, we show how the calculus for causal relevance can be used in the task of identifying causal structure from non-observational data.