Causal Reasoning with Causal Models

We introduce and discuss the use of Bayesian networks for causal modeling. Despite their growing popularity and utility in this application, numerous objections to it have been raised. We address the claims that Chickering's arc reversal rule undermines a causal interpretation and that failures of Reichenbach's Common Cause Principle, or again failures of faithfulness, invalidate causal modeling. We also argue against Pearl's deterministic interpretation of causal models. Against these objections we propose new model-building principles which evade some of the difficulties, and we put forward a concept of causal faithfulness which holds when faithfulness simpliciter fails. Finally, we particularize our account of type causal relevant to token causal relevance, providing an alternative to the recent deterministic accounts of token causation due to Hitchcock and Halpern & Perl.