Transitive observation-based causation, saliency, and the Markov condition

If A caused B and B caused C, did A caused C? Although causality is generally regarded as transitive, some philosophers have questioned this assumption, and models of causality in artificial intelligence are often agnostic with respect to transitivity: They define causation, then check whether the definition makes all, or only some, causal arguments transitive. We consider two formal models of observation-based causation, which differ in the way they represent uncertainty. The quantitative model uses a standard probabilistic definition; the qualitative model uses a definition based on nonmonotonic consequence. The two models identify different sufficient conditions for the transitivity of causation: The Markov condition on events for the quantitative model, and a Saliency condition (if B is true then generally A is true) for the qualitative model. We explore the formal relations between these sufficient conditions, and between the underlying definitions of observation-based causation. These connections shed light on the range of applicability of both models. © 2008 Springer-Verlag