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

Abstract

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.