If A caused B and B caused C, did A cause C? Although laypersons commonly perceive causality as being transitive, some philosophers have questioned this assumption, and models of causality in artificial intelligence are often agnostic with respect to transitivity. We consider two formal models of causation that differ in the way they represent uncertainty. The quantitative model uses a crude probabilistic definition, arguably the common core of more sophisticated quantitative definitions; the qualitative model uses a definition based on nonmonotonic consequence relations. Different sufficient conditions for the transitivity of causation are laid bare by the two models: The Markov condition on events for the quantitative model, and a so-called saliency condition (A is perceived as a typical cause of B) for the qualitative model. We explore the formal and empirical relations between these sufficient conditions, and between the underlying definitions of perceived causation. These connections shed light on the range of applicability of each model, contrasting commonsense causal reasoning (supposedly qualitative) and scientific causation 312 J.-F. Bonnefon et al.(more naturally quantitative). These speculations are supported by a series of three behavioral experiments.

Abstract. Ascribing causality amounts to determining what elements in a sequence of reported facts can be related in a causal way, on the basis of some knowledge about the course of the world. The paper offers a comparison of a large span of formal models (based on structural equations, non-monotonic consequence relations, trajectory preference relations, identification of violated norms, graphical representations, or connectionism), using a running example taken from a corpus of car accident reports. Interestingly enough, the compared approaches focus on different aspects of the problem by either identifying all the potential causes, or selecting a smaller subset by taking advantages of contextually abnormal facts, or by modeling interventions to get rid of simple correlations. The paper concludes by a general discussion based on a battery of criteria (several of them being proper to AI approaches to causality).