Abstract
Pearl opened the door to formally defining actual causation using causal models. His approach rests on two strategies: first, capturing the widespread intuition that X = x causes Y = y iff X = x is a Necessary Element of a Sufficient Set for Y = y, and second, showing that his definition gives intuitive answers on a wide set of problem cases. This inspired dozens of variations of his definition of actual causation, the most prominent of which are due to Halpern & Pearl. Yet all of them ignore Pearl’s first strategy, and the second strategy taken by itself is unable to deliver a consensus. This paper offers a way out by going back to the first strategy: it offers six formal definitions of causal sufficiency and two interpretations of necessity. Combining the two gives twelve new definitions of actual causation. Several interesting results about these definitions and their relation to the various Halpern & Pearl definitions are presented. Afterwards the second strategy is evaluated as well. In order to maximize neutrality, the paper relies mostly on the examples and intuitions of Halpern & Pearl. One definition comes out as being superior to all others, and is therefore suggested as a new definition of actual causation.
Highlights
Two decades have passed since Judea Pearl’s groundbreaking book on causality was published [16]
We extend this genealogical terminology in the usual manner, by taking the ancestor relation to be the transitive closure of the parent relation (i.e., Y is an ancestor of X iff there exist variables so that Y is a parent of V1, V1 is a parent of V2, ..., and Vn is a parent of X)
We have shown that all twelve definitions we developed are instantiations of the General Definition of Causation (Def. 15), and thereby they improve upon Original HP and Updated HP as far as the first strategy goes
Summary
Two decades have passed since Judea Pearl’s groundbreaking book on causality was published [16]. Instead I offer what is the most natural route down the first strategy, namely to look at formalizations of causal sufficiency (as opposed to logical sufficiency) and combine them with two interpretations of necessity Taken together this results in twelve distinct formal definitions of actual causation. We use these six notions to formalize actual causation along the NESS intuition, and discuss several interesting results. After this theoretical groundwork, we start looking for the best definition.
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