From Causal Models To Counterfactual Structures

Counterfactual reasoning arises in broad array of fields, from statistics to economics to law. Not surprisingly, there has been a great deal of work on giving semantics to counterfactuals. Perhaps the best-known approach is due to Lewis [1973] and Stalnaker [1968], and involves possible worlds. The idea is that a counterfactual of the form "ifAwere the case thenB would be the case", typically written A B, is true at a worldwifB is true at all the worlds closest tow whereAis true. Of course, making this precise requires having some notion of "closeness" among worlds. More recently, Pearl [2000] proposed the use of causal models based on structural equations for reasoning about causality. In causal models, we can examine the effect of interventions, and answer questions of the form "if random variable X were set to x, what would the value of random variable Y be". This suggests that causal models can also provide semantics for (at least some) counterfactuals. The relationship between the semantics of counterfactuals in causal models and in counterfactual structures (i.e., possible-worlds structures where the semantics of counterfactuals is given in terms of A preliminary version of this paper appears in the Proceedings of the Twelfth International Conference on Principles of Knowledge Representation and Reasoning (KR 2010), 2010.