Abstract The structural interpretation of counterfactuals as formulated in Balke and Pearl (1994a,b) [1, 2] excludes disjunctive conditionals, such as “had X $X$ been x1 or x2 $x_1~\mbox{or}~x_2$,” as well as disjunctive actions such as do(X=x1 or X=x2) $do(X=x_1~\mbox{or}~X=x_2)$. In contrast, the closest-world interpretation of counterfactuals (e.g. Lewis (1973a) [3]) assigns truth values to all counterfactual sentences, regardless of the logical form of the antecedent. This paper leverages “imaging” – a process of “mass-shifting” among possible worlds, to define disjunction in structural counterfactuals. We show that every imaging operation can be given an interpretation in terms of a stochastic policy in which agents choose actions with certain probabilities. This mapping, from the metaphysical to the physical, allows us to assess whether metaphysically-inspired extensions of interventional theories are warranted in a given decision making situation.

中文翻译：

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物理和形而上学的反事实：评估分离行为

摘要 Balke and Pearl (1994a,b) [1, 2] 中对反事实的结构解释排除了分离条件，例如“had X $X$ be x1 or x2 $x_1~\mbox{or}~x_2$, ”以及诸如 do(X=x1 或 X=x2) $do(X=x_1~\mbox{or}~X=x_2)$ 之类的析取动作。相比之下，反事实的最接近世界解释（例如 Lewis (1973a) [3]）将真值分配给所有反事实句子，而不管先行词的逻辑形式如何。本文利用“成像”——一种在可能世界之间“质量转移”的过程，来定义结构性反事实中的分离。我们表明，每个成像操作都可以根据随机策略给出解释，其中代理选择具有特定概率的动作。这种映射，从形而上学到物理，