Miller recently proposed a definition of contrastive (counterfactual) explanations based on the well-known Halpern-Pearl (HP) definitions of causes and (non-contrastive) explanations. Crucially, the Miller definition was based on the original HP definition of explanations, but this has since been modified by Halpern; presumably because the original yields counterintuitive results in many standard examples. More recently Borner has proposed a third definition, observing that this modified HP definition may also yield counterintuitive results. In this paper we show that the Miller definition inherits issues found in the original HP definition. We address these issues by proposing two improved variants based on the more robust modified HP and Borner definitions. We analyse our new definitions and show that they retain the spirit of the Miller definition where all three variants satisfy an alternative unified definition that is modular with respect to an underlying definition of non-contrastive explanations. To the best of our knowledge this paper also provides the first explicit comparison between the original and modified HP definitions.

该研究提出了三种定义对比解释及其效果的方法，并提供了第一次对原始和修改后的HP定义进行明确比较的研究。

对米勒对比（反事实）解释定义的修改