Modifications of the Miller definition of contrastive (counterfactual) explanations

TL;DR

This paper examines and improves upon Miller's contrastive explanation definition by addressing issues inherited from the original and modified Halpern-Pearl definitions, proposing more robust variants that retain core principles.

Contribution

It introduces two new variants of Miller's contrastive explanation definition based on modified HP and Borner definitions, improving robustness and consistency.

Findings

The original Miller definition inherits issues from the original HP definition.

The proposed variants address these issues and are more robust.

All variants satisfy a unified, modular explanation framework.

Abstract

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.