In the quest for Explainable Artificial Intelligence (XAI) one of the questions that frequently arises given a decision made by an AI system is, ``why was the decision made in this way?'' Formal approaches to explainability build a formal model of the AI system and use this to reason about the properties of the system. Given a set of feature values for an instance to be explained, and a resulting decision, a formal abductive explanation is a set of features, such that if they take the given value will always lead to the same decision. This explanation is useful, it shows that only some features were used in making the final decision. But it is narrow, it only shows that if the selected features take their given values the decision is unchanged. It's possible that some features may change values and still lead to the same decision. In this paper we formally define inflated explanations which is a set of features, and for each feature of set of values (always including the value of the instance being explained), such that the decision will remain unchanged. Inflated explanations are more informative than abductive explanations since e.g they allow us to see if the exact value of a feature is important, or it could be any nearby value. Overall they allow us to better understand the role of each feature in the decision. We show that we can compute inflated explanations for not that much greater cost than abductive explanations, and that we can extend duality results for abductive explanations also to inflated explanations.

翻译：在可解释人工智能（XAI）的研究中，针对AI系统做出的决策，一个常见的问题是：“为何以这种方式做出决策？”形式的可解释性方法通过构建AI系统的形式化模型，并利用它来推理系统的属性。给定被解释实例的一组特征值及其对应的决策结果，形式化的溯因解释是一组特征，使得当这些特征取给定值时，始终会导致相同的决策结果。这种解释很有用，它表明只有部分特征参与了最终决策的制定。但它也有局限性：它仅表明当所选特征取给定值时，决策结果不会改变。实际上，某些特征的值可能发生变化，但仍然会导致相同的决策结果。本文正式定义了“膨胀解释”，它是一组特征，且对于每个特征，给定一组可能的值（始终包含被解释实例的对应值），使得决策结果保持不变。膨胀解释比溯因解释信息量更丰富，例如，它们可以让我们观察特征的精确值是否重要，还是任何邻近的值都可以接受。总之，它们能帮助我们更好地理解每个特征在决策中的作用。我们证明，计算膨胀解释的额外成本并不比计算溯因解释高太多，并且可以将溯因解释的对偶性结果扩展到膨胀解释。