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In the quest for Explainable Artificial Intelligence (XAI) one of thequestions that frequently arises given a decision made by an AI system is,``why was the decision made in this way?'' Formal approaches to explainabilitybuild a formal model of the AI system and use this to reason about theproperties of the system. Given a set of feature values for an instance to beexplained, and a resulting decision, a formal abductive explanation is a set offeatures, such that if they take the given value will always lead to the samedecision. This explanation is useful, it shows that only some features wereused in making the final decision. But it is narrow, it only shows that if theselected features take their given values the decision is unchanged. It'spossible that some features may change values and still lead to the samedecision. In this paper we formally define inflated explanations which is a setof features, and for each feature of set of values (always including the valueof the instance being explained), such that the decision will remain unchanged.Inflated explanations are more informative than abductive explanations sincee.g they allow us to see if the exact value of a feature is important, or itcould be any nearby value. Overall they allow us to better understand the roleof each feature in the decision. We show that we can compute inflatedexplanations for not that much greater cost than abductive explanations, andthat we can extend duality results for abductive explanations also to inflatedexplanations.

Delivering Inflated Explanations