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The rise of AI methods to make predictions and decisions has led to apressing need for more explainable artificial intelligence (XAI) methods. Onecommon approach for XAI is to produce a post-hoc explanation, explaining why ablack box ML model made a certain prediction. Formal approaches to post-hocexplanations provide succinct reasons for why a prediction was made, as well aswhy not another prediction was made. But these approaches assume that featuresare independent and uniformly distributed. While this means that "why"explanations are correct, they may be longer than required. It also means the"why not" explanations may be suspect as the counterexamples they rely on maynot be meaningful. In this paper, we show how one can apply backgroundknowledge to give more succinct "why" formal explanations, that are presumablyeasier to interpret by humans, and give more accurate "why not" explanations.In addition, we show how to use existing rule induction techniques toefficiently extract background information from a dataset, and also how toreport which background information was used to make an explanation, allowing ahuman to examine it if they doubt the correctness of the explanation.

Eliminating The Impossible, Whatever Remains Must Be True