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Motivated by distinct, though related, criteria, a growing number of attribution methods have been developed tointerprete deep learning. While each relies on the interpretability of the concept of "importance" and our ability to visualize patterns, explanations produced by the methods often differ. As a result, input attribution for vision models fail to provide any level of human understanding of model behaviour. In this work we expand the foundationsof human-understandable concepts with which attributionscan be interpreted beyond "importance" and its visualization; we incorporate the logical concepts of necessity andsufficiency, and the concept of proportionality. We definemetrics to represent these concepts as quantitative aspectsof an attribution. This allows us to compare attributionsproduced by different methods and interpret them in novelways: to what extent does this attribution (or this method)represent the necessity or sufficiency of the highlighted inputs, and to what extent is it proportional? We evaluate our measures on a collection of methods explaining convolutional neural networks (CNN) for image classification. We conclude that some attribution methods are more appropriate for interpretation in terms of necessity while others are in terms of sufficiency, while no method is always the most appropriate in terms of both.