<p>Two types of explanations for the decisions made by classifiers have been studied extensively in the AI literature. The first type explains why a decision was made and is known as a sufficient reason for the decision. The second type explains how a decision can be changed and is known as a necessary reason for the decision. Earlier results showed that these two types of explanations correspond to two particular syntactic forms of the complete reason, which is a condition on the classifier’s input (i.e., instance) that is both sufficient and necessary for the decision. More recently, we showed that when non-binary features are present, a relaxation of the complete reason, called the general reason, contains more information about the decision and the underlying classifier and can be used to formulate explanations that generalize sufficient and necessary reasons. We provide a reconstruction and summary of these earlier results that is founded on viewing the complete and general reasons as “instance abstractions.” We also study the general-reason abstraction further, showing how it can provide information about decisions and classifiers beyond what was identified earlier. Our treatment will give rise to two pillars for modern work on explainability in AI: sufficient and necessary logical conditions which played a central role in certain formulations in philosophy, and minimized syntactic forms (of a condition) which have been developed mainly in computer science.</p>