Qualitative conditionals of the form “If A, then usually B” are often used to model nonmonotonic inference relations. Evaluating conditionals as three valued logical objects, allows for a classification of all conditionals over a given propositional signature. These classes of conditionals and their properties in terms of nonmonotonic inference are useful for the task of calculating the closures of concrete nonmonotonic inference relations. In this paper, we present a rigorous classification of conditionals in terms of semantic properties. We also present and evaluate an approach for calculating closures of inference relations by exploiting our classification of conditionals. We discuss the usefulness of the availability of the complete closure of inference relations by using the results of our approach to systematically evaluate several inference relations with respect to postulates proposed for nonmonotonic inference relations.

“如果是A，那么通常为B”形式的定性条件条件通常用于建模非单调推理关系。将条件语句评估为三个有价值的逻辑对象，可以对给定命题签名上的所有条件语句进行分类。这些类别的条件及其在非单调推断方面的性质对于计算具体非单调推断关系的闭合性很有用。在本文中，我们针对语义属性提出了严格的条件分类。我们还提出并评估一种通过利用我们的条件分类来计算推断关系闭合的方法。