Semantic classification of qualitative conditionals and calculating closures of nonmonotonic inference relations

Abstract

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.