Syllogistic reasoning in fuzzy logic and its application to usuality and reasoning with dispositions

A fuzzy syllogism in fuzzy logic is defined to be an inference schema in which the major premise, the minor premise and the conclusion are propositions containing fuzzy quantifiers. A basic fuzzy syllogism in fuzzy logic is the intersection/product syllogism. Several other basic syllogisms are developed that may be employed as rules of combination of evidence in expert systems. Among these is the consequent conjunction syllogism. Furthermore, we show that syllogistic reasoning in fuzzy logic provides a basis for reasoning with dispositions; that is, with propositions that are preponderantly but not necessarily always true. It is also shown that the concept of dispositionality is closely related to the notion of usuality and serves as a basis for what might be called a theory of usuality — a theory which may eventually provide a computational framework for commonsense reasoning.