Gradual inference rules in approximate reasoning

Abstract Gradual inference rules of the form “The more X is F , the more Y is G ” (or of similar forms with “the less” instead of “the more”), which express a progressive change of the degree to which the entity Y satisfies the gradual property G when the degree to which the entity X satisfies the gradual property F is modified, are often encountered in commonsense reasoning. A representation of such rules by means of fuzzy sets is proposed and discussed. This representation turns out to be based on a special implication function already considered in multiple-valued logic. Patterns of reasoning involving gradual inference rules are formalized. Their links with interpolation mechanisms are pointed out.