A Proposal of Fuzzy Chained Syllogism based on the Concept of Synonymy

Syllogistic reasoning is a type of inference pattern that involves quantified statements through the chaining of two terms by a middle term. In its classical version, only classical crisp quantifiers (all, no, some and some…not) and crisp sets in the terms are considered. If the syllogism involves vagueness, this can appear in the quantifiers (fuzzy quantifiers) or in the terms. The case of the vagueness in the quantification is analysed in Fuzzy Logic under the label of fuzzy syllogism but vagueness in the terms was not approached before now in the same depth. In this paper, we study this kind of syllogism and make a proposal for qualifying the conclusion by a degree of confidence that depends on the degree of similarity between the middle terms.