An analysis of reasoning with quantifiers within the Aristotelian syllogistic framework

In this paper, the Aristotelian approach is proposed as an adequate framework for analyzing, categorizing and reviewing the fuzzy models for syllogistic reasoning proposed in the literature. From the analysis performed it is concluded that Zadeh and Yager´s models present an incompatible structure with Aristotelian syllogistics although they can be considered as an alternative approach to syllogistic reasoning. Dubois and Prade´s, nevertheless, develop an approach that is compatible with the Aristotelian framework. Although none of the revised proposals are genuinely fuzzy, the latter can be considered as an starting point to build an extension of the Aristotelian system to the fuzzy field.