基于Barwise、Cooper、Keenan、Peters、Westerstahl和vanEijck等人的研究成果，作者提出并证明了若干事实和推论。这些事实和推论表明：（1）不同三段论之间的可化归性本质上反映了广义量词的单调性、对称性等语义性质之间的可转换性，因此，我们可以根据四个亚氏量词的语义性质之间的转换关系来验证亚氏三段论的可化归性；（2）利用广义量词的语义性质可以验证扩展三段论的不同推理模式之间的可化归关系。由于广义量词在自然语言中普遍存在，因此，本文的研究对广义量词理论的发展和自然语言的信息处理都具有积极意义。%This paper draws chiefly on the ideas and methods in Barwise & Cooper, Keenan and Peters & Westersthl, and van Eijck, among many others. It attempts not only to expand on but also to make novel proposals. Some new facts and corollaries proved in this paper. They bring to light the following relationships: (1) The reducibility of different syllogisms essentially reflects transformability of different semantic properties (such as monotonicity and symmetry and so on) of generalized quantifiers. Therefore, the reducibility of Aristotelian syllogisms can be verified by the transformable relations between semantic properties of four Aristotelian quantifiers; (2) The reducible relations of different extended syllogistic schemes can be verified by semantic properties of gener- alized quantifiers. We provide many instances of valid extended syllogisms in this paper. Since generalized quantiflers are ubiquitous in natural languages, the present study will make contributions to the development of generalized quantifier theory as well as bring- ing about consequences to natural language information processing.
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