基于广义量词理论的亚氏三段论

Research on Aristotelian Syllogisms Based on Generalized Quantifier Theory

揭示了如何从广义量词理论的角度来理解三段论推理。有效的亚氏三段论可以通过作为广义量词特例的亚氏量词的语义定义加以证明。从亚氏量词的语义性质,比如单调性、对称性可以说明亚氏三段论的有效性。亚氏三段论的可化归性反映了亚氏量词与其三种否定量词的语义性质(比如单调性)之间的可转换性。

This paper aims to show how our understanding of syllogistic reasoning may benefit from research on generalized quantifier theory. Valid Aristotelian syllogisms can be proved by semantic definition of Aristotelian quantifiers which are instances of generalized quantifiers, and they can be illustrated from properties of Aristotelian quantifiers, such as montonicity and symmetry. Reducibility be- tween/among syllogisms reflects to transformability between/among the semantic properties （such as monotonicity） of Aristotelian quantifiers and that of their three types of negation. It is hoped that this study will make contributions to the development of generalized quantifier theory, and will inject new vitality for knowledge representation and reasoning in computer science.