基于广义量词单调性的广义三段论的有效性

The Validity of Generalized Syllogism Based on the Monotonicity of Generalized Quantifiers

随着广义量词理论的兴起和发展,逻辑学家们开始研究比传统三段论更为复杂的广义三段论及其有效性。在广义量词单调性的基础上,给出十二个有效的广义三段论推理模式及其相应的有效的广义三段论实例,重点研究可以表征这十二个有效的广义三段论推理模式之间的可化归关系的四个推论。研究不仅说明了利用广义量词的单调性等语义性质可判定广义三段论的有效性,而且还说明了广义三段论的有效性,也表征了广义量词的单调性质等语义性质。

With thedevelopment of generalized quantifier theory, logicians began to study the validity of generalized syllogisms, which are more complex than traditional syllogisms. Based on the monotonicity of gen. eralized quantifiers and two propositional transformation rules, this paperfirstly gives 12 valid generalized syl. logistic reasoning modes and their corresponding valid examples of generalized syllogisms, and then presents four corollaries that can characterize the reducibility relationship between these 12 valid generalized syllogis. tic reasoning modes. It not only shows that the validity ofgeneralized syllogisms can be judged by the monoto. nicity of generalized quantifiers, but also shows that the validity of generalized syllogisms is characterized by its semantic properties such as the monotonicity of generalized quantifiers.