如何根据AAA-1三段论推导出其余23个有效三段论  

How to Deduce the Remaining 23 Valid Syllogisms from the AAA-1 syllogism

作　　者：张晓君 ZHANG Xiao-jun(School of Philosophy,Anhui University,Hefei,Anhui230039,China)

机构地区：[1]安徽大学哲学学院,安徽合肥230039

出　　处：《贵州工程应用技术学院学报》2022年第1期48-53,共6页Journal of Guizhou University Of Engineering Science

基　　金：2018年国家社科基金重大项目“面向自然语言理解的逻辑构建和符号接地问题的哲学、心理学研究”,项目编号:18ZDA032。

摘　　要：在广义量词理论的基础上,充分利用直言命题具有Q(X, Z)这样的三分结构、亚氏量词的真值定义、亚氏量词的单调性与其三种否定量词单调性的可转换关系、亚氏量词no和some的对称性以及反三段论推理规则,仅仅把第一格AAA式三段论作为基础公理,就可以推导出其余23个有效的三段论,从而为亚氏三段论逻辑建立起极简的形式化公理系统。On the basis of generalized quantifier theory, this paper makes full use of the idea that the categorical proposition has the tripartite structure of Q(X, Z), the true value definition of Aristotelian quantifiers,the transformable relationship between the monotonicity of Aristotelian quantifiers and its three type negative quantifiers, the symmetry of Aristotelian quantifiers, no and some, and the reasoning rules of anti-syllogisms,only takes the first figure AAA syllogism(i.e. Barbara) as the basic axiom, the remaining 23 valid syllogisms can be deduced from it, thus can establish a minimalist formalized axiom system for traditional syllogism logic.

关 键 词：亚氏三段论 亚氏量词 公理化 单调性 对称性 

分 类 号：B81[哲学宗教—逻辑学]