亚里士多德模态三段论逻辑的形式化公理系统探讨  

On the Formal Axiomatic System for Aristotelian Modal Syllogism Logic

作　　者：张晓君[1] 袁娇娇 ZHANG Xiao-jun;YUAN Jiao-jiao(Institute of Logic and Information,Sichuan Normal University,Chengdu 610068,China)

机构地区：[1]四川师范大学逻辑与信息研究所,四川成都610068

出　　处：《湖南科技大学学报（社会科学版）》2019年第1期31-37,共7页Journal of Hunan University of Science and Technology(Social Science Edition)

基　　金：国家社会科学基金项目(16BZX081)

摘　　要：利用广义量词理论、可能世界语义学和集合论,可以简洁明了地对亚里士多德模态三段论进行形式化和有效性的证明。根据有效的亚里士多德模态三段论应该遵守的基本规则,可以从6 656个亚里士多德模态三段论中,筛选出有效的384个模态三段论。把通过向有效的直言三段论AAA-1和EAE-1中添加模态词而得到的20个有效模态三段论作为基础公理,就可以为亚里士多德模态三段论逻辑建立起形式化公理系统。By means of generalized quantifier theory,possible world semantics and set theory,it is possible to succinctly and explicitly formalize Aristotelian modal syllogisms and prove their validity. According to the basic rules for valid Aristotelian modal syllogisms,all of 384 valid modal syllogisms can be screened out from 6656 Aristotelian modal syllogisms. By using the 20 valid modal syllogisms obtained by adding modal operators to valid categorical syllogisms AAA-1 and EAE-1 as the basic axioms,a formal axiomatic system can be established for Aristotelian modal syllogism logic.

关 键 词：亚里士多德模态三段论 可能世界语义学 形式化 公理化 

分 类 号：B819[哲学宗教—逻辑学]