基于广义量词理论的亚氏三段论逻辑的公理化  

Axiomatization of Aristotelian Syllogistic Logic based on Generalized Quantifier Theory

作　　者：李慧[1] 张呈 LI Hui;ZHANG Cheng(School of Philosophy,Anhui University,Hefei 230039,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》2023年第4期77-86,共10页Journal of Guizhou University Of Engineering Science

基　　金：2022年国家社科基金后期项目“面向人工智能的信念-愿望-意图逻辑的哲学基础及其前沿问题研究”,项目编号:22FZXB092。

摘　　要：仅仅以EIO-3亚氏三段论为基础公理,利用亚氏量词的三种否定量词的定义、亚氏量词no和some的对称性、多个命题推理规则,就可以给出亚氏三段论逻辑直观明了的形式化公理系统;利用典范模型的方法,就可以较为简洁地证明其完全性和可靠性,从而大大简化了之前完全性和可靠性的证明。这一创新研究不仅而且有助于人工智能中的知识表示和知识推理,而且有助于亚氏三段论逻辑的进一步发展。Only taking EIO-3 syllogism as the basic axiom,and making use of the definition of three negative quantifiers of Aristotelian quantifiers,the symmetry of Aristotelian quantifiers“no”and“some”,and several propositional reasoning rules,one can give the intuitive and clear formal axiomatic system for Aristotelian syllogistic logic.Moreover,by using the method of canonical model,one can prove its completeness and soundness more concisely,which greatly simplifies the previous proofs of completeness and soundness.This innovative research not only contributes to knowledge representation and knowledge reasoning in artificial intelligence,but also contributes to the further development of Aristotelian syllogistic logic.

关 键 词：亚氏三段论 公理 亚氏量词 规则 

分 类 号：B81[哲学宗教—逻辑学]