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

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.