基本Łukasiewicz m-值条件句逻辑  

BasicŁukasiewicz m-valued Conditional Logics

作　　者：霍书全[1] Shuquan Huo

机构地区：[1]河南大学哲学与公共管理学院

出　　处：《逻辑学研究》2024年第5期1-20,共20页Studies in Logic

基　　金：国家社会科学基金重大项目“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”(18ZDA032)。

摘　　要：经典条件句逻辑被广泛地研究过,近几年,一些非经典的条件句逻辑也开始出现。多值逻辑承认命题可以取多个真值,具有容错能力,其蕴涵词和经典蕴涵词类似,同样可以刻画条件句,因此我们也应该有多值逻辑条件句逻辑。本文将基于Łukasiewicz m-值命题逻辑构建基本条件句逻辑系统ŁCK和ŁCK2,证明这些系统的可靠性、完全性和有穷模型性质。最后把ŁCK推广到无穷值情形。Classical conditional logic has been studied extensively.In recent years,some nonclassical conditional logic has also appeared.Many-valued logic admits that propositions can take many truth values,has fault-tolerant ability,its implication word is similar to the classical implication word,and can also describe conditionals sentence,so we should have many-valued conditional logic.In this paper,we will construct the basic conditional logic systemsŁCK andŁCK2 based onŁukasiewicz m-valued propositional logic,and prove the reliability,completeness,and finite model properties of these systems.Finally we generalizeŁCK to the infinite-valued case.

关 键 词：基本条件句逻辑 Łukasiewicz m-值逻辑 多值模态逻辑 Kripke语义 

分 类 号：B81[哲学宗教—逻辑学]