摘要
一般认为卢卡锡维茨Ł_(3)系统中的排中律与(不)矛盾律都不成立,对此有许多不同解释。按照STRF理论的简化、等值与增力的“三合一”极致原则,在完全接受Ł_(3)句法和维持其已有语义的前提下,更深层次上“第三真值”这个逻辑常量其实是一个严格等价隐变量,也即“1/2”真其实是“真与并非真”的一种组合,但同一组合有不同排列,甚至同一个真值度存在不同的真值分布。显然由此可计算出Ł_(3)中的排中律与(不)矛盾律仍然都是定理,Ł_(3)当然是完全的,不过就是没被彻底认识的经典命题逻辑系统CP。
It is generally believed that the law of excluded middle and the law of(non)contradiction do not apply to the three valued logic systemŁ_(3)created by JanŁukasiewicz.Many different interpretations have been provided for this mystery.According to the“three-in-one”ultimate principle of simplification,equiva-lence and strengthening in the STRF theory and on the premise of fully accepting the syntax and maintaining the given semantics,the logical constant“third truth value”is actually a logical hidden variable at a deeper level.The third truth value“one-half true”in systemŁ_(3)is actually a combination of“true”and“non-true”.The combination has different arrangements,that is,there are different truth distributions for one degree of truth.It is obvious that the law of excluded middle and the law of(non)contradiction are still theorems within systemŁ_(3).SystemŁ_(3)is just a classical propositional logic system that has not been thoroughly and correctly understood.
作者
万小龙
徐亮
WAN Xiaolong;XU Liang
出处
《安徽大学学报（哲学社会科学版）》
CSSCI
北大核心
2022年第5期32-40,共9页
Journal of Anhui University(Philosophy and Social Sciences Edition)
基金
电子科技大学“杰出人才”基金“量子信息与逻辑的哲学研究”(A1098531023601302)。
关键词
Ł_(3)系统
排中律
(不)矛盾律
最低限度语义隐变量
systemŁ_(3)
the law of excluded middle
the law of(non)contradiction
minimal semantic hidden variable
