摘要
以合舍作为唯一初始联结词,在括号表示法中,只需要使用一对左右括号“「」”就可以无歧义地表达所有的逻辑函数,并进而建立包括括号“「」”的引入规则和消去规则在内的自然推演系统NPD1,可以证明该系统与通常的命题逻辑推理系统相等价。通过定义可以给出常见的其他联结词并证明相关定理。受亚里士多德化归思想的启发,构建了系统NPD1的7组化归规则,并给出化归程序;依据此程序,可以将系统内的任一定理能行地化归为一个形如<A(A)>的公式。
In the parenthesis notation,with joint denial as the only primitive connective,all that needed is a pair of parenthesis“「」”to express unambiguously all the logical functions,and then the natural deduction system NPD1 including the introduction and elimination rules of the parenthesis“「」”is set up.It can be proved that NPD1 is equivalent to the usual propositional logic deduction system.Other common connectives can be provided through definition and related theorems can be proved.Inspired by Aristotle’s idea of reduction,7 sets of reduction rules of system NPD1 are constructed and a reduction process is provided.Any theorem of the system can be effectively reduced to a formula in the form of<A(A)>according to this process.
作者
杜国平
DU Guoping(Institute of Philosophy, Chinese Academy of Social Sciences, Beijing 100732, China)
出处
《重庆理工大学学报（社会科学）》
2021年第6期53-61,共9页
Journal of Chongqing University of Technology（Social Science）
基金
中国社会科学院创新工程项目“人工智能重大哲学问题研究”(2021ZXSCXB04)。
关键词
括号表示法
合舍
化归
证明
能行
parenthesis notation
joint denial
reduction
proof
effectively
