关于“不用联结词的逻辑系统”的注记

A note on “logical systems without connectives”

张清宇先生在20世纪90年代创建了不用联结词的逻辑系统,在其中使用括号表达命题联结词和量词的功能,这是一项逻辑符号技术的创新性工作。波兰表示法和括号表示法是逻辑符号表示法的两个相互映衬的典范。在括号表示法中,"不用联结词"指的仅仅是语形层面上的,而不是语义层面上的。基于括号表示法的命题逻辑公理系统H和一阶逻辑系统QH都可以进一步简化。

In the 1990s,Mr. Zhang Qingyu created a logical system without connectives,in which parentheses were used to express the functions of propositional connectives and quantifiers,which is an innovative work of logical symbol technology. Polish notation and parenthesis notation are two mutually complementary examples of logical symbolic notation. In the parenthetical notation,“without connectives” refers only to morphological level rather than semantic level. Both the axiom system H of propositional logic and the first-order logic system QH based on parenthesis notation can all be further simplified.