联合演算对传统词项逻辑的等价描述

Uniting Calculation Equivalence Description to the Traditional Lexical Logic

希尔柏特和阿克曼并没有解决传统性质判断及其构成的推理式在联合演算中的等价表述问题,而克劳斯对传统推论的理解和翻译则有更大的偏差。一个能够刻画所有传统推理式的统一的模式,必须同时限之以主项非空类,谓项非全类。在这一模式下,传统直言判断的逻辑方阵在联合演算中可以找到等价的描述,不仅如此,传统词项逻辑的所有有效式在联合演算中无一例外地是永真式,而传统词项逻辑的所有无效式在联合演算中无一例外地是永假式。传统意义上翻译的传统推论表明,传统词项逻辑在其自身所把握的范围内是封闭的和完备的,但一旦超出这一范围,即扩展为现代意义上的,就不再是一个严密的体系。

Hilbert and Ackermann have not solved the problem of traditional nature judgment and its inference equivalence description in uniting calculation.Furthermore,Claus's translation to the traditional deduction has a bigger deviation.The subject with non-empty and the predicate with non-entire will limit the pattern that can portray all traditional inference.According to the pattern,the traditional judgment logic phalanx may find out the equivalence description in uniting calculation.In addition,all efficient formulas of traditional lexical logic become the external true formula without exception,and the inefficient become the external false.The traditional deduction indicates that traditional lexical logic is closed and complete in its own scope,otherwise it will not be a strict system any longer.