基于量词语义与性质的扩展三段论

Extended Categorical Syllogism based on Semantic and Nature of Binary Quantifiers

在广义量词理论中,如果一个表达两个集合外延关系的二元量词具有单调性等性质,那么该量词及其外否定、内否定和对偶否定在单调性方面存在相互制约关系,从而构成单调方阵。基于二元量词的语义和单调性等性质,可以简洁明了地进行包括传统三段论在内的扩展三段论推理,从而极大地提高了三段论的表达能力和对日常思维的规范能力。

In theory of general quantifier, a quantifier Q of type 〈1,1〉 associates with each universe M a binary relation Q between subsets of M. Every such quantifier spans a square of opposition about the monotonicity of general quantifier. The extended categorical syllogism,including traditional syllogism are based on the nature of the quantifier Q, such as directional distribution. Moreover,the validities of the large number of reasoning outside the traditional syllogism can be decided easily.Thereby,It greatly enhance the logical expressive,as well as the ability to regulate the daily thinking, including legal thinking.