含有预设关系语句的形式化

Improvements to the First-order Language Model

要赋予一阶谓词公式确定的含义,首先要确定个体域。个体域确定之后,个体变项的变化范围也就确定下来了,进而可给出个体常项、谓词符号的解释。个体域的确定、个体常项和谓词符号的解释构成了一阶语言的模型。事实上,受谓词的限制,个体变项的实际取值范围达不到个体域,只是个体域的子集,一旦超过实际取值范围,就会使语句发生句法错误。对个体变项实际取值范围的限制要靠预设得以实现。于是怎么把这种预设关系体现在形式语句中就是一个关键点了。

The first-order predicate formula to be given meaning,first of all,the individual domain needs determining.The individual domain determined,the range of variation of the individual variables is determined and the interpretation of the individual constants and the predicate symbols can be given.The determination of the individual domain and the interpretation of the individual constants and the predicate symbols constitute a model of the first-order language.In fact,due to the limitation of predicates,the actual value range of individual variables does not reach the individual domain,but only a subset of the individual domain.Once the actual value range is exceeded,the sentence will be syntactically wrong,and the actual value ranges of the different individual variables are not the same,which puts forward a new requirement for the first-order language model-to increase the interpretation of the actual value ranges of constraint variables.The limitation on the actual value range of individual variables depends on the presupposition,so how to put this transcendental relationship into the formal statement is a key point.