一阶逻辑公式相对真度的计算形式

摘要

The simplified computational definition of the relative satisfiability degrees of first-order formulae in a finite interpretation is proposed. It is pointed out that the relative satisfiability degree of a nonclosed first-order formula is just related to the free-occurred variables in the formula, not the free variables occurred in the formula;and it is proved that the relative satisfiability degree of a first-order formula can be unchanged although the amount of the variables occurring in the formula is increased, so that the matter of the relative satisfiablity degrees among formulae can be transversely studied according to the computational definition of the relative satisfiability degrees of first-order formulae.%对二值谓词逻辑中一阶公式关于有限解释的相对真度定义进行了简化，给出其计算形式。指出一阶非闭逻辑公式的相对真度只与其中自由出现的变元有关，而非只与其中的自由变元有关；证明可以增加公式中出现的变元个数，而不会改变公式的相对真度，从而可以依据相对真度的计算形式横向研究公式间的相对真度问题。