二值命题逻辑中有限理论的相对偏差及其应用

The Relative Deviation of Finite Theory and Its Applications in Two-valued Propositional Logic

理论的相对偏差是确定近似推理误差的逻辑度量之一,由于缺乏与理论特征相关联的真度表示,而导致其计算和应用上的不便.以公式真度为基础,给出了二值命题逻辑系统中有限理论相对偏差的真度表示式以及公式是有限理论的Ⅲ-型误差不大于ε结论的判定条件,并证明了有限理论的Ⅰ,Ⅱ,Ⅲ-型误差不大于ε的结论的等价性以及基于蕴涵真度的三种近似推理模式的等价性.

Relative deviation in the theory is one of the logical measurements which can identify the error of finite theory. Unfortunately, the shortage of the truth degree expressions which are related to the characteristics of theories could lead to be inconvenient, especially in the calculation and application. Based on the truth degree of formula in two--valued propositional logic, we get the truth degree expression of relative deviation in finite theory and obtain the determination criterion of formula for the Ⅲ --typical error of less than ε. Meanwhile we prove the equivalence of the conclusions for the Ⅰ , Ⅱ , Ⅲ --typical errors of less thane. And hence, we also testify the equivalence of the three approximate reasoning modes which are resulted from the implication truth degree.