二值命题逻辑中逻辑方程τ(A→X)=m/2~n解集的结构

Solution Set Structure for the Logic Equation τ(A→X)=m/2~n in Two-valued Propositional Logic

二值命题逻辑中τ(A→X)=α型逻辑方程在有限理论结论集的结构以及近似推理研究中有着重要应用。给出了二值命题逻辑中公式是逻辑方程τ(A→X)=m2n解的几个充要条件,得到了该逻辑方程的解集分别按真度相等关系和逻辑等价关系的分类定理,并给出了逻辑方程解集中公式的伪距离上确界的数值表示,为进一步研究此类逻辑方程的解集提供了结构性方法。

In the two-valued propositional logic system, the type of τ（A→x）=m/2^=a logic equation plays an important role in the study of the structure of conclusion set in finite theory, as well as the approximate reasoning. In this paper, we obtain some necessary and sufficient conditions which can judge whether or not the formula in the two-valued propositional logic is the solution of the logic equation τ（A→x）=m/2^n= . We also get the classification theorem of the logic equation＇s solution set described above according to the equivalence of the truth degree and logical equivalence respectively. Meanwhile, we discuss the numerical representation of the supreme of formula＇s pseudo metric in the solution set of logic equation which can supply some useful structural methods for further study of the solution set above-mentioned.