逻辑方程解的性质

The Properies of Logic Equation

以二值命题逻辑的真度理论为基础,提出了基于真度理论的逻辑方程的概念,并给出了此种逻辑方程解的存在性定理,并就τ(A→X)=α的逻辑方程展开了讨论,其中,A是含有n个原子公式的合式公式,X是待定的公式,A的真度τ(A)=2kn,α=2mn,且1-τ(A)<α≤1。我们得到了如下结论:(1)以上逻辑方程的解的等价类个数为Cmk+k-2n.22n-k。(2)α≠1时,上述方程的解集合是不相容的。(3)解集合中公式的相似度最大值为1-21n,相似度的最小值为2n+1-2 2nm-k。(4)形如τ((A→X)∧(X→A))=α的逻辑方程其解集合是不相容的。

Based on the theory of the truth degree of proposition logic, the properies of the logic equations which it forms is （A →X） = α were discussed, where A is the given formula contain n previous formulas,x is unknow, the truth degree of A, τ（A）=k/2^n,α=m/2^2,and 1-τ（A）〈α≤1 We get the following results, （1） the number of classicifition of the solution of the above logic equations is （2）when α≠1, the solution set of the above logic equations is inconsistence. （3）The max value of thesimilary degree of the solution set is 1 -1/2^n,The min value of the similary degree of the solution set is ｜2^n＋1-2m-k＋/2^n. （4）The set of the solutions of the equivation likes r （（A→X） ∧ （X→A）） = α is not consistent.