摘要
引入了平衡逻辑公式的概念,证明了和一个平衡逻辑公式等价的逻辑公式是平衡逻辑公式。并且n元平衡逻辑公式中等价类关于→,∨,∧,→运算封闭,等价类之集[A](A是n元平衡逻辑公式)关于包含序在∨,∧下构成一个格。证明了n元平衡逻辑公式只占全体n元逻辑公式的很小一部分,其比例随n的增大而趋向于零。其次,n元平衡逻辑公式的真度总是等于1/2,任一n元平衡逻辑公式的任意小的邻域内都有非平衡逻辑公式,但是这些公式的真度随n的增大而趋向于1/2。最后,给出了平衡逻辑公式的表示定理。
The present paper introduces the concepts of equilibrium logic formulas, and proves that any formula equivalent to an equilibrium one is still an equilibrium formula. The set of all equilibrium formulas with n variables is closed under the operations -, V ,/k and this set constitutes a lattice w. r.t. V , A. It is also inferred that the partion of equilibrium formulas with n variables in all formulas limits to 0 as 1 n goes to infinity. Meanwhile, the truth degrees of equilibrium formulas always equal y, and there exist 1 many nonquilibrium formulas , whose truth degree limits to 1/2 as n goes to infinity, in arbitrarily small neighberhood of any equilibrium formula. Lastly, the representation theorem for equilibrium formulas is obtained in this paper.
出处
《模糊系统与数学》
CSCD
北大核心
2013年第1期55-62,共8页
Fuzzy Systems and Mathematics
基金
国家自然科学基金重点资助项目(11171200)
陕西省科技厅国际合作重点项目(2012KW-03-01)
关键词
平衡布尔函数
平衡逻辑公式
逻辑度量空间
真度
逻辑等价
Equilibrium Boolean Function Equilibrium Logic Formulas
Logic Metric Space Truth DegreeLogical Equivalence
