论文标题
通过求解二次函数方程的系统来计算命题逻辑中的重态性密度
Computing the density of tautologies in propositional logic by solving system of quadratic equations of generating functions
论文作者
论文摘要
在本文中，我们将提供一种方法来计算由$ m $变量，否定符号和含义符号组成的良好公式之间的重言式密度；它有可能应用于其他逻辑系统。本文包含两个，三个和四个可变情况的重言式密度的计算数值。此外，对于某些二次系统，我们将建立一个$ s $ cut概念的理论，以在我们通过蛮力计数计算比率时进行记忆时间进行权衡，并发现在奇异点上产生函数的值和系数比率之间的基本关系，这可以理解为Szeg®系统的另一种解释。通过这种关系，我们将提供一个渐近下限的$ m^{ - 1} - （7/4）m^{ - 3/2}+o（m $ m $变量，否定，$ m $，$ m $变量，
In this paper, we will provide a method to compute the density of tautologies among the set of well-formed formulae consisting of $m$ variables, the negation symbol and the implication symbol; which has a possibility to be applied for other logical systems. This paper contains computational numerical values of the density of tautologies for two, three, and four variable cases. Also, for certain quadratic systems, we will build a theory of the $s$-cut concept to make a memory-time trade-off when we compute the ratio by brute-force counting, and discover a fundamental relation between generating functions' values on the singularity point and ratios of coefficients, which can be understood as another interpretation of the Szegő lemma for such quadratic systems. With this relation, we will provide an asymptotic lower bound $m^{-1}-(7/4)m^{-3/2}+O(m^{-2})$ of the density of tautologies in the logic system with $m$ variables, the negation, and the implication, as $m$ goes to the infinity
