布尔逻辑

Finally, the equivalence properties between Boolean matrix representation and algebra representation of attribute reduction are proved.

建立了布尔矩阵与逻辑方程组的解和决策表中的属性集之间的关系；然后在此基础上给出了决策表中的粗糙集理论的布尔矩阵表示；最后证明了属性约简在布尔矩阵和代数两种不同表示下是等价的。

Using the theories of probability, algebra and spectral theory comprehensively, we investigate some related characteristics of logic functions in cryptography: Firstly, we introduce m order generalized s - correlation immunity of Boolean vector functions and prove that the higher order generalized ε- correlation immunity can guarantee the lower order generalized ε- correlation immunity. Then by applying decomposition formula of joint distribution of Boolean random vectors, we give a spectrum criterion of m order generalized e - correlation immunity of Boolean vector functions. Furthermore, we show that the algebraic degree of m order generalized e - correlation immune Boolean vector functions is not restricted by the correlation immune orders.

本文主要运用概率论的思想和方法，并结合代数学和频谱理论的相关知识，对密码学中逻辑函数的有关性质进行了研究，主要包括以下三个方面的内容：首先，对布尔向量函数的相关免疫性进行了拓展，给出了k维布尔向量函数m阶广义ε-相关免疫的概念，证明了布尔向量函数的高阶广义ε-相关免疫性蕴含低阶广义ε-相关免疫性，并根据布尔随机向量联合分布分解式得到了布尔向量函数m阶广义ε-相关免疫的一个谱判别条件，还说明了m阶广义ε-相关免疫布尔向量函数的代数次数不受相关免疫阶数的制约。

The course contains four sections as follows: mathematical logic (including basic concepts of propositional logic and predicate logic, propositional calculuses and inference theories), set theory (including set algebras, relations, functions and cardinal numbers), algebraic structure (including algebraic systems, semigroups and groups, rings and fields, lattices and Boolean algebras), graph theory (including basic concepts of graph, Euler graphs and Hamiltonian graphs, trees, planar graphs and coloring graphs, some special vertex subsets and edge subsets).

本课程包含四部分内容：数理逻辑（包含命题逻辑与一阶逻辑的基本概念、等值演算以及推理理论），集合论（包含集合代数、二元关系、函数和基数），代数结构（包含代数系统、半群与群、环与域、格与布尔代数），图论（包含图的基本概念、欧拉图与哈密顿图、树、平面图及图的着色、图的某些特殊的顶点子集与边子集）。

Discuss the relationship between fuzzy logic and probabilistic logic by comparing PL with the fuzzy logic based on distributive lattice with a boundary element and make clear some indiscriminations about this problem.

7给出值域为布尔代数的格值逻辑的概率解释；相对于值域为含分界元分配格的模糊逻辑作比较，讨论了模糊逻辑和概率逻辑的密切关系和根本区别，并据此澄清了逻辑文献中关于这一问题的某些混淆。

The LVC32A device performs the Boolean function Y = A + B or Y = A B in positive logic.

该LVC32A设备执行了积极的布尔逻辑函数Y =甲+乙或Y = AB公司。

Finally,a simplified case of BOFL,i.e.Boolean Operator Propositional Logicestablished on a Boolean algebra,is further discussed.A complete algorithmfor finding the true level and false level of a formula in BOPL,which subsumes the re-lated work by Wang H.in the propositional logic,is also provided.

对布尔算子模糊逻辑的简化情形一布尔算子命题逻辑作了进一步讨论，放宽了对真值域的要求，将布尔算子命题逻辑建立在布尔代数上，并推广了命题逻辑中的王浩算法，给出了一个完备的求给定公式恒真水平和恒假水平的机械推导算法。

And computer systems is much stronger. There is a one-to-one relationship between bool

但是布尔逻辑和计算机系统之间的关系却是很强的。

Boolean Logic is named after the 19th century mathematician, George Boole.

布尔逻辑以 19 世纪数学家 George Boole 的名字命名。

4Looking for the contents with keywords according to the Boole logic languages rules.

4按照布尔逻辑语言规则输入关键词搜索所需学习内容。

Mr Derbyshire, whose bookhas just been published in Britain after appearing in America last year, givesan intriguing account of these developments, and of the mathematiciansinvolved, such as George Boole, who "married algebra to logic" by inventingalgebraic ways to express logical arguments: he led an almost saintly life, butdied after his wife treated him for a chill by dousing him in buckets of icywater.

德比夏尔的这本书去年在美国出版，紧接着现在又在英国上市。书中对代数学的发展和历史上的数学家做了生动有趣的描述。例如乔治·布尔，他把&代数嫁给了逻辑&，用代数的方式表达逻辑参数。乔治·布尔一生圣洁，但是却死于他妻子淋头而下的冰水所致的风寒。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。