逻辑运算

A new network routing algorithm is proposed, which follows calculation rues of logic algebra and calculates routes with depression of order transformation of incidence martrix. For network with m nodes, m-2 times depression of order transformation operations can get all routes between two nodes. Furthermore, it accords with the communication transmission rules and avoids the close loop routes.

提出一种网络路由新算法，是按照逻辑代数运算规则，以关联矩阵降阶变换方式计算，对于有m个节点的网络，只需m-2次距阵降阶变换运算，就能够算得网络两节点间全部路由，且不会出现闭环路由问题，完全符合通信传输规则。

As for the second, logic can indeed be grounded in a symmetrical combining operation, but that operation is analogous to either of addition or multiplication.

至于第二点，逻辑的确是以对称结合运算为基础的，但这样的运算类似于加法或乘法。

From the viewpoint of axial symmetry or centrosymmetry between t and t in logic, this paper makes a minute analysis about the negation operation under different conditions in 1-order uncertainty, puts forward negation operation axiom, and does a systematic research on the definition, properties, and generation of negation operation.

从t与t在逻辑上具有轴对称性或中心对称性出发，详细分析了1阶不确定性中不同条件下的非运算，提出了"非"运算公理，系统研究了"非"运算的定义、性质和构造。

That is,the truth value of an implication compound proposition is just the compatibleness degree of the actual implication degree or implication rate between its sub-propositions with the language value that describes the feature of implication relation in this compound proposition.

关于复合命题A→B本身的真值，传统逻辑中是由其支命题A、B的实际真值通过某种真值运算(二值逻辑中用"实质蕴涵"，模糊逻辑中有众多的"蕴涵算子")而求得。我们称这种求蕴涵型复合命题真值的方法为逻辑方法。

The soundness and completeness theorem of this method were proved at last. This part consists of the following points: 1. The properties of the indecomposable extremely simple form of LP were discussed, the theorem shown that every logical formula of LP was equals of a generalized conjunction normal form. 2. The method for judging a logical formula is a indecomposable extremely simple form or not was discussed, the necessary and sufficient conditions of a logical formula with not more than three implicative connective being a indecomposable extremely simple form was given. 3. The α-resolution fields of the indecomposable extremely simple form of LP were discussed, some elementary results were obtained. 4. The automated reasoning method based on the resolution principle of classical logic was discussed, the author given a method to describe the set of clauses by using a matrix, and translated the resolution of two clauses to column operations of this matrix.

二、关于格值命题逻辑系统LP中α-自动推理方法的研究 1、对LP中不可分极简式的性质进行了研究，证明了LP中任何一个格值逻辑公式等值于一个广义合取范式； 2、对LP中不可分极简式的判定方法进行了研究，讨论了含有不超过3个蕴涵运算的格值逻辑式为不可分极简式的充分必要条件； 3、对LP中不可分极简式的α-归结域进行了研究，得到了一些基本结果； 4、对经典逻辑中基于归结原理的自动推理方法进行了研究，给出了用符号矩阵表示子句集合的一种方法，把不同的归结过程转换成矩阵的列变换。

This is an graduate introduction to Programming Theory, Logic of Programming, and Computability, with the programming language Scheme used to crystallize computability constructions and as an object of study itself.

这是一篇介绍研究程序理论、程序和运算逻辑，关于电脑程序语言惯于用的明确性的运算结构，就像自学对象。

A logical expression of the form a1︿a2︿…︿an where︿is the AND operation. A particular conjunction of interest is the conjunctive normal form of a Boolean expression involvingn variables x1, x2,…,xn.

一种逻辑表达式a1︿a2︿…︿an，其中︿是AND运算，一个特别重要的合取运算是涉及n个变量x1，x2，…，xn的布尔表达式的"合取范式"。

It introduces the basic knowledge and ideas of mathematical logic and classic set theory, including proposition logic and predicate logic, reasoning calculus and theorem proving methods, basic operations and properties of sets and relations, functions of any sets and their properties, the cardinals of infinite sets, and the applications of knowledge and ideas above in computer sciences.

本课程系统介绍数理逻辑与朴素集合论的基础知识，包括：命题逻辑和谓词逻辑、定理的推理演算和机器证明方法，集合和二元关系的基本运算和性质、任意集合中的函数及其性质，无穷集合的基数，以及上述知识在计算机科学中的应用。

To the predicate calculus on Intuitionistic Fuzzy Logic, a symmetric synthetic method for finding the truth of IFL propositions using membership and hesitancy degree is proposed on the basis of the hypothesis of an equilibrium state of supportability and opposability of neutral evidences indicated in the intuitionistic index. The fundamental operation rules on IFL propositions are presented.

摘要针对直觉模糊逻辑及命题演算，基于直觉指数所表征的中立证据中支持与反对的程度呈均衡状态的假设，提出利用隶属度与犹豫度计算直觉模糊逻辑命题真值的对称合成方法，给出直觉模糊逻辑命题的运算规则。

A multidirectional morphological filtering algorithm is proposed by use of the characteristics of morphology's multisolution analysis and fastly-computing.

充分利用形态学的不同结构元多方向形态滤波的多分辨率特性，以及形态学运算固有的能将大量的复杂图像处理运算转换为基本的逻辑与移位运算的组合来完成的特点，提出了一种多方向的形态滤波算法。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失