逻辑上的

The main contributions of the second part of this dissertation are focused on the cryptographic properties of logical functions over finite field, with the help of the properties of trace functions, and that of p-polynomials, as well as the permutation theory over finite field: The new definition of Chrestenson linear spectrum is given and the relation between the new Chrestenson linear spectrum and the Chrestenson cyclic spectrum is presented, followed by the inverse formula of logical function over finite field; The distribution for linear structures of the logical functions over finite field is discussed and the complete construction of logical functions taking on all vectors as linear structures is suggested, which leads to the conception of the extended affine functions over finite field, whose cryptographic properties is similar to that of the affine functions over field GF (2) and prime field F〓; The relationship between the degeneration of logical functions and the linear structures, the degeneration of logical functions and the support of Chrestenson spectrum, as well as the relation between the nonlinearity and the linear structures are discussed; Using the relation of the logical functions over finite field and the vector logical functions over its prime field, we reveal the relationship between the perfect nonlinear functions over finite field and the vector generalized Bent functions over its prime field; The existence or not of the perfect nonlinear functions with any variables over any finite fields is offered, and some methods are proposed to construct the perfect nonlinear functions by using the balanced p-polynomials over finite field.

重新定义了有限域上逻辑函数的Chrestenson线性谱，考察了新定义的Chrestenson线性谱和原来的Chrestenson循环谱的关系，并利用一组对偶基给出了有限域上逻辑函数的反演公式；给出了有限域上随机变量联合分布的分解式，并利用随机变量联合分布的分解式对有限域上逻辑函数的密码性质进行了研究；给出了有限域上逻辑函数与相应素域上向量逻辑函数的关系，探讨了它们之间密码性质的联系，如平衡性，相关免疫性，扩散性，线性结构以及非线性度等；讨论了有限域上逻辑函数各类线性结构之间的关系，并给出了任意点都是线性结构的逻辑函数的全部构造，由此引出了有限域上的"泛仿射函数"的概念；考察了有限域上逻辑函数的退化性与线性结构的关系、退化性与Chrestenson谱支集的关系；给出了有限域逻辑函数非线性度的定义，利用有限域上逻辑函数的非线性度与相应素域上向量逻辑函数非线性度的关系，考察了有限域上逻辑函数的非线性度与线性结构的关系；利用有限域上逻辑函数与相应素域上向量逻辑函数的关系，揭示了有限域上的广义Bent函数与相应素域上的广义Bent函数的关系，以及有限域上的完全非线性函数与相应素域上向量广义Bent函数之间的关系；给出了任意有限域上任意n元完全非线性函数存在性与否的完整证明，并利用有限域上平衡的p-多项式的性质给出了有限域上完全非线性函数的一些基本构造方法。

According to the problems that are encountered in designing the mathematical knowledge representation language in NKI (national knowledge infrastructure) and after the discussion of ontological assumptions for mathematical objects, two kinds of formalisms for the representation of mathematical knowledge are provided. One is a description logic in which the range of an attribute can be a formula in some logical language; and another is a first order logic in which an ontology represented by the description logic is a part of the logical language.

根据在设计NKI(national knowledge infrastructure)的数学知识表示语言中遇到的问题，并在讨论了数学对象的本体论假设的基础上提出了两种数学知识的表示方法：一种是以一个逻辑语言上的公式为属性值域的描述逻辑；另一种是以描述逻辑描述的本体为逻辑语言的一部分的一阶逻辑。

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。

Traditional ways of demarcation tends to focus on revelation of the characteristics of essential facilities that have proved far from satisfactory,among which,the criterion laid down by the court in the case of MCI seems tautological in logic;the public welfare criterion appears to transfer a vague issue into an even indefinite one;while the competitor standard ignores the integral effectiveness of the whole market;...

其中，美国"MCI"案中法院提出的标准存在逻辑上的同语反复；公共利益标准将有待澄清的问题转化为了另一个不确定的问题；竞争者标准忽略了市场的整体效果；消费者偏好标准只是对于特定情况的处理，不能成为一个基本的判断标准。核心设施界定的关键是对"不可复制性"的理解，通过借鉴相关市场界定的方法，可以确定替代发生的范围，以及替代实现的程度，从而对正确地适用核心设施理论提供新的思路。

He explained relevant clauses in Canon of Moism by referring to the theory of Western logic and Indian classical logic so that he could rather sufficiently revealed the logical meaning of many basic concept and propositions in Canon of Moism. Moreover his method had a great effect on the contemporary and following researchers of Chinese logical history.The fourth part is concluding remarks.

其次，正确运用逻辑方法深入地挖掘中国古代的逻辑思想，正确认识中国逻辑的特点，确立中正确认识中国逻辑的特点，确立中国古代逻辑在世界逻辑史上的地位，并通过中外逻辑思想的对比分析，找出我国逻辑科学发展中存在的问题及其原因，以推动我国逻辑科学的更大发展。

Almost everyone notes that there is no "time" in Las Vegas, no night and no day and no past and no future (no Las Vegas casino, however, has taken the obliteration of the ordinary time sense quite so far as Harold's Club in Reno, which for a while issued, at odd intervals in the day and night, mimeographed "bulletins" carrying news from the world outside); neither is there any logical sense of where one is.

几乎每一个来拉斯维加斯的人都注意到这里没有&时间&的概念，没有黑夜也没有白昼，没有过去也没有未来（然而拉斯维加斯的赌场里这种对于寻常时间观念的丢失没有影响到里诺的哈罗德俱乐部，那里每天早晨有那么一会儿，会发行油印的，承载着世界各地新闻的&公告&）；人们对于自己身处何方也没有任何逻辑上的认识。

Hyponymy上下义关系------refers to the sense relation between a more general, more inclusive word and a more specific word.

上下义关系实际是指两词意义之间的关系分别表示的是逻辑上的属的概念与种的概念。

Based on representative opinions about these questions which are raised by philosophers and logicians,the author thinks:1Truth and

作者分析了以往哲学家、逻辑学家对这些问题的一些代表性看法，认为：(1)&逻辑真&不是真的一个子类；(2)逻辑真只能测量观念形式上的关系；(3)逻辑真是认识论意义上的概念，它的本体论说明是一个&自足观念模式&的良性内循环结构。

Likewise, decrementing a bool sets the bool to its logically complemented value. C++ allows incrementing a bool (but marks the feature as deprecated, which means it might be removed in a future standard). C++ forbids decrementing a bool . C99 allows both.

同样的，对一个 bool 的递减把这个 bool 设置成它逻辑上的补码值。C++允许对 bool 的递增（但是把这个特性标记为弃用的，这表示它可能会在将来的标准中移出）。C++禁止对 bool 的递减。C99两者都允许。

This theory defended by the earlier Scholastics (Alexander of Hales, Albertus Magnus), as well as by the majority of the Molinists, and warmly recommended by St. Francis de Sales "as the truer and more attractive opinion", has this as its chief distinction, that it is free from the logical necessity of upholding negative reprobation.

这个理论辩护，由早前的scholastics （亚历山大的hales ，： Albertus思），以及被多数人的molinists ，并热烈推荐的圣弗朗西斯德卖&，因为更真实，更具吸引力的意见&，这是否为行政区别的，它是免费的，从逻辑上的必要性，坚持消极

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。