逻辑上

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。

Setting out from symbolic logic, Russell was the first philosopher who destroyed the law of excluded middle in classical logic, and provided leads for the research into formalized fuzzy logic o...

皮尔斯是西方哲学史上确认"语言本身的模糊性"的第一位哲学家；维特根斯坦强调语言确定性与模糊性的并存关系，并试图将二者统一；罗素从符号逻辑的水平上首次打破了古典逻辑的排中律，开辟了形式化模糊逻辑或多值逻辑的研究道路。

The controversy between the monist and pluralist conception of logic also happens in the field of logic teaching.

传统逻辑与现代逻辑的争论，主要表现在如何改革大学文科逻辑教材上，也表现在以哪种逻辑作为研究中国古代关于逻辑的理论发展史的工具更合适的问题上。

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。

This deontic logic should be logic about normal propositions rather than logic ab...

但是 ，在行动逻辑基础上构建的道义逻辑是一个有关规范命题的逻辑，而不是规范的逻辑，在相当程度上也可以看成是一个规范命题逻辑和规范逻辑的混成物。

This deontic logic should be logic about normal propositions ra...

但是 ，在行动逻辑基础上构建的道义逻辑是一个有关规范命题的逻辑，而不是规范的逻辑，在相当程度上也可以看成是一个规范命题逻辑和规范逻辑的混成物。

Thus, the editorial of the Royal Society has not reached the maturity in logic.

因此，这皇家学会的编辑部还未逹到逻辑上的成熟。

Quote8 i get your point but your idea can only explain that giffen good will not be transacted in market however, N.S.

换言之，嘉芬物品若在真实世界中存在，逻辑上它只能存在於鲁宾逊的一人世界中。

In an age known for the construction of metaphysical systems—such as those of Descartes, Malebranche, and Spinoza—Leibniz's metaphysics is perhaps the most tightly logically constructed system.

在一个到处都是形而上学理论的年代--笛卡尔，马勒伯朗士，斯宾诺莎--莱布尼茨的形而上学可能是逻辑上最紧凑的体系。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。