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Based on the outcome of Xu Yang and Qin Keyun about lattice implication algebra and lattice-valued prepositional logic LP with truth-value in a lattice implication algebra, the author studied the properties of lattice implication algebra and the α-automated reasoning method based on α-resolution principle of LP. The specific contents are as follows: The Study of Lattice Implication Algebra On the basis of previous results of lattice implication algebra, this part consists of the following three points: 1. Some properties of lattice implication algebra L were discussed, and some important results were given if L was a complete lattice implication algebra. 2. The properties of left idempotent elements of lattice implication algebras were discussed, and the conclusion that lattice implication algebra L was equals of the directed sum of the range and dual kernel of a left map constructed by a left idempotent element was proved. 3. The properties of the filters of lattice implication algebra were discussed, the theorem was shown that they satisfy the hypothetical syllogism and substitute theorem of the propositional logic. 4. The concept of weak niters of lattice implication algebras and their properties and structures are discussed. It is proved that all weak filters of a lattice implication algebra form a topology and the the implication isomorphism betweem two lattice implication algebras is a topological mapping between their topological spaces. The Study of α-automated reasoning method based on the lattice-valued propositional logic LP In this part, the author given an a-automated reasoning method based on the lattice-valued propositional logic LP.

本文基于徐扬和秦克云的关于格蕴涵代数和以格蕴涵代数为真值域的格值命题逻辑系统LP的研究工作，对格蕴涵代数以及格值命题逻辑系统LP中基于α-归结原理的自动推理方法进行了系统深入的研究，主要有以下两方面的研究成果：一、关于格蕴涵代数的研究 1、对格蕴涵代数的格论性质进行了研究，得到了当L为完备格蕴涵代数时，关于∨，∧，→运算的一些结果； 2、对格蕴涵代数的左幂等元进行了研究，证明了格蕴涵代数L可以分解为任何一个左幂等元所对应的左映射的像集合与其对偶核的直和； 3、对格蕴涵代数的滤子的性质进行了研究，证明了滤子的结构相似于逻辑学中的Hypothetical syllogism规则和替换定理； 4、给出了格蕴涵代数中弱滤子的概念，对弱滤子的性质个结构进行了研究，证明了格蕴涵代数的全体弱滤子构成一个拓扑结构，格蕴涵代数之间的蕴涵同构是相应的拓扑空间之间的拓扑映射。

Chapter three: Define fuzzy congruence relation of MTL-algebra, prove that fuzzy fiter and fuzzy congruence relation is a bijective function in MTL-algebra, quotient algebra induced by congruence relation still forms a MTL-algebra; Introduce the relation between some kinds of fiters and fuzzy filters maitained above in IMTL-algebra,i.e. BR_0 algebra, which is a MTL-algebra satisfied inversely odering and involutive relation.

第三章：定义了MTL-代数中的Fuzzy同余关系，证明了MTL-代数中Fuzzy滤子与Fuzzy同余关系是——对应的，由同余关系所诱导的商代数依然构成一个MTL-代数；介绍了在满足逆序对合对应的MTL-代数-IMTL-代数，即BR_0-代数中上述几中特殊滤子，Fuzzy滤子之间的关系。

The most famous rough algebras are Rough Double Stone Algebra, Rough Nelson Algebra and Approximation Space Algebra, and their corresponding general algebra structures are regular double Stone algebra, semi-simple Nelson algebra and pre-rough algebra respectively.

其中最有影响的粗代数分别是粗双Stone代数、粗Nelson代数和近似空间代数，它们对应的一般代数结构分别是正则双Stone代数、半简单Nelson代数和预粗代数。

The third part proposes in Luk the concept of lattice-valued truth degrees based on the second part by generalizing truth values from the MV-unit interval(a special MV-algebra) to a general MV-algebra. And the properties of lattice-valued truth degrees suggest that this generalization is natural and reasonable. Because of the equivalence between the two algebra systems, i.e. MV-algebra and lattice implication algebra, it's natural and easy to grade the truth of formulas in lattice-valued propositional logic whose basic algebra system is the lattice implication algebra.

中。 本文第三部分在第二部分的基础上，将Luk中公式的真度值推广到了一般的MV代数上，相对于第二部分的数值真度，给出公式的格值真度，并通过格值真度的性质说明格值真度是数值真度的合理推广。

The latter is essentially derived from the geometric realization of Happels triangulated equivalence between stable module category of repetitive algebra and bounded derived category of finite dimensional algebra. In terms of this realization, we deduce that the Lie algebra realized by derived category of a finite dimensional algebra is isomorphic to the Lie algebra realized by stable module category of the corresponding repetitive algebra.

后者本质上是Happel关于重复代数的稳定模范畴和导出范畴的三角等价的一个几何实现及其应用，使用这种几何实现，我们可以证明在重复代数的稳定模范畴上定义的李代数同构于相应的导出范畴上实现的李代数。

The questions covering pre-algebra and elementary algebra make up the Pre-Algebra/Elementary Algebra Sub score. The questions covering intermediate algebra and coordinate geometry make up the Intermediate Algebra/Coordinate Geometry sub score. The questions covering plane geometry and trigonometry make up the Plane Geometry/Trigonometry sub score.

包含有基础初等代数和初等代数的考题构成了基础初等代数/初等代数的技能分数，涉及到中等代数和坐标几何的考题构成了中等代数/坐标几何的技能分数，而涵盖平面几何和三角函数的考题则构成了平面几何/三角函数的技能分数。

Fuzzy logic is studied with algebraic tools in this paper. A kind of algebraic abstract of fuzzy logic, Implication Algebra on a partial ordered set, is given. The relations between Implication Algebra and other algebraic structures, such as MV-Algebra and Heyting Algebra etc., and the filter and the structure of Implication Algebra on a partial ordered set are studied.

本文的目的是使用代数工具对模糊逻辑进行研究，给出模糊逻辑的一类代数抽象，即偏序集上的蕴涵代数，研究偏序集上蕴涵代数与其它代数结构，如MV-代数，Heyting代数之间的关系，以及偏序集上蕴涵代数的滤子与其结构等。

31 Chapter 3 Number Systems and Boolean Algebra 3.2 Boolean Algebra Table 3-2 Distributivity Idempotency Absorption laws 分配律同一律吸收律 a=ab+ac a+= a+a=a aa=a a+ab=a a=a'=a'b''=a'+b' DeMorgan's laws德摩根定理计算机专业英语 3-32 Chapter 3 Number Systems and Boolean Algebra 3.2 Boolean Algebra Since a finite set of n elements has exactly 2n subsets, and it can be shown that the finite Boolean algebras are precisely the finite set algebras, each finite Boolean algebra consists of exactly 2n elements for some integer n.

由于n个元素的有限集有且只有个子集由于个元素的有限集有且只有2n个子集，而且很显然有限布个元素的有限集有且只有个子集，尔代数一定是有限集合代数，所以对某个整数n而言而言，尔代数一定是有限集合代数，所以对某个整数而言，每个有限布尔代数也有且只有2n个元素。例如，上文定义的集合T的限布尔代数也有且只有个元素。

In this paper, we characterize the multiplier algebras of JC-algebras by double centralizers , and study the relationship between multiplier algebra M of complex C*-algebra A and C*-algebra C* M(Asa generated by the multiplier algebra of JC-algebra Asa, the self-adjoint part of A, Finally, we study the extension of JB-algebras.

本文用双中心子刻画了JC代数的乘子代数，并且研究了复C*－代数的自伴部分的乘子代数生成的C*－代数与原C*－代数的乘子代数之间的关系，最后研究了JB代数的扩张。

Besides, the author also give a detailed analysis and conclusion from the four levels of the total layout, building flat surface layout, building space and the exterior space shape. First, the thesis analyzed the race building, aim at the special natural environment and social milieu, i.e. how its total layout is; the concrete nature adaptability to the natural and social features. Second, this thesis analyzes the feature of layout in this origin with the examples of store, house, general residence, house, courtyard, public buildings and the clues of person's living mode. Furthermore, the thesis launches from street space, courtyard space, indoors space to explore the villages and living room of the nationalities such as 汉,土家,苗,侗. Finally, the thesis gives a specific analysis of the exterior space and nature factor, unreasoned composition of exterior space and fortuity, the relationship between the exterior space and function, the exterior space and geography and hang feet floor and horoscope doors and fence etc.

首先，论文分析了民族建筑针对特殊的自然环境与社会环境，其总体布局如何；具体体现自然适应性和社会适应性的特色：其次，论文以店宅、一般住宅、宅院、公共建筑四种湘西民族建筑类型为主，以相应的人的生活模式为线索，分析湘西民族建筑的平面布局特色；再者，论文从街道空间、院落空间、室内空间三个部分展开，同时对湘西地区汉族、土家族、苗族、侗族的村镇和民居建筑空间分别进行了颇有民族特色的着力探寻；最后，论文分外部空间造型与自然因素、外部空间造型的非理性与偶成、外部空间造型与功能关系、外部空间造型与地形关系、吊脚楼及八字门与围墙等六个部分，具体分析湘西民族建筑外部空间造型特色。

The network space is the typical form of abstract space when it comes to the digital stage.

网络空间是抽象空间数字化阶段的典型形式。

The Notarial System,as the system of judicial certification in our country,is both the constructor and the defender of social credit system,It has its special value and function in the social honesty.

公证制度作为我国司法证明制度，既是社会信用体系的建设者，同时也是社会信用的捍卫者，在诚信中有其特殊的价值和功能。