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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。

Companies in five divisions and the 1st Division: Note-aircraft division, which makes vacuum-injection machine, low-pressure perfusion machines, ovens, etc.; second division: liquid crystal display devices division, the main products of ACF Tiezhao , IC of the crew, COG pressing machines, TAB machine, polarizing slicing machine, glass and other automatic friction; Third Division: non-standard equipment Division, the main products are various fixture, metal molds, measuring devices And an aging furnace; Fourth Division: metal stamping division, processing all kinds of metal stamping parts; Fifth Division: Distribution Division, the external Aoxiangyingfeng Co., Ltd.

公司分五个分部，第一分部：注型机分部，主要生产真空注型机、低压灌注机、烤箱等；第二分部：液晶显示周边设备分部，主要产品有ACF贴着机、IC对位机、COG热压机、TAB机、偏光切片机、玻璃自动摩擦机等；第三分部：非标设备分部，主要产品有各种工装夹具、金属模具、测量装置及老化炉等；第四分部：五金冲压分部，加工各种金属冲压件；第五分部：经销分部，对外以《深圳市敖翔盈丰有限公司》的名义开展国内外商贸活动，销售本公司生产的各种设备，同时代理国外化工材料、钢丝等产品

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。

Bureau of organs inside the 18 functional departments, namely, office, party office to the Personnel Section, Finance Audit Division, law enforcement Supervision Department to monitor the room, Market Management Division, Property Management Section, Housing Management Division, Property Management Division, Demolition Management Division, Housing Reform Business Management Section, Management Section, affordable housing, and housing reform fund management division transformation of the old Management Section, the Development Enterprise Management Division, Development Project Management Division, residential property management section.

局机关内设18个职能科室，即办公室、党委办公室、组织人事科、财务审计科、执法监察科、监察室、市场管理科、产权管理科、房屋管理科、物业管理科、拆迁管理科、房改业务管理科、经济适用住房管理科、房改资金管理科、旧城改造管理科、开发企业管理科、开发项目管理科、住宅产业管理科。

1605 Antiaircraft Artillery Regiment, 4 Bomber Aircraft Corps (202, 219, 321 Bomber Aircraft Division), 5 Ground Attack Aircraft Corps (4 Guards, 264 Ground Attack Aircraft Division), 8 Ground Attack Aircraft Corps (224, 227 Ground Attack Aircraft Division), 5 Fighter Aircraft Corps (8 Guards, 256 Fighter Aircraft Division), 10 Fighter Aircraft Corps (10 Guards, 235 Fighter Aircraft Division), 10 Guards Ground Attack Aircraft Division, 331 Fighter Aircraft Division, 208 Night Bomber Aircraft Division, 98 Guards, 50 Recon Aircraft Regiment, 372, 1002 Separate Artillery Regiment

第1254﹑1554﹑1555﹑1605防空炮团，第4轰炸机军(第202﹑219﹑321轰炸机师)，第5强击机军(第4近卫强击机师，第264强击机师)，第8强击机军(第224﹑227强击机师)，第5歼击机军(第8近卫歼击机师，第256歼击机师)，第10歼击机军(第10近卫歼击机师，第235歼击机师)，第10近卫强击机师，第331歼击机师，第208夜间轰炸机师，第98近卫侦察机团，第50侦察机团，第372﹑1002独立炮兵团

Guards Rifle Corps (151, 161, 237, 395 Rifle Division), 30 Rifle Corps (129 Guards, 30, 141 Rifle Division), 47 Rifle Corps (280, 309 Rifle Division), 52 Rifle Corps (183, 316 Rifle Division), 74 Rifle Corps (147, 155, 276 Rifle Division), 107 Rifle Corps (127, 167, 304 Rifle Division),3 Breakthrough Artillery Division (15 Light Artillery Brigade, 5 Gun Artillery Brigade, 1 Howitzer Brigade, 116 Gun Artillery Brigade, 7 Mortar Brigade); 4, 317 Guards, 130, 222, 1075, 1506, 1642, 1672 Antitank Artillery Regiment, 525 Mortar Regiment, 329 Guards Mortar Regiment, 25 Antiaircraft Artillery Division (1067, 1356, 1362, 1368 Antiaircraft Artillery Regiment), 269 Guards, 580 Antiaircraft Artillery Regiment, 31 Guards Separate Antiaircraft Artillery Battalion 4 Guards Tank Corps 12, 13, 14 Guards Tank Brigade, 3 Guards Motorised Rifle Brigade, 756 Antitank Artillery Regiment, 752 Separate Antitank Artillery Battalion, 264 Mortar Regiment, 76 Motorcycle Battalion, 240 Guards Mortar Battalion (rocket launchers, 120 Guards Antiaircraft Artillery Regiment, 1, 12 Guards Separate Tank Regiment, 46 Separate Armored Train Battalion

第18近卫步兵军(第151﹑161﹑237﹑395步兵师)，第30步兵军(第129近卫步兵师，第30﹑141步兵师)，第47步兵军(第280﹑309步兵师)，第52步兵军(第183﹑316步兵师)，第74步兵军(第147﹑155﹑276步兵师)，第107步兵军(第127﹑167﹑304步兵师)，第3突击炮兵师(第15轻型炮兵旅，第5加农炮旅卖底1榴弹炮旅，第116加农炮旅，第7迫击炮旅)，第4﹑317进位反坦克炮团，第130﹑222﹑1075﹑1506﹑1642﹑1672反坦克炮团，第525迫击炮团，第329近卫迫击炮团，第25防空炮师(第1067﹑1356﹑1362﹑1368防空炮团)，第269近卫防空炮团，第580防空炮团，第31近卫独立防空炮营，第4近卫坦克军(第12﹑13﹑14近卫坦克旅，第3近卫摩托化步兵旅，第756反坦克炮团，第752独立反坦克炮营，第264迫击炮团，第76摩托车营，第240近卫迫击炮营，第120近卫防空炮团)，第1﹑12近卫独立坦克团，第46独立装甲列车营，第6工程兵旅，第3舟桥旅，第27独立工兵营

The two-acre Dunbar Community Garden in Little Rock has served as a model for several years.

几年来，坐落于小石城，占地两英亩的邓巴社区菜园树立了一个标杆。

Jerry points to the jacket hanging in the bathroom. It's ruined, and unwearable What?

杰瑞指着洗手间里挂着的夹克，毁了，不能穿了）什么？