查询词典 complemented lattice

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。

Based on the traits of dyadic wavelet decomposition of signal and that of the distribution of wavelet image coefficients, PLVQ and ZR are conjoined by making use of D\-4 lattice. Firstly, Pyramidal lattice vector quantization is adopted to quantize wavelet image coefficients. Nonzero lattice vectors and zero lattice vectors are formed. Secondly, nonzero lattice vectors are dealt with by adopting complex entropy coding. Finally, in order to fix on the position of nonzero lattice vector effectively, that is, to deal with zero lattice vectors effectively, the concept of significant map is introduced into. The significant map is scanned two times from down to up and from up to down.

根据信号的二进小波分解特点和小波图象系数的分布特点，利用D\-4格将PLVQ和零树结合起来，提出了一种基于零树和金字塔格型矢量量化的小波图象编码方法，该方法首先采用金字塔格型矢量方法来量化小波图象系数，以得到非零格点和零格点；然后采用复合熵编码来处理非零格点；最后为了有效确定非零格点的位置，也就是为了有效地处理零格点，又引进了重要图的概念。

The concepts of weight lattice structure, sphere lattice structure and lienor lattice structure are introduced to describe it, some properties of the k-error lattice structure are given, and a relationship between the k-error lattice structure and the k-error linear complexity is presented. These create a elementary frame of the stability theory of the lattice structure.

提出了伪随机序列格结构的稳定性问题，引入重量格结构、球体格结构、k-错格结构等概念来描述之，给出了k-错格结构的一些基本性质，并研究了k-错格结构与k-错线性复杂度的关系。

Secondly, in a more generalized framestructrue--lattice-ordered monoids,the notion of lattice-valued Mealy-type automata is introduced,we traverse some algebraic properties of this automata and investigate the congruences and homomorphisms of this type automata.Our main results indicate that the algebraic properties of lattice-valued Mealy-type automata have Close links to the algebraic properties of lattice-ordered monoids which automata take values in.Futhermore we study the minimization of lattice-valued Mealy-type automata and provide an algorithm to achieve the minimal lattice-valued Mealy-type automata within finite steps.

其次，在更一般的框架—格半群意义下，提出具有输入和输出字符的自动机——格值Mealy自动机的概念，从代数角度出发较详细地研究了此类自动机具有的性质，同时研究了此类自动机的同余和同态，揭示了此类自动机的代数性质和格半群的紧密联系，最终研究了格值Mealy自动机的极小化问题，并给出了在有限步可实现此极小化的算法。

The study of lattice implication algebras On the basis of previous results of lattice implication algebras, we firstly studied some properties of implication filters, prime implication filters, maximal implication filters and ultrafilters. Then we laid stress on the study of two kinds of relatively general lattice implication algebras, i. e. complete and atomic lattice implication algebra and injective lattice implication algebra.

关于格蕴涵代数的研究本文在已有的格蕴涵代数研究结果基础上，首先研究了格蕴涵代数中蕴涵滤子、素蕴涵滤子、极大蕴涵滤子和超滤等的性质和相互的关系，然后重点较系统地研究了两类覆盖面较广的格蕴涵代数：完备的且原子的格蕴涵代数和内射的格蕴涵代数。

The study of lattice-valued propositional logic system based on lattice implication algebra.On the bases of previous study, by using the concepts and methods of T algebras we established the lattice-valued propositional logic system LP , whose truth values domain is a lattice implication algebra, and discussed systematically the semantical and syntactical properties of LP , proved the soundness theorem 、consistency theorem、deduction theorem and the decidability of validity of the system when the truth values lattice is finite. We also discussed the relationship between the α-theorem of some premise, say A, and the closed sets that contain A.

本文在前人研究工作的基础上，利用T代数的概念与方法，建立了真值取于格蕴涵代数的格值命题逻辑系统LP，对它的语义及语法性质进行了较系统的研究，得到了它的可靠性定理、协调性定理及演绎定理等，证明了值格有限时系统"有效性"的可判定性并讨论了某一前提A下的α定理与包含A的闭集之间的关系。

A special kind of prime dual ideals are defined in a lattice implication algebra, then their structures and properties are discussed. It is proved that the implication operation on this lattice implication algebra is determined by these prime dual ideals, and all of these prime dual ideals compose a lattice implication algebra which is lattice implication isomorphic to the former lattice implication algebra.

在格蕴涵代数中定义了一类特殊的素对偶理想，讨论了它们的结构和性质，证明了该格蕴涵代数中的蕴涵运算可以由这些特殊的素对偶理想所确定，并且这些特殊的素对偶理想全体自然地构成一个格蕴涵代数，它和原格蕴涵代数具有格蕴涵代数同构关系。

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。

It is proved that a semiring is complemented if and only if it is a direct product of some Boolean algebra and Boolean ring by studying the relations of congruences on the complemented semiring, so the complemented semiring is the commutative semiring.

s-内射模。通过研究可补半环S的性质及S上的同余关系，证明出可补半环与布尔环和布尔代数的直积是等价的，因而可补半环是交换半环。

Finally, it is proved that any semimodule over complemented semirings must have a ζ_s-injective hull and the complemented semiring must be the rPP semiring and the endomorphism semiring of every principal right ideal is still complemented semiring.

最后指出任一可补半环上的半模必存在内射包络、可补半环必是rPP半环且对于可补半环的任一主右理想的自同态集仍是可补半环。

A carrier gas such as nitrogen is directed through line 20 and valve 22 to connect with line 26 and mix with the gas sample.

如氮气之类的载体通过管线20和阀22引入，与管线26相通，与气体样品混合。

But for the most part, knaves and parasites had the command of his fortune

然而支配他的家产的大多是恶棍和寄生虫。