查询词典 implication

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。

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。

On the one hand, Implication paradox provides semantics grounding for two conditional inference principles; on the other hand, the discovery of implication paradox arouses logicians discussion to the implication theory and makes them put forward many new implication theories such as: strict implication -, relevant implication and etc., and promotes the development of the implication theory and makes implication theory step down mysterious palace, and gradually penetrates into many other concrete sciences.

一方面，正是由于蕴涵怪论为传统逻辑两个假言推理规则提供了语义学根据；另一方面，正是由于蕴涵怪论的发现，引发了逻辑学家们对蕴涵理论的深入探讨，提出了许多新的蕴涵理论如严格蕴涵，相干蕴涵，衍推蕴涵等等，推动了逻辑学蕴涵理论的发展，并促使蕴涵理论走下神秘的殿堂，而逐步深入到许多具体的学科中去。

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。

This article discusses the track of the development of implication theory, generalizes B.Russell"s idea about implication,simply induces such implication theories as C.I.Lewis""strict implication" W.Ackermann"s "relevant implication" and so on, and analyzes the relations among these theories, emphasizes that material implication"s basic status in mathematical logic.

论文还从历史发展的角度阐述了蕴涵理论发展的轨迹，总结了罗素对蕴涵问题的认识，简要归纳了刘易斯的"严格蕴涵"、阿克曼等的"相干蕴涵"及安德森和贝尔纳普的"衍涵"等为代表的蕴涵理论的几种形态，并对这几种理论形态之间的关系进行了细致地对照，强调了实质蕴涵在数理逻辑中的基础地位。

Firstly, it studies the definition of implication and its classification, basing on this, deeply analyzes the relations between implication and the connective "if, then" universally used in our ordinary life. Then the article points out that implication is logical abstract to the connective "If, then" used in the natural language. However, because of different understanding and mastering to it, implication may have different classification, it can't be given a right definition. We must master it by all kinds of concrete implications. According to different criterion, implication has different categories. This article mainly discusses its classification from two sides: Ancient Greece and Medieval's and metalogic's.

首先，论文简要地考察了蕴涵概念的界定，指出蕴涵是对自然语言中连接词"如果，则"的逻辑抽象，而对它的意义的不同理解和把握，则可以有不同种类的蕴涵，不能笼而统之地对蕴涵下一定义，只有通过各种具体蕴涵去掌握有关蕴涵的理论；依据不同的分类标准，蕴涵可以有不同的类型，本文主要讨论古希腊及中世纪对蕴涵所作的分类及从记号学这一元逻辑的角度出发对蕴涵作的分类。

That is,the truth value of an implication compound proposition is just the compatibleness degree of the actual implication degree or implication rate between its sub-propositions with the language value that describes the feature of implication relation in this compound proposition.

关于复合命题A→B本身的真值，传统逻辑中是由其支命题A、B的实际真值通过某种真值运算(二值逻辑中用"实质蕴涵"，模糊逻辑中有众多的"蕴涵算子")而求得。我们称这种求蕴涵型复合命题真值的方法为逻辑方法。

Then the interpolation representations of fuzzy controllers with Mamdani implication operator, algebra product implication operator, Zadeh implication operator and implication operator are introduced separately.

然后分别获得了基於POFI方法的Mamdani蕴涵算子模糊控制器、代数积蕴涵运算子模糊控制器、Zadeh蕴涵运算子模糊控制器及加乘运算子模糊控制器的插值表示，由此发现这些模糊控制器具有函数逼近的泛性。

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。

It is argued that strict implication proposed by Lewis is essentially the same as material implication in that it is a truth-unction based defintion of implication.

严格蕴涵和实质蕴涵本质上都是基于命题真假函项的蕴涵概念的定义方法，并不能从根本上解决实质蕴涵会导致蕴涵怪论的问题。

In contrast to the ubiquitous rising-sun-with-rays military flag of the Japanese, Chinese banners and ensigns feature a range of designs.

与遍地都是的太阳军旗不同，中国人的旗帜和徽章设计得各式各样。

From their small corner of Feng's Guangzhou headquarters -- a jumble of pink leashes, squeezable rubber steaks, and plastic doggy Santas for Fido's stocking -- Soleil's designers come up with at least five new products a month.

从Feng 设在广州总部的产品展示柜台上可以看到，Soleil的设计师每月至少设计出5件新产品。