逻辑系统

The soundness and completeness theorem of this method were proved at last. This part consists of the following points: 1. The properties of the indecomposable extremely simple form of LP were discussed, the theorem shown that every logical formula of LP was equals of a generalized conjunction normal form. 2. The method for judging a logical formula is a indecomposable extremely simple form or not was discussed, the necessary and sufficient conditions of a logical formula with not more than three implicative connective being a indecomposable extremely simple form was given. 3. The α-resolution fields of the indecomposable extremely simple form of LP were discussed, some elementary results were obtained. 4. The automated reasoning method based on the resolution principle of classical logic was discussed, the author given a method to describe the set of clauses by using a matrix, and translated the resolution of two clauses to column operations of this matrix.

二、关于格值命题逻辑系统LP中α-自动推理方法的研究 1、对LP中不可分极简式的性质进行了研究，证明了LP中任何一个格值逻辑公式等值于一个广义合取范式； 2、对LP中不可分极简式的判定方法进行了研究，讨论了含有不超过3个蕴涵运算的格值逻辑式为不可分极简式的充分必要条件； 3、对LP中不可分极简式的α-归结域进行了研究，得到了一些基本结果； 4、对经典逻辑中基于归结原理的自动推理方法进行了研究，给出了用符号矩阵表示子句集合的一种方法，把不同的归结过程转换成矩阵的列变换。

Conditional sentences in two-valued logical systems are incapable of supplying solutions, consequently have to advance to a three-valued logical system, in order to secure a valid conditional sentence truth-table and solve the paradox of The Verification of the Paradox.

条件语句的问题在二値逻辑的系统无法获得解决，因此我们必须进一步诉诸一套三值的逻辑系统，才能得到合理的条件语句眞值表，并且解决像「检证的吊诡」一类的矛盾。

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。

Proposition logic takes the proposition as the fundamental research object mathematization logical system,propo- sition logic is the mathematical logic foundation,also is the theoretical basic of computer science and the technical.

命题逻辑是一个以命题为基本研究对象的数学化的逻辑系统，命题逻辑是数理逻辑的基础，也是计算机科学与技术的理论基础。

Professor Zhang Qing-yu gets paraconsistent modal proposition logic C〓G'on the base ofCosta's paraconsistent proposition logic system C〓.

张清宇教授在科斯塔的弗协调命题逻辑系统C 的基础上得到弗协调模态命题逻辑系统CnG＇。

Having combination of the theory of truth degree in metrology of logic with the theory of ∑-α-tautologies in fuzzy logic, which have been introduced by professor G.J.Wang, the theory of ∑Γ-truth degree was introduced, and its properties which induce a pseudometric on F were investigated. The results gained have complemented and enhanced the original theory, and the work delivers a new frame for fuzzy reasoning.

将模糊命题逻辑中的∑-α-重言式理论与计量逻辑学中的真度理论相结合，在经典二值命题演算系统L中引入了公式相对于有限理论的∑Γ-真度理论，较为详细地讨论了它们的性质，并利用∑Γ-真度的性质在公式集F上引入了ρΓ-伪距离，对原有的理论进行了加强和补充，为在模糊命题逻辑系统的有限理论中讨论结论的程度化问题奠定了基础。

At the basic of knowledge implication propositional logic, a system of knowledge implicational model prepositional logic system has been built. It can describe inference mechanism of inconsistent knowledge system which includes in modal information.

在知识蕴涵命题逻辑的基础上，构建了一个知识蕴涵模态命题逻辑系统，它可以描述包含模态信息的不协调知识系统的推理机制。

ABSTRACT Motived by the status of theoretical studies and the requirements of engineering applications in the fuzzy control system, the characters of fuzzy logic systems are analyzed, the mathematic model of a class of fuzzy logic system is built, especially the ways how to use the model to identify the nonlinear dynamic system and design the adaptive control system are researched deeply in this paper.

本论文根据模糊控制理论研究的发展现状、存在的主要问题以及工程实际应用的基本要求，分析了模糊逻辑系统的特性，建立起一类模糊逻辑系统的数学模型，并对其用于非线性动态系统辨识与自适应控制系统设计方法等方面进行了深入的研究，为解决某些传统方法难以解决的工程实际问题提供了新的思路。

Based on the production of other researchers such as professor Xu Yang and professor Qin Keyun, this paper discusses the structure and properties of lattice implication algebra, tautologies in some lattice-valued systems, automated reasoning methods, lattice-valued propositional logic system.

本文的工作是在徐扬教授、秦克云教授等研究成果的基础上，对格蕴涵代数的性质、结构、格值命题逻辑系统中的重言式、自动推理方法、格值命题逻辑系统等进行了一些研究。

When appling paraconsistent logic to alethic modal logic,we get a deontic logic system which avoids the ...

当将弗协调逻辑运用于真值模态逻辑时，可得到一避免了善良的撒玛利亚人悖论的道义逻辑系统，于是我们可得出结论：道义逻辑可归约为弗协调真值模态逻辑

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新