逻辑系统

Wang-type fuzzy logic system and its functional approximation ability are researched deeply, A class of Gauss-type fuzzy logic system is presented and studied What it defers from Wang-type fuzzy logic system is its using Gauss fuzzifier The analytical expression of this fuzzy logic system is derived detailed Its universal approximation theorem for nonlinear functions is proved by StoneWeiestrass theorem.

通过对两类模糊系统作为非线性辨识器的仿真研究显示出高斯型模糊逻辑系统在抗数据干扰方面比Wang型模糊系统有优势。对非线性动态系统的辨识问题，借助递归神经网络的研究成果，提出一种基于递归网络结构的自适应模糊逻辑系统和参数学习算法。

Then we deeply studied the completeness of LP . Consequently, we established:(1) The completeness theorem of LP with truth-value in finite Lukasiewiczchain;(2) The completeness theorem of LP with truth-value in complete and atomic lattice implication algebras;(3) The completeness theorem of LP with truth-value in injective lattice implication algebras.

建立了：（1）基于Lukasiewicz有限链的格值命题逻辑系统LP的完备性定理；（2）基于完备的且原子的格蕴涵代数的格值命题逻辑系统LP的完备性定理；（3）基于内射的格蕴涵代数的格值命题逻辑系统LP的完备性定理。

Studies on the tautologies in some lattice valued logic systems and formula computation by means of neural net works.(1) Tautologies play a significant role in logic applications.

二、一类格值逻辑系统中的重言式和逻辑公式的神经网络计算 1、重言式在逻辑系统的应用中起着重要的作用。

In terms of this framework, we have designed a pointer logic system for a subset of C language. The style of this logic is something like the style of Hoare logic. It can be used for accurate pointer analysis of pointer programs. The information from the analysis can be used to prove the side conditions of typing rules and then to support static type checking of programs.

根据这个框架，我们为C语言的一个子集设计了一种指针逻辑系统，该逻辑系统的形式和Hoare逻辑的形式类似，它可用来对指针程序进行精确的指针分析，所获得信息用来证明指针程序是否满足定型规则的附加条件，以支持程序的静态类型检查。

Using the infinite product of unevenly distributed probability space with potential of 3, the concept of formula truth degree was introduced into the Gdel 3-valued propositional logic system. Moreover, it was proved that in the 3-value (1/4, 1/2, 1/4), measure the set of truth of degree of propositions was dense in [0, 1], and a general expression of truth degree was obtained, providing a basis for further developing approximate reasoning of 3-valued propositional logic system.

利用势为3的非均匀概率空间的无穷乘积，在Gdel三值命题逻辑系统中引入公式的真度概念，在三值逻辑(四分之一，二分之一，四分之一)测度下证明G3中全体公式的真度值之集在[0， 1]上是稠密的，并给出公式真度的表达通式，为进一步在三值命题逻辑系统中展开近似推理奠定基础。

WT9.BZ: Theory of generalized tautology in logic system , W and W k is generalized and applied to Lukasiewicz logic system. The main results are as follows: congruence about on set of logic formulas F has been obtained in the system; it is proved that in this system, for any irrational number α, there does not exist accessible α-tautology; and for any real number α, there does not exist accessible α+-tautology; and the relation theorems have been given between categori...

将逻辑系统 W ，W ，Wk 中的广义重言式理论进行推广并应用到Lukasiewicz逻辑系统中，主要结果是：得到了逻辑公式集F在该系统中关于﹁同余的分划；证明了在该逻辑系统中对每个无理数α而言，不存在可达α重言式，且对每个实数α而言，不存在可达α+重言式；给出了广义重言式、广义矛盾式各类之间的关系定理。

As the logical foundation of sematics, it is Known that the model theory treats the relationships between syntactic constructs and semantical features thereof, and that the model theoretic logic cares, under the frame of abstract logic, for the similarity, distinctness and interrelationships among various extended logics.

作为语义方法的逻辑基础，模型论是研究逻辑的语法构造与语义属性之间联系的一门数理逻辑的分支；而模型论逻辑则是在抽象逻辑的框架中，用模型论的方法研究各种扩充逻辑系统的异、同及相互关系。

Part Three The study of Lattice-valued Modal First-order Logic System and Its Resolution Principle In this part, we introduced quantifiers and predicate into LMP, put up lattice-valued modal first-order logic system LMF, and gave its semantic interpretation and syntax structure, proved soundness theorem and consistence theorem. Moreover, in order to judge the satisfiability of formula, defined Skolem standard type and H-interpretation. Based on these work, made a primary discussion of a - resolution principle based on LMF.

第三部分：关于格值模态一阶逻辑系统及其归结原理的研究第n页西南交通大学博士研究生学位论文这一部分主要是在格值模态命题逻辑系统LMP队）中引进量词和谓词，建立格值模态一阶逻辑系统LMF（广并给出其语又解释和语法结构，证明了系统的可靠性和协调性；另外，为了判断公式的可满足性，定义了格值模态一阶公式的 Skolem标准型和体解释；在此基础上，对基于系统LMF的a一归结原理进行了初步探讨。

Keywords: logic of tasks;decidable;description language;multi-agent system;organization model

将所构造的逻辑系统应用于具有组织的多主体系统行为建模，建立了基于描述任务逻辑的多主体组织模型和建模框架，并且表明应用描述任务逻辑构造应用系统具有表达能力强、结构紧凑的特点。

With the background of application of fuzzy control techniques to a rather typical complex control system, gas-burning water heater, theories, applications and techniques of fuzzy information processing have been studies. The obtained results include:(1) For lattice-valued logic systems based on lattice implication algebras, two dynamical lattice-valued propositional logic Lvpl and lattice-valued first-order logic Lvfl have been constructed, and some theories and methods of fuzzy reasoning have been proposed based on fuzzy set theory and multi-valued logic.(2) Some methods for designing and optimizing fuzzy control systems and some corresponding control algorithms have been proposed, and some new theories and methods for fuzzy control rule base and fuzzy control system performance analysis have been introduced.(3) 6 fuzzy control systems have been developed, and some difficult problems on craft of manufacture, batch consistency, quality stability, installation and main

本项目以模糊控制技术用于燃气热水器这一较典型的复杂控制系统为应用背景，在模糊信息处理的理论、应用和技术三个层次开展了相关的研究工作：(1)进一步研究了基于格蕴涵代数的格值逻辑系统，建立了两种动态的格值命题逻辑Lvpl和格值一阶逻辑Lvfl，并基于模糊集理论和多值逻辑提出了多种模糊推理的理论与方法；(2)提出了模糊控制系统的多种设计及优化方法与控制算法，建立了模糊控制规则库和模糊控制系统性能分析的一些新理论与新方法；(3)研制完成了6个模糊控制系统，还特别解决了模糊控制燃气热水器和智能控制燃气热水器在产业化过程中的生产工艺、批量一致、质量稳定、安装维修和性能价格等一系列难题，做好了批量生产前的技术准备，现已小批量生产。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。