输入调解法和单元调解法在Horn集上的完备性

本文证明了调解法的提升引理,以及输入调解法对Horn集的完备性,进而证出了单元调解法对Horn集的完备性。     

广义λ—调解

本文提出了算子模糊逻辑中的广义λ－调解方法，证明了它和广义λ－归结的联合使用，对于λＥ－不可满足广义子句集是完备的。     

广义λ－调解

本文提出了算子模糊逻辑中的广义λ－调解方法，证明了它和广义λ－归结的联合使用，对于λＥ－不可满足广义子句集是完备的．     

NC线性对称调解

本文提出了NC调解方法,证明了NC对称调解与NC归结的结合及广义对称调解与广义归结的结合的线性演绎都是完备的。     

广义Mandelbrot和Julia组合集

Based on the switched mapping advanced by autbor,the method constructing the general Mandelbort and Julis combination sets was elaborated,and a series of the general Mandelort and Julis combination sets were constructed.The trajectories of a starting point in the complex z-plane under switch mapping were analyzed,the construction characteristics of the general Mandelbort and julia combination sets were described.The algorithm constructing the general Mandelbort and Julia combination sets was researched,the conclusions that the evoutions of the general Mandelbort and Julia combination sets rely on the choice of principal range for the phase angle were given.     

一类复指数映射的复合的广义M-J集

一种常见的构造分形图象的方法是利用复映射的迭代,所使用的一般是复幂映射和复指数映射.Shirriff 在文献[1]中描述了一种利用两个复映射的复合构造分形图象的方法,不过在那里只使用了两个简单的复多项式映射.本文将Shirriff的方法进行了推广,构造了两个复指数映射的复合的广义M集和广义J集,证明了广义M集和广义J集的一些性质.通过大量的计算机实验,总结了广义M集和广义J集的演化规律,并从理论上分析了当两个复映射的参数变化时,广义J集的变化规律.     

Julia集的广义同步

研究了两个不同的Julia集耦合实现广义同步的问题. 不同于以往对Julia集的研究仅限于对一个独立的Julia集的性质, 制图等方面的讨论, 本文提出了两个不同的Julia集广义同步的思想, 并以经典的复二次多项式系统z_n+1 = z²_n+c为例, 分别采用线性和非线性耦合的方法对该系统不同参数的Julia集进行了广义同步. 仿真结果表明了方法的有效性.     

覆盖广义粗集理论中的拓扑学方法

本文是从拓扑学的角度来看覆盖广义粗集理论,先引进拓扑空间的相对内部和相对闭包的概念并对其进行了较深入的研究.主要结果有,(1)相对内部和相对闭包的基本性质;(2)同一拓扑的两个子基生成相同的相对内部和相对闭包的充分必要条件;(3)相对内部运算和相对闭包运算的公理化.这些结果可以看作是覆盖广义粗集的理论基础,同时对于覆盖广义粗集理论的研究也提供了一种尝试的方法.     

D4对称平面排列映射广义充满Julia集

为了更加直观、有效地在参数空间挑选参数构造出具有D4对称特性的平面排列映射的混沌吸收子和广义充满Julia集，在参数空间任选两个实参数构造参数断面，构造其上的广义M集。在这种广义M集的周期区域中挑选参数，可以由计算机生成大量新颖的广义充满Julia集。为了揭示出这种广义充满Julia集内部的复杂结构，给出了两种构造方法。为具有平面对称特性的动力系统的计算机图形化研究工作增添了新形式的艺术图像。     

基于广义归结的定理机器证明系统

本文使用Ｃ—ＰＲＯＬＯＧ语言在ＳＵＮ工作站上设计实现了基于广义归结和基于归结的两个定理机器证明系统ＧＲＭ,ＲＭ,证明了《数学原理》中Ｐａｒｔ１：ｍａｔｈｅｍａｔｉｃａｌｌｏｇｉｃ中ＳｅｃｔｉｏｎＡ与ＳｅｃｔｉｏｎＢ中全部定理（３５０个）．讨论ＧＲＭ和ＲＭ的时、空复杂性,并在实现设计中提出新的全局调度策略及归结式的化简、排序策略,以单子句恒真、恒假的判断代替了广义归结中的自归结,实现了带ＯＣＣＵＲ检查的模式匹配．     

Inductive expansion: A calculus for verifying and synthesizing functional and logic programs

Guarded Horn clauses over a many-sorted polymorphic signature provide a powerful syntax for design specifications. Expressed as a set of positive Gentzen clauses with a common guard, requirements to such a specification can be proved top-down by inductive expansion: conclusions and generators of the clauses are transformed via resolution and paramodulation upon axioms, lemmas and induction hypotheses into the guard. Case distinctions are generated when axioms or lemmas are applied in parallel. They split the proof into subexpansions, which are later rejoined by applying disjunctive lemmas. Induction orderings need not be selected before redices for induction hypotheses have been created.The controlled expansion of requirements to a function (or predicate) may produce axioms representing a program for that function. This generalizes traditional approaches to program synthesis such as fold& unfold, divide&conquer or deductive tableaus. Ground confluent and strongly terminating design specifications yield decidable criteria for constructors and unsolvable goals and thus reduce the search space of inductive expansion.     

Horn equational theories and paramodulation

A language of equational programs together with an inference system, based on paramodulation is defined. The semantics of the language is given with respect to least models, least fixpoints and success sets and its soundness and completeness is proven using fixpoint theory. The necessity of the functional reflexive axioms is investigated in detail. Finally, the application of these ideas to term rewriting systems is outlined by discussing directed paramodulation and narrowing.     

一种基于广义模糊性质集的图像分割方法

本文提出了一种基于广义模糊性质集的图像分割方法，它利用图像的广义隶属函数，把图像灰度转换成广义的模糊集合，通过对图像作多次增强而实现图像分割。实验结果表明，本文提出的方法与Ｏｔｓｕ法、熵函数法和ＦＣＭ２Ｄ法相比，在分割速度和分割质量上，都有下同程度的提高。     

Experiments with semantic paramodulation

A semantic restriction is presented for use with paramodulation in automated theorem-proving programs. The method applies to first-order formulas with equality whole clause forms are Horn sets. In this method, an interpretation is given to the program along with the set of clauses to be refuted. The intention is to have the interpretation serve as an example to guide the search for a refutation. The semantic restriction was incorporated into an existing automated theorem-proving program, and a number of experiments were conducted on theorems in abstract algebra. Semantic paramodulation is an extension of set-of-support paramodulation. A comparison of the two strategies was used as the basis for experimentation. The semantic searches performed markedly better than the corresponding set-of-support searches in many of the comparisons. The semantic restriction seems to make the program less sensitive to the choice of rewrite rules and supported clauses.     

二阶多智能体系统的线性广义一致性

首次针对二阶多智能体系统提出广义一致性的概念;然后探讨有向网络拓扑结构下的二阶多智能体系统的线性广义一致性问题.通过设计有效的控制协议,使用代数图论和稳定性理论,推导获得二阶的多智能体系统以及带有通信延迟的二阶系统实现线性广义一致性的充分且必要条件.结果表明,在有向网络中,耦合增益参数和拉普拉斯矩阵的特征值对达到广义一致起着关键作用;最后,数值仿真验证了结果的正确性.     

模糊集间的语义关联度及其应用

本文提出了一种描述模糊集间近似程度的语义关联度概念,它不仅与模糊集论域元素的隶属度有关,而且考虑了论域元素间的语义近似程度,因此它比过去模糊数学中定义的各种距离和贴近度等概念更加精细地刻划了模糊集间的相似性,从而在人工智能和其它领域中可有广泛应用,文中列举了它在情报检索和正文分类等方面的应用实例。此外,论文还给了两种近似地计算语义关联度的算法。     

基于层次分析法的广义M-J集颜色特征向量描述

针对广义M-J集,提出一种基于层次分析法的颜色特征向量描述。在对广义M-J集颜色特征描述的过程中,利用层次分析法原理,只需两两比较不同颜色特征的表示方法来描述目标图像颜色的重要性,方法简单,可以避免原始方法中因为人的主观性、随意性而带来的不一致、不统一的现象。实验结果表明,该描述方法相对单一方法更有效。     

广义不确定系统稳定鲁棒控制

利用李雅普诺夫稳定理论和矩阵范数性质研究了广义不确定系统的稳定鲁棒控制问题.在不同情况下,分别给出了保证闭环不确定系统渐进稳定的两类稳定鲁棒控制:状态反馈、正常动态补偿器的设计方法,得到了鲁棒稳定控制的不确定量的范数界,而且提出了在多个稳定鲁棒控制器中寻找具有最大的不确定量范数界的控制器的方案.