几何信息压缩在计算机自动推理系统中的研究

着力于在推理系统中合理地组织几何信息的数据结构,提高推理的效率,减小算法的时间复杂度,对信息进行了描述,采用了等价类、角的压缩和归一化、信息组对等方法,阐述了几何信息在推理时压缩的实现,介绍了压缩信息的展开与提取技术,并通过计算机程序证明该类方法可以实现。实验结果表明,对较复杂的几何问题来说,采用这种方法可以显著提高推理效率。     

相干命题逻辑自然推理系统NR的自动证明*

给出了相干命题逻辑自然推理系统NR的自动证明算法。首先将待证命题公式A的子公式组成一个初始集合P,对其中的元素采用系统NR的推理规则得到新的命题公式加入P,当得到秩为0的A时命题得证;然后对A的证明树进行整理即得到演绎序列。对系统NR的大部分定理证明取得了良好的效果,算法生成的演绎序列清晰可读,接近手工推理。     

基于前向推理的平面解析几何自动推理系统研究与实现

采用传统的前向推理策略，使用了代数和几何相结合的推理方法，把解方程作为核心思想，较完善地实现了平面解析几何的自动推理系统。实践证明，本系统可以对大部分初等平面解析几何问题进行自动解题。     

重言衍推系统的试探法自动证明

提出针对重言衍推系统的模仿人类思维方式的生成可读证明的算法:试探法.试探法将待证的命题逐步分解成子命题并构造一颗证明树,对重言衍推系统中的定理证明取得了较好的效果.     

亲属关系的逻辑意义及其自动推理

用一阶谓词逻辑设计了一个亲属关系的自动推理模型。首先,把亲属关系（称谓）视为谓词,相关的人物视为变元,把亲属关系和有关性质用“或”、“与”及“逆”等运算符号联结成亲属关系表达式。然后,选取11种基本的亲属关系作为亲属基元,并构造亲属基元转换和化简的九大定理,用以描写和定义其他一百多种亲属关系,从而形成亲属关系转换的核心知识库。最后,给出一种简洁的亲属关系转换算法,主要包括连接、求逆、化简和组配等运算。     

双向推理系统在初等几何自动解题中的实现*

目前采用较多的初等几何自动推理方法是单向推理法（包括前向推理和后向推理）,探讨将前推法与后推法结合起来进行初等几何的推理。实践证明,对较为复杂的几何问题来说,采用这种方法可以显著提高推理效率。     

支持用户自定义谓词的自动定理证明的研究

在先前设计的一个出具证明编译器原型基础上,增加了可用来描述数据结构性质的自定义谓词,对断言语言表达能力方面做了提升.在出具证明编译器的框架内,借助自动定理证明技术,针对自定义谓词的特点,设计了专门的推理规则,由此实现自定义谓词专用的自动定理证明器原型,并将它并入系统原来的自动定理证明器中.该原型可以用来证明操作单链表、二叉树等共享数据结构的程序的性质,其程序规范中可以使用自定义谓词描述数据有序性、链表长度等性质.     

案例推理在智能化网站自动生成系统中的应用

案例推理是专家系统（ES）中一种重要的推理技术,本文将基于案例的推理方法应用于网站自动生成系统中.系统通过提供与当前网站相似的网站案例,增强领域专家的类比推理及记忆能力,充分利用案例中隐含的专家常识知识,大大地缩短开发Website项目的周期,提高工作效率.文章在最后通过应用实例表明了该系统的有效性和可行性.     

自动推理中反证法的研究

计算机自动解几何问题,已经有不少研究成果.前推搜索法能够产生可读证明,因此也是应用较多的一种方法.在目前诸多算法中,一般是采用直接证明的方法.在手工证明几何问题的方法中,间接证明也是一种重要的方法,其中反证法是较为有效的方法之一.在计算机自动推理研究中,如何运用反证法,是自动推理中的一个难题,关于这方面的研究成果也少有报道.给出一个算法:根据命题的结论将命题分类,针对不同类型,设计不同的解决方案.有效地实现了反证法在自动推理中的运用.     

相干命题逻辑系统R的一种演绎生成算法

本文提出了相干命题逻辑系统R的一种演绎生成算法--试探法。该算法采用后向推理法,依据推理规则将待证命题逐步分解成子命题并构造一棵证明树,对系统R中的定理证明取得了较好的效果。     

三角函数表达式的计算机自动化简

从人的思维模式和技巧出发,通过观察专家直觉导出了一套三角函数化简规则链表.利用这套规则链表进行推理可以有效地化简一些对人工推导来说也有一定难度的三角函数表达式,同时产生可读的化简过程.有关算法已用Lisp编程实现.文中将它与Maple9和Mathematica作了测试对比,结果显示在三角函数化简功能方面作者的软件明显优于Maple和Mathematica.     

Missing Proofs Found

For close to a century, despite the efforts of fine minds that include Hilbert and Ackermann, Tarski and Bernays, ukasiewicz, and Rose and Rosser, various proofs of a number of significant theorems have remained missing – at least not reported in the literature – amply demonstrating the depth of the corresponding problems. The types of such missing proofs are indeed diverse. For one example, a result may be guaranteed provable because of being valid, and yet no proof has been found. For a second example, a theorem may have been proved via metaargument, but the desired axiomatic proof based solely on the use of a given inference rule may have eluded the experts. For a third example, a theorem may have been announced by a master, but no proof was supplied. The finding of missing proofs of the cited types, as well as of other types, is the focus of this article. The means to finding such proofs rests with heavy use of McCune's automated reasoning program OTTER, reliance on a variety of powerful strategies this program offers, and employment of diverse methodologies. Here we present some of our successes and, because it may prove useful for circuit design and program synthesis as well as in the context of mathematics and logic, detail our approach to finding missing proofs. Well-defined and unmet challenges are included.     

正向推理型故障模糊预测系统的知识表示与推理

根据故障预测问题的要求,利用模糊数学理论,对预测知识进行了模糊集合描述,提出了一种面向正向推理的知识表示法,给出正向推理型故障模糊预测的推理过程。     

Automating the Search for Elegant Proofs

The research reported in this article was spawned by a colleague's request to find an elegant proof (of a theorem from Boolean algebra) to replace his proof consisting of 816 deduced steps. The request was met by finding a proof consisting of 100 deduced steps. The methodology used to obtain the far shorter proof is presented in detail through a sequence of experiments. Although clearly not an algorithm, the methodology is sufficiently general to enable its use for seeking elegant proofs regardless of the domain of study. In addition to (usually) being more elegant, shorter proofs often provide the needed path to constructing a more efficient circuit, a more effective algorithm, and the like. The methodology relies heavily on the assistance of McCune's automated reasoning program OTTER. Of the aspects of proof elegance, the main focus here is on proof length, with brief attention paid to the type of term present, the number of variables required, and the complexity of deduced steps. The methodology is iterative, relying heavily on the use of three strategies: the resonance strategy, the hot list strategy, and McCune's ratio strategy. These strategies, as well as other features on which the methodology relies, do exhibit tendencies that can be exploited in the search for shorter proofs and for other objectives. To provide some insight regarding the value of the methodology, I discuss its successful application to other problems from Boolean algebra and to problems from lattice theory. Research suggestions and challenges are also offered.     

时空推理研究进展

与时态和空间有关的推理问题是人工智能研究中重要的组成部分,在地理信息系统、时空数据库、CAD/CAM等领域有着重要应用.从本体、表示模型和推理方法3个方面分别介绍了时态推理和空间推理的发展,并在此基础上综述了时空结合推理的研究进展.讨论了目前时空推理领域存在的问题,并指出了今后的发展方向.     

A Milestone Reached and a Secret Revealed

In this special issue of the Journal of Automated Reasoning, this article sets the stage for the succeeding articles, all of which focus on finding proofs of theorems of formal logic and on the various methodologies that were employed. The proofs that are offered mark an important milestone for automated reasoning and for logic, for each of them is indeed new. One key question this article answers is why an automated reasoning program was able to find proofs that had eluded some of the finest mathematicians and logicians for many, many decades.