Proof validation in real analysis: Inferring and checking warrants

In the study reported here, we investigate the skills needed to validate a proof in real analysis, i.e., to determine whether a proof is valid. We first argue that when one is validating a proof, it is not sufficient to make certain that each statement in the argument is true. One must also check that there is good reason to believe that each statement follows from the preceding statements or from other accepted knowledge, i.e., that there is a valid warrant for making that statement in the context of this argument. We then report an exploratory study in which we investigated the behavior of 13 undergraduates when they were asked to determine whether or not a particular flawed mathematical argument is a valid mathematical proof. The last line of this purported proof was true, but did not follow legitimately from the earlier assertions in the proof. Our findings were that only six of these undergraduates recognized that this argument was invalid and only two did so for legitimate mathematical reasons. On a more positive note, when asked to consider whether the last line of the proof followed from previous assertions, a total of 10 students concluded that the statement did not and rejected the proof as invalid.     

Concept of Compound-Agent and Its Application

The novel concept of Compound-Agent is proposed, which consists of some independent sub-agents that share common beliefs and employ community actions. The Explicit Model of Coordination, which is used in the coordination of the sub-agents of Compound-Agent, is provided. The actions of each sub-agent are rule-based determined, and the rule base can be adjusted on time. The approximate fuzzy reasoning is used to improve the speed of learn and reduce the number of rules, which makes Compound-Agent suitable for real time and dynamic applications. A real application, the design of the control system of flat-knitting machine employing the concept of Compound-Agent, is discussed briefly.     

三I方法综述——它的提出、发展、应用和逻辑版本

对三I方法提出的背景、三I方法的推广与应用作了综述,介绍三I方法在数理逻辑学中的版本。     

更新理论推理过程及其应用

更新过程和马尔可夫更新过程中均有相对应的更新方程,实际问题中有许多变量都满足更新方程.但是在运用更新方程时,对于一些感兴趣的变量很难直接套用更新方程,这就使更新方程在实际问题的应用有许多困难.针对这个问题,总结归纳了应用更新方程的更新理论推理过程,给出了具体的推理方法和步骤,并举例进行了说明.     

Investigating high-school students’ reasoning strategies when they solve linear equations

A cross-curricular structured-probe task-based clinical interview study with 44 pairs of third-year high-school mathematics students, most of whom were high achieving, was conducted to investigate their approaches to a variety of algebra problems. This paper presents results from one problem that involved solving a set of three linear equations of the form ax ± b = cx ± d. One of the equations had a unique solution, another was an identity, and the third resulted in a contradiction. Most pairs of students were able to solve the equation resulting in a unique solution using symbol-manipulation algorithms or by a graphical approach. On the equations resulting in an identity or a contradiction, most student pairs did not know how to interpret the results of their symbol manipulation, and few turned to another representation when symbol manipulation failed them. The constructs of versatility and adaptability [Sfard, A., & Linchevski, L. (1994). The gains and the pitfalls of reification—The case of algebra. Educational Studies in Mathematics, 26, 191-228] guided our interpretation of the findings.     

典型模糊控制器的插值形式

推导出了单输入单输出、双输入单输出典型Mamdani模糊控制器的插值解析表达式，并推广到输出采用输入变量函数的典型T—S模糊控制器。典型Mamdani模糊控制器的输入采用正规模糊集、三角形全交迭的隶属函数，输出采用单点模糊数。这些插值表达式在一定程度上揭示了典型模糊控制器的本质特征，为设计和优化提供了准确的解析模型，同时也为模糊控制器的实际应用提供了一种快速精确的控制算法。     

Investigating written expressions of mathematical reasoning for students with learning disabilities

Assessment results from two open-construction response mathematical tasks involving fractions and decimals were used to investigate written expression of mathematical reasoning for students with learning disabilities. The solutions and written responses of 51 students with learning disabilities in fourth and fifth grade were analyzed on four primary dimensions: (a) accuracy, (b) five elements of mathematical reasoning, (c) five elements of mathematical writing, and (d) vocabulary use. Results indicate most students were not accurate in their problem solution and communicated minimal mathematical reasoning in their written expression. In addition, students tended to use general vocabulary rather than academic precise math vocabulary and students who provided a visual representation were more likely to answer accurately. To further clarify the students struggles with mathematical reasoning, error analysis indicated a variety of error patterns existed and tended to vary widely by problem type. Our findings call for more instruction and intervention focused on supporting students mathematical reasoning through written expression. Implications for research and practice are presented.     

基于格值命题逻辑系统LP(X)的不确定性推理

讨论了基于格值命题逻辑系统LP（X）的不确定性推理，证明了FMP和FMT等不确定推理规则，为进一步讨论语言值逻辑推理提供逻辑基础。     

一种新的模糊推理方法

模糊推理作为模糊控制的主要部分已有将近三十年的研究历史 ,但其基本原理未有公论。本文提出一种新的推理方法 ,引入优化思想来说明模糊推理的基本原理     

基于Web智能化网络系统配置管理的研究与实现

介绍了基于Web网络管理的总体实现和重要框图，及人工智能技术在网络管理的应用，基于规则的推理、基于事件的推理，大大简化了网络管理，提高了网络管理系统的性能．作者给出了所研究的网络管理系统的总体设计，并对网络管理做了总结和展望。