辅助线（点）自动添加的研究及在立体几何中的应用

发布时间：2018-07-03 04:28

本文选题：立体几何 + 辅助线(点)　；参考：《电子科技大学》2017年硕士论文

【摘要】：数学作为整个自然科学与信息技术的基础,是联系科学与技术至关重要的纽带。随着人工智能技术的飞速发展,数学已经逐步深入渗透到信息技术的方方面面,从认知、推理证明和计算角度研究数学问题,提高其自动求解的智能性,逐渐成为一个新的热门研究领域。对由自然语言、符号、公式等元素表示的数学问题进行自动题意分析与理解以及问题的自动求解证明,有助于促进数学自动推理理论和方法的研究,进而推进自动解题和符号计算在智慧教育中的应用和推广。辅助线(点)的添加一直以来都是初等数学立体几何问题求解中的重点和难点问题之一,而寻求一种自动添加辅助线(点)的方法来实现问题自动求解则更具挑战。本文的主要研究方向是基于策略网和价值网的蒙特卡洛树搜索自动添加辅助线(点)及在立体几何问题自动求解中的应用。本文的研究内容主要由以下三部分内容组成:1.立体几何知识表示与基础规则库的构建对初等数学立体几何知识体系中涉及的常见实体及实体间的关系属性进行命名与建模,建立问题自动求解的统一基础数据结构;并将初等几何中的定义、定理、推论、数学公式以及常用解题技巧方法等编写为推理规则,构建立体几何问题自动求解的基础规则库。2.初等数学辅助线(点)认知建模及知识库的构建通过对大量初等数学立体几何问题求解中常用辅助线(点)添加方法进行收集和分类,并综合分析与归纳每种方法的内在特征及意义,构建一套较为完整的辅助线(点)类型体系。以此体系为依托,总结每种辅助线(点)添加的共性和特性,建立统一的辅助线(点)认知模型。3.辅助线(点)自动添加方法在立体几何问题求解中的应用基于自然语言理解(NLP:Natural Language Processing)技术对题干信息进行语义理解和知识表示,在推理系统Drools的框架下,结合基础规则库与辅助线(点)认知模型,采用蒙特卡洛树搜索方式为策略控制系统,融合推理上下文事实库、规则库、图形配置和辅助线(点)的价值评估体系,准确添加满足解题需求的辅助线(点),完成问题的自动求解并根据知识推导网络生成类人解答过程。
[Abstract]:Mathematics, as the foundation of the whole natural science and information technology, is the crucial link between science and technology. With the rapid development of artificial intelligence technology, mathematics has gradually penetrated into all aspects of information technology. It has gradually become a new hot research field. The automatic analysis and understanding of mathematical problems represented by natural language, symbols, formulas, and the automatic solution of the problems are helpful to the study of the theory and method of mathematical automatic reasoning. And then promote the application and popularization of automatic problem solving and symbol calculation in wisdom education. The addition of auxiliary lines (points) has always been one of the key and difficult problems in solving the problems of elementary mathematics solid geometry, but it is more difficult to find a method of automatically adding auxiliary lines (points) to solve the problems automatically. The main research direction of this paper is to add auxiliary lines (points) automatically in Monte Carlo tree search based on strategy net and value net and its application in the automatic solution of solid geometry problems. The research content of this paper is composed of three parts as follows: 1. The representation of solid Geometry knowledge and the Construction of basic rules Database name and model the common entities and the relation attributes of the entities involved in the knowledge system of elementary mathematics solid geometry, and establish the unified basic data structure for automatic problem solving. The definitions, theorems, corollaries, mathematical formulas and common problem-solving techniques in elementary geometry are written as reasoning rules, and the basic rule base for automatic solution of solid geometry problems is constructed. The cognitive modeling of elementary mathematics auxiliary lines (points) and the construction of knowledge base are collected and classified by adding auxiliary lines (points) to a large number of elementary mathematics solid geometry problems. The intrinsic characteristics and significance of each method are analyzed and summarized synthetically, and a set of complete auxiliary line (point) type system is constructed. Based on this system, this paper summarizes the commonness and characteristics of each auxiliary line (point), and establishes a unified cognitive model of auxiliary line (point). Application of Auxiliary Line (Point) Auto-add method in solving solid Geometry problems; semantic understanding and knowledge representation of problem information based on NP: natural language processing. Under the framework of the reasoning system drools. Combining the basic rule base with the cognitive model of auxiliary line (point), using Monte Carlo tree search as the strategy control system, combining the inference context fact base, rule base, graph configuration and the value evaluation system of auxiliary line (point), the paper introduces the basic rule base and the auxiliary line (point) value evaluation system. Add the auxiliary line (point) to meet the need of solving problem accurately, complete the automatic solution of the problem, and derive the process of generating humanoid solution according to the knowledge.
【学位授予单位】：电子科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O182

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