本文選題：立體幾何 + 輔助線(點)　； 參考：《電子科技大學(xué)》2017年碩士論文

【摘要】：數(shù)學(xué)作為整個自然科學(xué)與信息技術(shù)的基礎(chǔ),是聯(lián)系科學(xué)與技術(shù)至關(guān)重要的紐帶。隨著人工智能技術(shù)的飛速發(fā)展,數(shù)學(xué)已經(jīng)逐步深入滲透到信息技術(shù)的方方面面,從認知、推理證明和計算角度研究數(shù)學(xué)問題,提高其自動求解的智能性,逐漸成為一個新的熱門研究領(lǐng)域。對由自然語言、符號、公式等元素表示的數(shù)學(xué)問題進行自動題意分析與理解以及問題的自動求解證明,有助于促進數(shù)學(xué)自動推理理論和方法的研究,進而推進自動解題和符號計算在智慧教育中的應(yīng)用和推廣。輔助線(點)的添加一直以來都是初等數(shù)學(xué)立體幾何問題求解中的重點和難點問題之一,而尋求一種自動添加輔助線(點)的方法來實現(xiàn)問題自動求解則更具挑戰(zhàn)。本文的主要研究方向是基于策略網(wǎng)和價值網(wǎng)的蒙特卡洛樹搜索自動添加輔助線(點)及在立體幾何問題自動求解中的應(yīng)用。本文的研究內(nèi)容主要由以下三部分內(nèi)容組成:1.立體幾何知識表示與基礎(chǔ)規(guī)則庫的構(gòu)建對初等數(shù)學(xué)立體幾何知識體系中涉及的常見實體及實體間的關(guān)系屬性進行命名與建模,建立問題自動求解的統(tǒng)一基礎(chǔ)數(shù)據(jù)結(jié)構(gòu);并將初等幾何中的定義、定理、推論、數(shù)學(xué)公式以及常用解題技巧方法等編寫為推理規(guī)則,構(gòu)建立體幾何問題自動求解的基礎(chǔ)規(guī)則庫。2.初等數(shù)學(xué)輔助線(點)認知建模及知識庫的構(gòu)建通過對大量初等數(shù)學(xué)立體幾何問題求解中常用輔助線(點)添加方法進行收集和分類,并綜合分析與歸納每種方法的內(nèi)在特征及意義,構(gòu)建一套較為完整的輔助線(點)類型體系。以此體系為依托,總結(jié)每種輔助線(點)添加的共性和特性,建立統(tǒng)一的輔助線(點)認知模型。3.輔助線(點)自動添加方法在立體幾何問題求解中的應(yīng)用基于自然語言理解(NLP:Natural Language Processing)技術(shù)對題干信息進行語義理解和知識表示,在推理系統(tǒng)Drools的框架下,結(jié)合基礎(chǔ)規(guī)則庫與輔助線(點)認知模型,采用蒙特卡洛樹搜索方式為策略控制系統(tǒng),融合推理上下文事實庫、規(guī)則庫、圖形配置和輔助線(點)的價值評估體系,準確添加滿足解題需求的輔助線(點),完成問題的自動求解并根據(jù)知識推導(dǎo)網(wǎng)絡(luò)生成類人解答過程。
[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.
【學(xué)位授予單位】：電子科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O182

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