Solving Algebraic Problems with Geometry Diagrams Using Syntax-Semantics Diagram Understanding

Litian Huang, Xinguo Yu, Lei Niu, Zihan Feng
{"title":"Solving Algebraic Problems with Geometry Diagrams Using Syntax-Semantics Diagram Understanding","authors":"Litian Huang, Xinguo Yu, Lei Niu, Zihan Feng","doi":"10.32604/cmc.2023.041206","DOIUrl":null,"url":null,"abstract":"Solving Algebraic Problems with Geometry Diagrams (APGDs) poses a significant challenge in artificial intelligence due to the complex and diverse geometric relations among geometric objects. Problems typically involve both textual descriptions and geometry diagrams, requiring a joint understanding of these modalities. Although considerable progress has been made in solving math word problems, research on solving APGDs still cannot discover implicit geometry knowledge for solving APGDs, which limits their ability to effectively solve problems. In this study, a systematic and modular three-phase scheme is proposed to design an algorithm for solving APGDs that involve textual and diagrammatic information. The three-phase scheme begins with the application of the state-transformer paradigm, modeling the problem-solving process and effectively representing the intermediate states and transformations during the process. Next, a generalized APGD-solving approach is introduced to effectively extract geometric knowledge from the problem’s textual descriptions and diagrams. Finally, a specific algorithm is designed focusing on diagram understanding, which utilizes the vectorized syntax-semantics model to extract basic geometric relations from the diagram. A method for generating derived relations, which are essential for solving APGDs, is also introduced. Experiments on real-world datasets, including geometry calculation problems and shaded area problems, demonstrate that the proposed diagram understanding method significantly improves problem-solving accuracy compared to methods relying solely on simple diagram parsing.","PeriodicalId":93535,"journal":{"name":"Computers, materials & continua","volume":"2015 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computers, materials & continua","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.32604/cmc.2023.041206","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

Abstract

Solving Algebraic Problems with Geometry Diagrams (APGDs) poses a significant challenge in artificial intelligence due to the complex and diverse geometric relations among geometric objects. Problems typically involve both textual descriptions and geometry diagrams, requiring a joint understanding of these modalities. Although considerable progress has been made in solving math word problems, research on solving APGDs still cannot discover implicit geometry knowledge for solving APGDs, which limits their ability to effectively solve problems. In this study, a systematic and modular three-phase scheme is proposed to design an algorithm for solving APGDs that involve textual and diagrammatic information. The three-phase scheme begins with the application of the state-transformer paradigm, modeling the problem-solving process and effectively representing the intermediate states and transformations during the process. Next, a generalized APGD-solving approach is introduced to effectively extract geometric knowledge from the problem’s textual descriptions and diagrams. Finally, a specific algorithm is designed focusing on diagram understanding, which utilizes the vectorized syntax-semantics model to extract basic geometric relations from the diagram. A method for generating derived relations, which are essential for solving APGDs, is also introduced. Experiments on real-world datasets, including geometry calculation problems and shaded area problems, demonstrate that the proposed diagram understanding method significantly improves problem-solving accuracy compared to methods relying solely on simple diagram parsing.
利用语法-语义图理解求解几何图的代数问题
由于几何对象之间的几何关系复杂多样,用几何图求解代数问题是人工智能领域的一个重大挑战。问题通常涉及文本描述和几何图形,需要对这些模态的共同理解。虽然在解决数学应用题方面已经取得了长足的进步,但解决APGDs的研究仍然无法发现解决APGDs的隐式几何知识,这限制了其有效解决问题的能力。本文提出了一种系统化、模块化的三阶段方案,设计了一种求解包含文本信息和图表信息的APGDs的算法。三相方案从状态转换器范例的应用开始,对解决问题的过程进行建模,并有效地表示过程中的中间状态和转换。其次,介绍了一种广义的apgd求解方法,从问题的文本描述和图表中有效地提取几何知识。最后,设计了一种针对图形理解的具体算法,利用向量化语法语义模型从图形中提取基本几何关系。本文还介绍了一种生成衍生关系的方法,该方法是求解APGDs的关键。在实际数据集(包括几何计算问题和阴影区域问题)上的实验表明,与单纯依赖简单图解析的方法相比,本文提出的图理解方法显著提高了问题解决的准确性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信