Semantic extraction of domain-dependent mathematical text

doi:10.11772/j.issn.1001-9081.2021060924

Journal of Computer Applications ›› 2022, Vol. 42 ›› Issue (8): 2386-2393.DOI: 10.11772/j.issn.1001-9081.2021060924

• Artificial intelligence • Previous Articles

Semantic extraction of domain-dependent mathematical text

Xiaoyu CHEN¹^,²^,³, Wei WANG¹^,²()

^1.School of Mathematical Sciences，Beihang University，Beijing 100191，China
^2.Key Laboratory of Mathematics，Informatics and Behavioral Semantics，Ministry of Education （Beihang University），Beijing 100191，China
^3.Beijing Advanced Innovation Center for Big Data and Brain Computing，Beihang University，Beijing 100191，China

Received:2021-06-02 Revised:2021-07-27 Accepted:2021-08-06 Online:2022-08-09 Published:2022-08-10
Contact: Wei WANG
About author:CHEN Xiaoyu， born in 1982， Ph. D.， lecturer. His research interests include knowledge representation， machine learning.
WANG Wei， born in 1997， M. S. candidate. His research interests include mathematical knowledge management， natural language processing.

领域相关的数学文本语义抽取

陈肖宇¹^,²^,³, 王伟¹^,²()

^1.北京航空航天大学数学科学学院, 北京 100191
^2.数学、信息与行为教育部重点实验室(北京航空航天大学), 北京 100191
^3.北京航空航天大学大数据科学与脑机智能高精尖创新中心, 北京 100191

通讯作者: 王伟
作者简介:陈肖宇（1982—），男，辽宁沈阳人，讲师，博士，CCF会员，主要研究方向：知识表示、机器学习；
王伟（1997—），男，安徽宿州人，硕士研究生，主要研究方向：数学知识管理、自然语言处理。

Abstract

Abstract:

Aiming at the problem of insufficient acquisition of document semantic information in the field of science and technology，a set of rule-based methods for extracting semantics from domain-dependent mathematical text were proposed. Firstly， domain concepts were extracted from the text and semantic mapping between mathematical entities and domain concepts were realized. Secondly， through context analysis for mathematical symbols， entity mentions or corresponding text descriptions of mathematical symbols were obtained and the semantics of the symbols were extracted. Finally， the semantic analysis of expressions was completed based on the extracted semantics of mathematical symbols. Taking linear algebra texts as research examples， a semantic tagging dataset was constructed for experiments. Experimental results show that the proposed methods achieve a precision higher than 93% and a recall higher than 91% on semantic extraction of identifiers， linear algebra entities and expressions.

Key words: semantic extraction, entity mention, context analysis, mathematical language processing, mathematical text understanding

摘要：

针对科技领域文档语义信息获取不充分的问题，提出一套基于规则的数学领域相关文本的语义抽取方法。首先从文本中提取领域概念并实现数学实体与领域概念之间的语义映射；然后对数学符号的上下文进行分析，获取数学符号的实体指代或文字描述，进而抽取其语义；最后基于已抽取的数学符号语义实现表达式的语义分析。以线性代数文本为研究实例，构建了一个语义标注数据集并进行实验，实验结果表明所提方法对标识符、线性代数实体以及表达式的语义抽取具有93%以上的精确率和91%以上的召回率。

关键词: 语义抽取, 实体指代, 上下文分析, 数学语言处理, 数学文本理解

CLC Number:

TP391

Xiaoyu CHEN, Wei WANG. Semantic extraction of domain-dependent mathematical text[J]. Journal of Computer Applications, 2022, 42(8): 2386-2393.

陈肖宇, 王伟. 领域相关的数学文本语义抽取[J]. 《计算机应用》唯一官方网站, 2022, 42(8): 2386-2393.

Figures/Tables 12

Fig. 1 Framework of semantic extraction method

Fig. 2 Hierarchical structure of determinant concept

Fig. 3 Hierarchical structure of matrix concept

Tab. 1 List of sentence templates

编号	语句模板
1	TextDesc <ID>
2	TextDesc a （与\|和） <ID>
3	<ID> a （是\|为） TextDesc
4	<ID> （是\|为） TextDesc
5	用 <ID> 表示TextDesc

Fig. 4 Mention storage of identifier

Fig. 5 Semantic linking procedure of identifier

Fig. 6 Conversion from infix expression to expression tree

Tab. 2 List of semantics （Part ）

实体指代或文字描述	领域概念	段落序数	语句序数	表达式序数	起始索引	结束索引
$a 11 ⋯ a 1 n ⋮ ⋮ a m 1 ⋯ a m n$	$m × n$ 阶矩阵	3	8	7	2	4
对称矩阵	对称矩阵	5	9	10	3	5
$100010001$	三阶对角行列式	6	2	4	1	3
上三角行列式	上三角行列式	8	1	6	7	9

Tab. 2 List of semantics （Part ）

实体指代或文字描述	领域概念	段落序数	语句序数	表达式序数	起始索引	结束索引
$a 11 ⋯ a 1 n ⋮ ⋮ a m 1 ⋯ a m n$	$m × n$ 阶矩阵	3	8	7	2	4
对称矩阵	对称矩阵	5	9	10	3	5
$100010001$	三阶对角行列式	6	2	4	1	3
上三角行列式	上三角行列式	8	1	6	7	9

Tab. 3 Experimental data statistics

章节标题	实体数	标识符数	表达式数
合计	223	1 806	820
行列式	26	130	76
矩阵	105	646	309
向量组	34	157	94
线性方程组	11	139	46
相似变换	38	486	220
二次型	9	248	75

Tab. 4 Evaluation dataset

类型	样本数
实体	223
标识符	1 204
表达式	68

Tab. 5 Evaluation of semantic extraction results

抽取对象	strict matching			soft matching
抽取对象	P	R	F1	P	R	F1
标识符	0.983	0.920	0.950	1.000	0.936	0.967
实体	0.978	0.978	0.978	0.996	0.996	0.996
表达式	0.939	0.912	0.925	1.000	0.971	0.985

Fig. 7 Linear algebra user interface

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Semantic extraction of domain-dependent mathematical text

领域相关的数学文本语义抽取

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