Automatically Solving Number Word Problems by Semantic Parsing and Reasoning

By Shuming Shi, Yuehui Wang, Chin-Yew Lin, Xiaojiang Liu, Yong Rui. 2015

181 citations recorded by the source corpus.

This paper presents a semantic parsing and reasoning approach to automatically solving math word problems. A new meaning representation language is designed to bridge natural language text and math expressions. A CFG parser is implemented based on 9,600 semi-automatically created grammar rules. We conduct experiments on a test set of over 1,500 number word problems (i.e., verbally expressed number problems) and yield 95.4% precision and 60.2% recall.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Natural Language Processing

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Citations in the corpus

MAWPS: A Math Word Problem Repository (2016, background): “Specific topics include number word problems (Shi et al., 2015), logic puzzle problems (Mitra and Baral, 2015), arithmetic word problems (Hosseini et al.”
A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers (2020, background): “MWP category Annotation Size Dolphin1878 (Shi et al., 2015) Number-word problems Equation/answer 1,878 AI2 (Hosseini et al., 2014) IL (Roy et al., 2015) AllArith (Roy and Roth, 2017) Arithmetic word problems Equation/answer 395 562 831 KAZB (Kushman et al., 2014) ALGES (Koncel-Kedziorski et al.,…”
Semantically-Aligned Equation Generation for Solving and Reasoning Math Word Problems (2018, background): “…category treats math word problems as a parsing task about transforming natural language into the logical form (Roy et al., 2015; Roy and Roth, 2015; Shi et al., 2015; Koncel-Kedziorski et al., 2015; Roy et al., 2016; Roy and Roth, 2018), 2) the second one focuses on retrieving proper predeﬁned…”
Deep Neural Solver for Math Word Problems (2017, methodology): “al Shi et al. (2015) propose a system SigmaDolphin which automatically solves math word problems by semantic parsing and reasoning. In the same year, Koncel et.al KoncelKedziorski et al. (2015) also formalizes the problem of solving multi-sentence algebraic word problems as that of generating and sc”
How well do Computers Solve Math Word Problems? Large-Scale Dataset Construction and Evaluation (2016, methodology): “Dolphin1878: A collection built by Shi et al. (2015), containing 1,878 number word problems obtained from algebra.com and Yahoo! answers.”
A Goal-Driven Tree-Structured Neural Model for Math Word Problems (2019, methodology): “…1985; Bakman, 2007; Yuhui et al. , 2010], statistical machine learning methods [Kushman et al. , 2014; Zhou et al. , 2015; Mitra and Baral, 2016; Roy and Roth, 2018] and semantic parsing methods [ Shi et al. , 2015; Koncel-Kedziorski et al. , 2015; Huang et al. , 2017] RNN [Wang et al. , 2017].”
MathDQN: Solving Arithmetic Word Problems via Deep Reinforcement Learning (2018, neutral): “Reasoning techniques are studied in (Shi et al. 2015).”
Annotating Derivations: A New Evaluation Strategy and Dataset for Algebra Word Problems (2016, methodology): “Recent work (Kushman et al., 2014; Shi et al., 2015; Koncel-Kedziorski et al., 2015) has focused on developing solvers for algebra word problems, such as the one shown in Figure 1.”
QuaRel: A Dataset and Models for Answering Questions about Qualitative Relationships (2018, background): “Answering story problems has received attention in the domain of arithmetic, where simple algebra story questions (e.g., “Sue had 5 cookies, then gave 2 to Joe...”) are mapped to a system of equations, e.g., (Ling et al. 2017; Kushman et al. 2014; Wang, Liu, and Shi 2017; Shi et al. 2015).”
Mapping to Declarative Knowledge for Word Problem Solving (2017, background): “y the use of (one or more) variables in contructing (one or more) equations. These are typically middle or high school problems. Koncel-Kedziorski et al. (2015) looks at single equation problems, and Shi et al. (2015) focuses on number word problems. Kushman et al. (2014) introduces a template based”
Modeling Intra-Relation in Math Word Problems with Different Functional Multi-Head Attentions (2019, methodology): “…methods (Kushman et al., 2014; Mitra and Baral, 2016; Roy and Roth, 2018; Zhou et al., 2015; Huang et al., 2016) and semantic parsing-based methods (Shi et al., 2015; Koncel-Kedziorski et al., 2015; Roy and Roth, 2015; Huang et al., 2017), these methods do not need hand-crafted features and…”
Template-Based Math Word Problem Solvers with Recursive Neural Networks (2019, background): “…efforts have been mainly based on statistical machine learning (Kushman et al. 2014; Am-nueypornsakul and Bhat 2014; Zhou, Dai, and Chen 2015; Mitra and Baral 2016; Roy and Roth 2018) and semantic parsing (Shi et al. 2015; Koncel-Kedziorski et al. 2015; Roy and Roth 2015; Huang et al. 2017).”
Graph-to-Tree Learning for Solving Math Word Problems (2020, methodology): “…divided into statistical machine learning based (Kushman et al., 2014; Hosseini et al., 2014; Mitra and Baral, 2016; Roy and Roth, 2018; Zou and Lu, 2019a) and semantic parsing based (Shi et al., 2015; Koncel-Kedziorski et al., 2015; Roy and Roth, 2015; Huang et al., 2017; Zou and Lu, 2019b).”
Seeking Patterns, Not just Memorizing Procedures: Contrastive Learning for Solving Math Word Problems (2021, unknown): “…(Fletcher, 1985; Bakman, 2007), statistical machine learning methods (Kushman et al., 2014; Hos-seini et al., 2014), semantic parsing methods (Shi et al., 2015; Koncel-Kedziorski et al., 2015) and deep learning methods (Wang et al., 2017; Huang et al., 2018a,b; Xie and Sun, 2019; Zhang et…”
Investigating Math Word Problems using Pretrained Multilingual Language Models (2021, background): “, 2015), parsing-based methods (Shi et al., 2015) and generation-based methods (Wang et al.”
Learning from Explicit and Implicit Supervision Jointly For Algebra Word Problems (2016, background): “In (Shi et al., 2015), the authors focused on number word problems and proposed a system that is created using semi-automatically generated rules.”