A Meaning-Based Statistical English Math Word Problem Solver

Proceedings of NAACL-HLT 2018, pages 652–662 New Orleans, Louisiana, June 1 - 6, 2018. c⃝2018 Association for Computational Linguistics A Meaning-based Statistical English Math Word Problem Solver Chao-Chun Liang, Yu-Shiang Wong, Yi-Chung Lin and Keh-Yih Su Institute of Information Science, Academia Sinica, Taiwan {ccliang, yushiangwtw, lyc, kysu}@iis.sinica.edu.tw Abstract We introduce MeSys, a meaning-based ap- proach, for solving English math word problems (MWPs) via understanding and reasoning in this paper. It first analyzes the text, transforms both body and question parts into their corresponding logic forms, and then performs inference on them. The associated context of each quantity is rep- resented with proposed role-tags (e.g., nsubj, verb, etc.), which provides the flex- ibility for annotating an extracted math quantity with its associated context infor- mation (i.e., the physical meaning of this quantity). Statistical models are proposed to select the operator and operands. A noisy dataset is designed to assess if a solver solves MWPs mainly via under- standing or mechanical pattern matching. Experimental results show that our ap- proach outperforms existing systems on both benchmark datasets and the noisy da- taset, which demonstrates that the pro- posed approach understands the meaning of each quantity in the text more. 1 Introduction The math word problem (MWP) (see Figure 1) is frequently chosen to study natural language un- derstanding and simulate human problem solving (Bakman, 2007; Hosseini et al., 2014; Liang et al., 2016) for the following reasons: (1) the an- swer to the MWP cannot be simply extracted by performing keyword/pattern matching. It thus shows the merit of understanding and inference. (2) An MWP usually possesses less complicated syntax and requires less amount of domain knowledge, so the researchers can focus on the task of understanding and reasoning. (3) The body part of MWP that provides the given infor- mation for solving the problem consists of only a few sentences. The understanding and reasoning procedures thus could be more efficiently checked. (4) The MWP solver has its own appli- cations such as Computer Math Tutor (for stu- dents in primary school) and Helper for Math in Daily Life (for adults who are not good in solving mathematics related real problems). According to the approaches used to identify entities, quantities, and to select operations and operands, previous MWP solvers can be classified into: (1) Rule-based approaches (Mukherjee and Garain, 20081; Hosseini et al., 2014), which make all related decisions based on a set of rules; (2) Purely statistics-based approaches (Kushman et al., 2014; Roy et al., 2015; Zhou et al., 2015; Upadhyay et al., 2016), in which all related deci- sions are done via a statistical classifier; (3) DNN- based approaches (Ling et al., 2017; Wang et al., 2017), which map the given text into the corre- sponding math operation/equation via a DNN; and (4) Mixed approaches, which identify entities and quantities with rules, yet, decide operands and op- erations via statistical/DNN classifiers. This cate- gory can be further divided into two subtypes: (a) Without understanding (Roy and Roth, 2015; Koncel-Kedziorski et al., …

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