Citation:  ChangYang Wu, Xin Lin, ZhenYa Huang, Yu Yin, JiaYu Liu, Qi Liu, Gang Zhou. Clauselevel Relationshipaware Math Word Problems Solver. Machine Intelligence Research, vol. 19, no. 5, pp.425438, 2022. https://doi.org/10.1007/s1163302213512 
[1] 
T. Brants. Natural language processing in information retrieval. In Proceedings of Computational Linguistics in the Netherlands, University of Antwerp, Antwerp, Belgium, pp. 1–13, 2003.

[2] 
Y. K. Xian, Z. H. Fu, S. Muthukrishnan, G. De Melo, Y. F. Zhang. Reinforcement knowledge graph reasoning for explainable recommendation. In Proceedings of the 42nd International ACM SIGIR Conference on Research and Development in Information Retrieval, ACM, Paris, France, pp. 285–294, 2019. DOI: 10.1145/3331184.3331203.

[3] 
D. X. Zhang, L. Wang, L. M. Zhang, B. T. Dai, H. T. Shen. The gap of semantic parsing: A survey on automatic math word problem solvers. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 42, no. 9, pp. 2287–2305, 2019. DOI: 10.1109/TPAMI.2019.2914054.

[4] 
D. P. Huang, S. M. Shi, C. Y. Lin, J. Yin. Learning finegrained expressions to solve math word problems. In Proceedings of the Conference on Empirical Methods in Natural Language Processing, Association for Computational Linguistics, Copenhagen, Denmark, pp. 805–814, 2017. DOI: 10.18653/v1/D171084.

[5] 
Z. P. Xie, S. C. Sun. A goaldriven treestructured neural model for math word problems. In Proceedings of the 28th International Joint Conference on Artificial Intelligence Main track, Macao, China, pp. 5299–5305, 2019. DOI: 10.24963/ijcai.2019/736.

[6] 
Y. N. Hong, Q. Li, D. Ciao, S. Y. Huang, S. C. Zhu. Learning by fixing: Solving math word problems with weak supervision. In Proceedings of the AAAI Conference on Artificial Intelligence, vol. 35, no. 6, pp. 4959–4967, 2021.

[7] 
S. Roy, D. Roth. Unit dependency graph and its application to arithmetic word problem solving. In Proceedings of the 31st AAAI Conference on Artificial Intelligence, ACM, San Francisco, USA, pp. 3082–3088, 2017.

[8] 
J. R. Li, L. Wang, J. P. Zhang, Y. Wang, B. T. Dai, D. X. Zhang. Modeling intrarelation in math word problems with different functional multihead attentions. In Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics, Florence, Italy, pp. 6162–6167, 2019. DOI: 10.18653/v1/P191619.

[9] 
J. P. Zhang, L. Wang, R. K. W. Lee, Y. Bin, Y. Wang, J. Shao, E. P. Lim. Graphtotree learning for solving math word problems. In Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics, ACL, pp. 3928–3937, 2020. DOI: 10.18653/v1/2020.aclmain.362.

[10] 
D. A. Balota, G. B. F. d′Arcais, K. Rayner. Comprehension Processes in Reading. New York, USA: Routledge, 1990. DOI: 10.4324/9780203052389.

[11] 
T. A. Van Dijk, W. Kintsch. Strategies of Discourse Comprehension. New York, USA: Academic Press, 1983.

[12] 
M. Adoniou, Q. Yi. Language, mathematics and English language learners. The Australian Mathematics Teacher, vol. 70, no. 3, pp. 3–13, 2014.

[13] 
X. Lin, Z. Y. Huang, H. K. Zhao, E. H. Chen, Q. Liu, H. Wang, S. Wang. HMS: A hierarchical solver with dependencyenhanced understanding for math word problem. In Proceedings of AAAI Conference on Artificial Intelligence, vol. 35, no. 5, pp. 4232–4240, 2021.

[14] 
E. A. Feigenbaum, J. Feldman. Computers and Thought. New York, USA: McGrawHill, 1963.

[15] 
D. G. Bobrow. Natural Language Input for a Computer Problem Solving System, Series/Report no. AITR219, Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA, 1964.

[16] 
J. R. Slagle. Experiments with a deductive questionanswering program. Communications of the ACM, vol. 8, no. 12, pp. 792–798, 1965. DOI: 10.1145/365691.365960.

[17] 
C. R. Fletcher. Understanding and solving arithmetic word problems: A computer simulation. Behavior Research Methods,Instruments,

[18] 
Y. Bakman. Robust understanding of word problems with extraneous information. [Online], Available: https://arxiv.org/pdf/math/0701393.pdf, 2007.

[19] 
N. Kushman, Y. Artzi, L. Zettlemoyer, R. Barzilay. Learning to automatically solve algebra word problems. In Proceedings of the 52nd Annual Meeting of the Association for Computational Linguistics, Baltimore, Maryland, pp. 271–281, 2014. DOI: 10.3115/v1/P141026.

[20] 
A. Mitra, C. Baral. Learning to use formulas to solve simple arithmetic problems. In Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics, Berlin, Germany, pp. 2144–2153, 2016. DOI: 10.18653/v1/P161202.

[21] 
R. KoncelKedziorski, H. Hajishirzi, A. Sabharwal, O. Etzioni, S. D. Ang. Parsing algebraic word problems into equations. Transactions of the Association for Computational Linguistics, vol. 3, pp. 585–597, 2015. DOI: 10.1162/tacl_a_00160.

[22] 
S. M. Shi, Y. H. Wang, C. Y. Lin, X. J. Liu, Y. Rui. Automatically solving number word problems by semantic parsing and reasoning. In Proceedings of the Conference on Empirical Methods in Natural Language Processing, Lisbon, Portugal, pp. 1132–1142, 2015. DOI: 10.18653/v1/D151135.

[23] 
D. Q. Huang, S. M. Shi, C. Y. Lin, J. Yin, W. Y. Ma. How well do computers solve math word problems? Largescale dataset construction and evaluation. In Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics, Berlin, Germany, pp. 887–896, 2016. DOI: 10.18653/v1/P161084.

[24] 
Y. Wang, X. J. Liu, S. M. Shi. Deep neural solver for math word problems. In Proceedings of the Conference on Empirical Methods in Natural Language Processing, Copenhagen, Denmark, pp. 845–854, 2017. DOI: 10.18653/v1/D171088.

[25] 
L. Wang, D. X. Zhang, L. L. Gao, J. K. Song, L. Guo, H. T. Shen. MathDQN: Solving arithmetic word problems via deep reinforcement learning. In Proceedings of AAAI Conference on Artificial Intelligence, vol. 32, no. 1, pp. 5545–5552, 2018. DOI: 10.1609/aaai.v32i1.11981.

[26] 
L. Wang, Y. Wang, D. Cai, D. X. Zhang, X. J. Liu. Translating a math word problem to an expression tree. [Online], Available: https://arxiv.org/pdf/1811.05632.pdf, 2018.

[27] 
T. R. Chiang, Y. N. Chen. Semanticallyaligned equation generation for solving and reasoning math word problems. In Proceedings of the Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Association for Computational Linguistics, Minneapolis, Minnesota, pp. 2656–2668, 2018. DOI: 10.18653/v1/N191272.

[28] 
L. Wang, D. X. Zhang, J. P. Zhang, X. Xu, L. L. Gao, B. T. Dai, H. T. Shen. Templatebased math word problem solvers with recursive neural networks. In Proceedings of AAAI Conference on Artificial Intelligence, vol. 33, no. 1, pp. 7144–7151, 2019. DOI: 10.1609/aaai.v33i01.33017144.

[29] 
Q. Z. Wu, Q. Zhang, J. L. Fu, X. J. Huang. A knowledgeaware sequencetotree network for math word problem solving. In Proceedings of the Conference on Empirical Methods in Natural Language Processing, pp. 7137–7146, 2020. DOI: 10.18653/v1/2020.emnlpmain.579.

[30] 
Q. Z. Wu, Q. Zhang, Z. Y. Wei. An edgeenhanced hierarchical graphtotree network for math word problem solving. In Proceedings of the Findings of the Association for Computational Linguistics, Punta Cana, Dominican Republic, pp. 1473–1482, 2021. DOI: 10.18653/v1/2021.findingsemnlp.127.

[31] 
M. Yuhui, Z. Ying, C. Guangzuo, R. Yun, H. Ronghuai. Framebased calculus of solving arithmetic multistep addition and subtraction word problems. In Proceedings of the Second International Workshop on Education Technology and Computer Science, IEEE, Wuhan, China, pp. 476–479, 2010. DOI: 10.1109/ETCS.2010.316.

[32] 
Y. X. Cao, F. Hong, H. W. Li, P. Luo. A bottomup DAG structure extraction model for math word problems. Proceedings of AAAI Conference on Artificial Intelligence, vol. 35, no. 1, pp. 39–46, 2021.

[33] 
Y. Zhang, G. Y. Zhou, Z. W. Xie, J. X. Huang. HGEN: Learning hierarchical heterogeneous graph encoding for math word problem solving. IEEE/ACM Transactions on Audio,Speech,and Language Processing, vol. 30, pp. 816–828, 2022. DOI: 10.1109/TASLP.2022.3145314.

[34] 
Z. W. Liang, J. P. Zhang, L. Wang, W. Qin, Y. S. Lan, J. Shao, X. L. Zhang. MWPBERT: Numeracyaugmented pretraining for math word problem solving. Available: https://aclanthology.org/2022.findingsnaacl.74.pdf, 2022.

[35] 
J. H. Shen, Y. C. Yin, L. Li, L. F. Shang, X. Jiang, M. Zhang, Q. Liu. Generate & Rank: A multitask framework for math word problems. In Proceedings of the Findings of the Association for Computational Linguistics: EMNLP 2021, Punta Cana, Dominican Republic, pp. 2269–2279, 2021. DOI: 10.18653/v1/2021.findingsemnlp.195.

[36] 
W. J. Yu, Y. P. Wen, F. D. Zheng, N. Xiao. Improving math word problems with pretrained knowledge and hierarchical reasoning. In Proceedings of the Conference on Empirical Methods in Natural Language Processing, Punta Cana, Dominican Republic, pp. 3384–3394, 2021. DOI: 10.18653/v1/2021.emnlpmain.272.

[37] 
M. A. K. Halliday, C. M. I. Matthiessen. An Introduction to Functional Grammar. London, UK: Routledge, 2014.

[38] 
J. Ng, K. Lee, K. H. Khng. Irrelevant information in math problems need not be inhibited: Students might just need to spot them. Learning and Individual Differences, vol. 60, pp. 46–55, 2017. DOI: 10.1016/j.lindif.2017.09.008.

[39] 
K. Barker, S. Szpakowicz. Interactive semantic analysis of clauselevel relationships. In Proceedings of the 2nd Conference of the Pacific Association for Computational Linguistics, Brisbane, Australia, pp. 22–30, 1995.

[40] 
T. Ohno, S. Matsubara, H. Kashioka, T. Maruyama, H. Tanaka, Y. Inagaki. Dependency parsing of Japanese monologue using clause boundaries. Language Resources and Evaluation, vol. 40, no. 3, pp. 263–279, 2006. DOI: 10.1007/s105790079023y.

[41] 
D. S. McNamara, J. Magliano. Toward a comprehensive model of comprehension. Psychology of Learning and Motivation, vol. 51, pp. 297–384, 2009. DOI: 10.1016/S00797421(09)510092.

[42] 
T. Mikolov, I. Sutskever, K. Chen, G. Corrado, J. Dean. Distributed representations of words and phrases and their compositionality. In Proceedings of the 26th International Conference on Neural Information Processing Systems, ACM, Lake Tahoe, Nevada, pp. 3111–3119, 2013.

[43] 
J. Devlin, M. W. Chang, K. Lee, K. Toutanova. BERT: Pretraining of deep bidirectional transformers for language understanding. In Proceedings of the Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Association for Computational Linguistics, Minneapolis, Minnesota, pp. 4171–4186, 2018. DOI: 10.18653/v1/N191423.

[44] 
L. Pang, Y. Y. Lan, J. F. Guo, J. Xu, S. X. Wan, X. Q. Cheng. Text matching as image recognition. In Proceedings of the 30th AAAI Conference on Artificial Intelligence, ACM, Phoenix, USA, pp. 2793–2799, 2016.

[45] 
O. Vinyals, M. Fortunato, N. Jaitly. Pointer networks. In Proceedings of the 28th International Conference on Neural Information Processing Systems, ACM, Montreal, Canada, pp. 2692–2700, 2015.

[46] 
K. M. He, X. Y. Zhang, S. Q. Ren, J. Sun. Delving deep into rectifiers: Surpassing humanlevel performance on imageNet classification. In Proceedings of the IEEE International Conference on Computer Vision, IEEE, Santiago, Chile, pp. 1026–1034, 2015. DOI: 10.1109/ICCV.2015.123.

[47] 
C. Z. Wu, J. Sun, J. Wang, L. F. Xu, S. Zhan. Encodingdecoding network with pyramid selfattention module for retinal vessel segmentation. International Journal of Automation and Computing, vol. 18, no. 6, pp. 973–980, 2021. DOI: 10.1007/s1163302012770.

[48] 
L. J. Zhou, J. W. Dang, Z. H. Zhang. Fault classification for onboard equipment of highspeed railway based on attention capsule network. International Journal of Automation and Computing, vol. 18, no. 5, pp. 814–825, 2021. DOI: 10.1007/s1163302112912.
