New Generation Computing

, Volume 37, Issue 4, pp 429–452 | Cite as

Semantic Representation for Age Word Problems with Schemas

  • Sowmya S. SundaramEmail author
  • Savitha Sam Abraham


A method of representing algebraic age word problems for automated solving has been proposed. Schemas pertinent to the domain have been represented as logical predicates and functions and used as an intermediate representation. Though data-driven methods have dominated the paradigm for solving word problems recently, we demonstrate that representing these word problems formally has advantages. We illustrate that it outperforms a state-of-the-art method in terms of precision and accuracy on our newly curated and publicly available data set. Thus, we show how semantic information can improve some facets of natural language understanding.


Natural language understanding Knowledge representation and reasoning 



We thank Tata Consultancy Services for funding this research. The first author is a recipient of the research fellowship sponsored by the same. Then, we would like to thank Prof Deepak Padmanabhan for giving exhaustive and helpful comments on our manuscript. We also thank Prof Krishna M. Sivalingam for his constant encouragement and involvement.


  1. 1.
    Bakman, Y.: Robust understanding of word problems with extraneous information. (2007) arXiv preprint arXiv:math/0701393
  2. 2.
    Berners-Lee, T., Hendler, J., Lassila, O.: The semantic web. Sci. Am. 284(5), 34–43 (2001)CrossRefGoogle Scholar
  3. 3.
    Brachman, R.J., Levesque, H.J., Reiter, R.: Knowledge Representation. MIT press, London (1992)Google Scholar
  4. 4.
    Carlson, A., Betteridge, J., Kisiel, B., Settles, B., Hruschka Jr, E.R., Mitchell, T.M.: Toward an architecture for never-ending language learning. In: AAAI, vol. 5, p. 3. Atlanta (2010)Google Scholar
  5. 5.
    Dellarosa, D.: A computer simulation of childrens arithmetic word-problem solving. Behav. Res. Methods Instrum. Comput. 18(2), 147–154 (1986)CrossRefGoogle Scholar
  6. 6.
    Fletcher, C.R.: Understanding and solving arithmetic word problems: a computer simulation. Behav. Res. Methods Instrum. Comput. 17(5), 565–571 (1985)CrossRefGoogle Scholar
  7. 7.
    Hosseini, M.J., Hajishirzi, H., Etzioni, O., Kushman, N.: Learning to solve arithmetic word problems with verb categorization. In: Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP), pp. 523–533 (2014)Google Scholar
  8. 8.
    Koncel-Kedziorski, R., Hajishirzi, H., Sabharwal, A., Etzioni, O., Ang, S.D.: Parsing algebraic word problems into equations. Trans. Assoc. Comput. Linguist. 3, 585–597 (2015)CrossRefGoogle Scholar
  9. 9.
    Kushman, N., Artzi, Y., Zettlemoyer, L., Barzilay, R.: Learning to automatically solve algebra word problems. ACL 1, 271–281 (2014)Google Scholar
  10. 10.
    Liang, P.: Learning executable semantic parsers for natural language understanding. Commun. ACM 59(9), 68–76 (2016)CrossRefGoogle Scholar
  11. 11.
    Ling, W., Yogatama, D., Dyer, C., Blunsom, P.: Program induction by rationale generation: Learning to solve and explain algebraic word problems (2017). arXiv preprint arXiv:1705.04146
  12. 12.
    Manning, C.D., Surdeanu, M., Bauer, J., Finkel, J., Bethard, S.J., McClosky, D.: The stanford corenlp natural language processing toolkit. In: Proceedings of 52nd Annual Meeting of the Association for Computational Linguistics: System Demonstrations, pp. 55–60 (2014)Google Scholar
  13. 13.
    Marshall, S.P.: Schemas in Problem Solving. Cambridge University Press, Cambridge (1996)Google Scholar
  14. 14.
    Miller, E.: An introduction to the resource description framework. Bull. Am. Soc. Inf. Sci. Technol. 25(1), 15–19 (1998)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Mitra, A., Baral, C.: Learning to use formulas to solve simple arithmetic problems. In: Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pp. 2144–2153 (2016)Google Scholar
  16. 16.
    Mukherjee, A., Garain, U.: A review of methods for automatic understanding of natural language mathematical problems. Artif. Intell. Rev. 29(2), 93–122 (2008)CrossRefGoogle Scholar
  17. 17.
    Pennington, J., Socher, R., Manning, C.: Glove: Global vectors for word representation. In: Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP), pp. 1532–1543 (2014)Google Scholar
  18. 18.
    Raedt, L.D., Kersting, K., Natarajan, S., Poole, D.: Statistical relational artificial intelligence: logic, probability, and computation. Synth. Lect. Artif. Intell. Mach. Learn. 10(2), 1–189 (2016)CrossRefGoogle Scholar
  19. 19.
    Robaidek, B., Koncel-Kedziorski, R., Hajishirzi, H.: Data-driven methods for solving algebra word problems (2018). arXiv preprint arXiv:1804.10718
  20. 20.
    Roy, S., Roth, D.: Solving general arithmetic word problems (2016). arXiv preprint arXiv:1608.01413
  21. 21.
    Shi, S., Wang, Y., Lin, C.Y., Liu, X., Rui, Y.: Automatically solving number word problems by semantic parsing and reasoning. In: Proceedings of the Conference on Empirical Methods in Natural Language Processing (EMNLP), Lisbon, Portugal (2015)Google Scholar
  22. 22.
    Singhal, A.: Introducing the Knowledge Graph: things, not strings, Official Google Blog (2012).
  23. 23.
    Smullyan, R.R.: First-order logic, vol. 43. Springer, Berlin (2012)zbMATHGoogle Scholar
  24. 24.
    Stanovsky, G., Dagan, I., et al.: Open ie as an intermediate structure for semantic tasks. In: Proceedings of the 53rd Annual Meeting of the Association for Computational Linguistics and the 7th International Joint Conference on Natural Language Processing (Volume 2: Short Papers), vol. 2, pp. 303–308 (2015)Google Scholar
  25. 25.
    Sundaram, S.S., Abraham, S.S.: Solving simple arithmetic word problems precisely with schemas. In: International Conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems, pp. 542–547. Springer (2018)Google Scholar
  26. 26.
    Sundaram, S.S., Khemani, D.: Natural language processing for solving simple word problems. In: 12th International Conference on Natural Language Processing, p. 390 (2015)Google Scholar
  27. 27.
    Wang, L., Wang, Y., Cai, D., Zhang, D., Liu, X.: Translating a math word problem to an expression tree (2018). arXiv preprint arXiv:1811.05632
  28. 28.
    Wang, L. et al.: Mathdqn: Solving arithmetic word problems via deep reinforcement learning. In: Thirty-Second AAAI Conference on Artificial Intelligence (2018)Google Scholar
  29. 29.
    Wang, Y., Liu, X., Shi, S.: Deep neural solver for math word problems. In: Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing, pp. 845–854 (2017)Google Scholar
  30. 30.
    Wielemaker, J., Schrijvers, T., Triska, M., Lager, T.: SWI-Prolog. Theor. Pract. Logic Program. 12(1–2), 67–96 (2012)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Zhou, L., Dai, S., Chen, L.: Learn to solve algebra word problems using quadratic programming. In: Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing, pp. 817–822 (2015)Google Scholar

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© Ohmsha, Ltd. and Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringIIT MadrasChennaiIndia

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