Skip to main content
SpringerLink
Log in

Semantic Representation for Age Word Problems with Schemas

  • Published:
New Generation Computing Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

Notes

  1. https://github.com/Sowms/agewps/blob/master/questions.json.

  2. http://ejml.org.

  3. https://github.com/Sowms/agewps.

  4. https://github.com/Sowms/agewps/blob/master/questions.json.

References

  1. Bakman, Y.: Robust understanding of word problems with extraneous information. (2007) arXiv preprint arXiv:math/0701393

  2. Berners-Lee, T., Hendler, J., Lassila, O.: The semantic web. Sci. Am. 284(5), 34–43 (2001)

    Article  Google Scholar 

  3. Brachman, R.J., Levesque, H.J., Reiter, R.: Knowledge Representation. MIT press, London (1992)

    Google Scholar 

  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)

  5. Dellarosa, D.: A computer simulation of childrens arithmetic word-problem solving. Behav. Res. Methods Instrum. Comput. 18(2), 147–154 (1986)

    Article  Google Scholar 

  6. Fletcher, C.R.: Understanding and solving arithmetic word problems: a computer simulation. Behav. Res. Methods Instrum. Comput. 17(5), 565–571 (1985)

    Article  Google Scholar 

  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)

  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)

    Article  Google Scholar 

  9. Kushman, N., Artzi, Y., Zettlemoyer, L., Barzilay, R.: Learning to automatically solve algebra word problems. ACL 1, 271–281 (2014)

    Google Scholar 

  10. Liang, P.: Learning executable semantic parsers for natural language understanding. Commun. ACM 59(9), 68–76 (2016)

    Article  Google Scholar 

  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. 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)

  13. Marshall, S.P.: Schemas in Problem Solving. Cambridge University Press, Cambridge (1996)

    Google Scholar 

  14. Miller, E.: An introduction to the resource description framework. Bull. Am. Soc. Inf. Sci. Technol. 25(1), 15–19 (1998)

    Article  MathSciNet  Google Scholar 

  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)

  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)

    Article  Google Scholar 

  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)

  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)

    Article  Google Scholar 

  19. Robaidek, B., Koncel-Kedziorski, R., Hajishirzi, H.: Data-driven methods for solving algebra word problems (2018). arXiv preprint arXiv:1804.10718

  20. Roy, S., Roth, D.: Solving general arithmetic word problems (2016). arXiv preprint arXiv:1608.01413

  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)

  22. Singhal, A.: Introducing the Knowledge Graph: things, not strings, Official Google Blog (2012). http://googleblog.blogspot.com/2012/05/introducing-knowledge-graph-things-not.html

  23. Smullyan, R.R.: First-order logic, vol. 43. Springer, Berlin (2012)

    MATH  Google Scholar 

  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)

  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)

  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)

  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. Wang, L. et al.: Mathdqn: Solving arithmetic word problems via deep reinforcement learning. In: Thirty-Second AAAI Conference on Artificial Intelligence (2018)

  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)

  30. Wielemaker, J., Schrijvers, T., Triska, M., Lager, T.: SWI-Prolog. Theor. Pract. Logic Program. 12(1–2), 67–96 (2012)

    Article  MathSciNet  Google Scholar 

  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)

Download references

Acknowledgements

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.

Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, IIT Madras, Chennai, India

    Sowmya S. Sundaram & Savitha Sam Abraham

Authors
  1. Sowmya S. Sundaram
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Savitha Sam Abraham
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sowmya S. Sundaram.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sundaram, S.S., Abraham, S.S. Semantic Representation for Age Word Problems with Schemas. New Gener. Comput. 37, 429–452 (2019). https://doi.org/10.1007/s00354-019-00069-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00354-019-00069-9

Keywords

Search

Navigation