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Building a Discourse Parser for Informal Mathematical Discourse in the Context of a Controlled Natural Language

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7816))

Abstract

The lack of specific data sets makes difficult the discourse parsing for Informal Mathematical Discourse (IMD). In this paper, we propose a data driven approach to identify arguments and connectives in an IMD structure within the context of Controlled Natural Language (CNL). Our approach follows a low-level discourse parsing under Peen Discourse TreeBank (PDTB) guidelines. Three classifiers have been trained: one that identifies the Arg2, other that locates the relative position of Arg1 and a third that identifies the (Arg1 and Arg2) arguments of each connective. These classifiers are instances of Support Vector Machines (SVMs), fed from an own Mathematical TreeBank. Finally, our approach defines an End-to-End discourse parser into IMD, whose results will be used to classify of informal deductive proofs via the low level discourse in IMD processing.

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References

  1. Asher, N.: Reference to Abstract Objects in Discourse. Kluwer Academic Publishers (1993)

    Google Scholar 

  2. Bikel, D.: Design of a Multilingual, Parallel Processing Statistical Parsing Engine. In: 2nd International Conference on Human Language Technology Research HLT 2002, pp. 178–182. Morgan Kaufmann Publishers Inc., San Francisco (2002)

    Chapter  Google Scholar 

  3. Cramer, M., Fisseni, B., Koepke, P., Kühlwein, D., Schröder, B., Veldman, J.: The Naproche Project Controlled Natural Language Proof Checking of Mathematical Texts. In: Fuchs, N.E. (ed.) CNL 2009. LNCS, vol. 5972, pp. 170–186. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  4. Dinesh, N., Lee, A., Miltsakaki, E., Prasad, R., Joshi, A., Webber, B.: Attribution and the (Non-)Alignment of Syntactic and Discourse Arguments of Connectives. In: CorpusAnno 2005 Proceedings of the Workshop on Frontiers in Corpus Annotations II: Pie in the Sky, pp. 29–36. Association for Computational Linguistics (ACM), Stroudsburg (2005)

    Chapter  Google Scholar 

  5. Elwell, R., Baldridge, J.: Discourse Connective Argument Identification with Connective Specific Rankers. In: ICSC 2008 Proceedings of the 2008 IEEE International Conference on Semantic Computing, pp. 198–205. IEEE Computer Society, Washington (2008)

    Chapter  Google Scholar 

  6. Fawcet, T.: An Introduction to ROC Analysis. Pattern Recognition Letters- Specialissue: ROC Analysis in Pattern, 861–874 (2006)

    Google Scholar 

  7. Ghosh, S., Johansson, R., Riccardi, G., Tonelli, S.: Shallow Discourse Parsing with Conditional Random Fields. In: 5th International Joint Conference on Natural Language Processing, Chiang Mai, Thailand, pp. 1071–1079 (2011)

    Google Scholar 

  8. Gutiérrez de Piñerez, R.E., Díaz, J.F.: Preprocessing of Informal Mathematical Discourse in Context of Controlled Natural Language. In: Proceedings of the 21st ACM International Conference on Information and Knowledge Management (CIKM 2012). Association for Computing Machinery, ACM (2012)

    Google Scholar 

  9. Humayoun, M., Raffalli, C.: MathAbs: A Representational Language for Mathematics. In: Proceedings of 8th International Conference on Frontiers of Information Technology, Islamabad, Pakistan, p. 37 (2010)

    Google Scholar 

  10. Joachims, T.: Making large-Scale SVM Learning Practical. In: Schlkopf, B., Burges, C., Smola, A. (eds.) Advances in Kernel Methods - Support Vector Learning. MIT Press (1999)

    Google Scholar 

  11. Kamareddine, F., Maarek, M., Retel, K., Wells, J.B.: Narrative Structure of Mathematical Texts. In: Kauers, M., Kerber, M., Miner, R., Windsteiger, W. (eds.) MKM/CALCULEMUS 2007. LNCS (LNAI), vol. 4573, pp. 296–312. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  12. Lin, Z., Ng, H.T., Kan, M.: A PDTB-Styled End-to-End Discourse Parser. The Computing Research Repository 1011 (2011)

    Google Scholar 

  13. Manning, C.D., Raghavan, P., Schtze, H.: Introduction to Information Retrieval. Cambridge University Press, New York (2008)

    Book  MATH  Google Scholar 

  14. Marcus, M., Santorini, B., Ann Marcinkiewicz, A.: Building a Large Annotated Corpus of English: the Penn Treebank. Computational Linguistics 19(2), 313–330 (1993)

    Google Scholar 

  15. Prasad, R., Dinesh, N., Lee, A., Miltsakaki, E., Robaldo, L., Joshi, A., Webber, B.: The Penn Discourse TreeBank 2.0. In: Proceedings of the 6th International Conference on Languages Resources and Evaluations (LREC 2008), Marrakech, Marocco (2008)

    Google Scholar 

  16. Ruesga, S.L., Sandoval, S.L., Len, L.F.: Spanish Treebank: Specifications version 5. Universidad Autnoma de Madrid (1999)

    Google Scholar 

  17. Vapnik, V.N.: The Nature of Statistical Learning Theory. Springer, New York (1995)

    MATH  Google Scholar 

  18. Wellner, B., Pustejovsky, J.: Automatically Identifying the Arguments of Discourse Connectives. In: Proceedings of the 2007 Joint Conference on Empirical Methods in Natural Language Processing and Computational Natural Language Learning (EMNLP-CoNLL), pp. 92–101. Association for Computational Linguistics, Prague (2007)

    Google Scholar 

  19. Wolska, M., Vo, B.Q., Tsovaltzi, D., Kruijff-Korbayov, I., Karagjosova, E., Horacek, H., Fiedler, A., Benzmller, C.: Annotated Corpus of Tutorial Dialogs on Mathematical Theorem Proving. In: Proceedings of 4th International Conference on Language Resources and Evaluation, Lisbon, Portugal, pp. 1007–1010 (2004)

    Google Scholar 

  20. Wolska, M.: A Language Engineering Architecture for Processing Informal Mathematical Discourse. In: Towards Digital Mathematics Library, Birmingham, United Kingdom, pp. 131–136. Masaryk University (2008)

    Google Scholar 

  21. Zinn, C.: Understanding Informal Mathematical Discourse. Ph.D. thesis. Universitat Erlangen-Nürnberg Institut für Informatik (2004)

    Google Scholar 

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de Piñerez Reyes, R.E.G., Frias, J.F.D. (2013). Building a Discourse Parser for Informal Mathematical Discourse in the Context of a Controlled Natural Language. In: Gelbukh, A. (eds) Computational Linguistics and Intelligent Text Processing. CICLing 2013. Lecture Notes in Computer Science, vol 7816. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37247-6_43

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  • DOI: https://doi.org/10.1007/978-3-642-37247-6_43

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-37246-9

  • Online ISBN: 978-3-642-37247-6

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