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Elementary Algebra Proof Exercises Using a Theorem Proving System

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Practical Applications of Intelligent Systems

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 124))

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Abstract

This paper presents the modules and features of an e-learning system which can automatically assessing the answers of elementary algebra proving problems. The system translates the answer given by a student, which is written in Chinese, into its corresponding formal proof, which is the semantic of the original sentences in the answer, and then automatically verifies the correctness of the formal proof.

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References

  1. Maple, http://www.maplesoft.com/

  2. Maxima, http://www.maxima.sourceforge.org/

  3. Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle/HOL: A Proof Assistant for Higher-Order Logic. Springer (2002)

    Google Scholar 

  4. Yu, S.: Dictionary of Modern Chinese Grammar Information. Tsinghua University Press, Beijing (2003)

    Google Scholar 

  5. Zhan, W.: A Study of Constructing Rules of Phrases in Contemporary Chinese for Chinese Information Processing. Tinghua University Press, Beijing (2000)

    Google Scholar 

  6. Li, P.: High School Mathematical Problem Sets and Solutions. Northeast Normal University Press, Changchun (2008)

    Google Scholar 

  7. Tang, X.: Mathematical Problem Sets and Solutions in Algebra. Lexicographical Publishing House, Shanghai (1985)

    Google Scholar 

  8. Nederpelt, R.P., Geuvers, J.H., de Vrijer, R.C.: Selected Papers on Automath. North-Holland, Amsterdam (1994)

    Google Scholar 

  9. Nederpelt, R.: Weak Type Theory: A formal language for mathematics. Technical Report, Eindhoven University of Technology, Department of Math. and Comp. Sc. (2002)

    Google Scholar 

  10. Kamareddine, F., Wells, J.B.: Computerizing Mathematical Text with MathLang. Electronic Notes in Theoretical Computer Science, ENTCS 205, 5–30 (2008)

    Article  MathSciNet  Google Scholar 

  11. Rudnicki, P.: An Overview of the MIZAR Project. In: Proceedings of the 1992 Workshop on Types for Proofs and Programs. Chalmers University of Technology, Bastad (1992)

    Google Scholar 

  12. Wenzel, M., Wiedijk, F.: A Comparison of Mizar and Isar. Journal of Automated Reasoning 29, 389–411 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  13. Zinn, C.: Understanding Informal Mathematical Discourse. PhD thesis, University of Erlangen-Nuremberg (2004)

    Google Scholar 

  14. Kamp, H., Reyle, U.: From Discourse to Logic. Kluwer Academic Publishers (1993)

    Google Scholar 

  15. Bundy, A.: The Use of Explicit Plans to Guide Inductive Proofs. In: Lusk, E., Overbeek, R. (eds.) CADE 1988. LNCS, vol. 310, Springer, Heidelberg (1988)

    Chapter  Google Scholar 

  16. Kuhlwein, D., Cramer, M., Koepke, P., Schröder, B.: The Naproche System. In: Intelligent Computer Mathematics. LNCS, vol. 3, Springer, Heidelberg (2009); ISBN: 978-3-642-02613-3, 2009

    Google Scholar 

  17. Humayoun, M., Raalli, C.: MathNat - Mathematical Text in a Controlled Natural Language. In: 11th International Conference on Intelligent Text Processing and Computational Linguistics, Iai, Romania, pp. 293–310 (2010)

    Google Scholar 

  18. Benzmüller, C., Fiedler, A., Gabsdil, M., Horacek, H., Kruijff-Korbayová, I., Pinkal, M., Siekmann, J., Tsovaltzi, D., Vo, B.Q.: Magdalena Wolska. Tutorial dialogs on mathematical proofs. In: Proceedings of the IJCAI Workshop on Knowledge Representation and Automated Reasoning for E-Learning Systems, Acapulco, pp. 12–22 (2003)

    Google Scholar 

  19. Sangwin, C.J.: Assessing Elementary Algebra with STACK. International Journal of Mathematical Education in Science and Technology 38, 987–1002 (2008)

    Article  Google Scholar 

  20. Abel, A., Chang, B.-Y.E., Pfenning, F.: Human-Readable Machine-Verifiable Proofs for Teaching Constructive Logic. In: PTP 2001, Siena, Italy (2001)

    Google Scholar 

  21. Andrews, P., Brown, C., Pfenning, F., et al.: Etps: A system to help students write formal proofs. Journal of Automated Reasoning 32, 75–92 (2004)

    Article  Google Scholar 

  22. Billingsley, W., Robinson, P.: Student Proof Exercises Using MathsTiles and Isabelle/HOL in an Intelligent Book. Journal of Automated Reasoning 39, 181–218 (2007)

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, 730000, Lanzhou, Gansu, China

    Bing Li & Lian Li

  2. School of Information Engineering, Lanzhou Commercial College, 730020, Lanzhou, Gansu, China

    Bing Li

Authors
  1. Bing Li
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  2. Lian Li
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, 200240, Shanghai, China

    Yinglin Wang

  2. School of Information Science and Technology, Southwest Jiaotong University, 610031, Chengdu, Sichuan Province, China

    Tianrui Li

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© 2011 Springer-Verlag Berlin Heidelberg

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Li, B., Li, L. (2011). Elementary Algebra Proof Exercises Using a Theorem Proving System. In: Wang, Y., Li, T. (eds) Practical Applications of Intelligent Systems. Advances in Intelligent and Soft Computing, vol 124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25658-5_34

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  • DOI: https://doi.org/10.1007/978-3-642-25658-5_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25657-8

  • Online ISBN: 978-3-642-25658-5

  • eBook Packages: EngineeringEngineering (R0)

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