Graph Mining for Automatic Classification of Logical Proofs

Karel Vaculík, Luboš Popelínský

Abstract

We introduce graph mining for evaluation of logical proofs constructed by undergraduate students in the introductory course of logic. We start with description of the source data and their transformation into GraphML. As particular tasks may differ—students solve different tasks—we introduce a method for unification of resolution steps that enables to generate generalized frequent subgraphs. We then introduce a new system for graph mining that uses generalized frequent patterns as new attributes. We show that both overall accuracy and precision for incorrect resolution proofs overcome 97%. We also discuss a use of emergent patterns and three-class classification (correct/incorrect/unrecognised).

References

  1. Brauner, B. (2013). Data mining in graphs. http://is. muni.cz/th/255742/fi_b/.
  2. Cook, D. J. and Holder, L. B. (2006). Mining Graph Data. John Wiley & Sons.
  3. Dong, G. and Li, J. (1999). Efficient mining of emerging patterns: Discovering trends and differences. pages 43-52.
  4. Dovier, A., Pontelli, E., and Rossi, G. (2001). Set unification. CoRR, cs.LO/0110023.
  5. GraphML team (2007). The graphml file format. http: //graphml.graphdrawing.org/ [Accessed: 2014- 01-09].
  6. Hall, M., Frank, E., Holmes, G., Pfahringer, B., Reutemann, P., and Witten, I. H. (2009). The WEKA data mining software: an update. SIGKDD Explor. Newsl., 11(1):10-18.
  7. Huan, J., Wang, W., and Prins, J. (2003). Efficient mining of frequent subgraphs in the presence of isomorphism. In Proceedings of the Third IEEE International Conference on Data Mining, ICDM 7803, pages 549-, Washington, DC, USA. IEEE Computer Society.
  8. Kerber, R., L. B. S. E. (1995). A hybrid system for data mining. In Goonatilake, S., K. S., editor, Intelligent Hybrid Systems, chapter 7, pages 121-142. Willey & Sons.
  9. Ketkar, N. S., Holder, L. B., and Cook, D. J. (2005). Subdue: Compression-based frequent pattern discovery in graph data. In Proceedings of the 1st International Workshop on Open Source Data Mining: Frequent Pattern Mining Implementations, OSDM 7805, pages 71-76, New York, NY, USA. ACM.
  10. Srinivasan, A. (2001). The Aleph Manual. http://web.comlab.ox.ac.uk/oucl/research/ areas/machlearn/Aleph/ [Accessed: 2014-01-09].
  11. Yan, X. and Han, J. (2002). gspan: Graph-based substructure pattern mining. In Proceedings of the 2002 IEEE International Conference on Data Mining, ICDM 7802, pages 721-, Washington, DC, USA. IEEE Computer Society.
  12. Zaki, M. J. (2005). Efficiently mining frequent embedded unordered trees. Fundam. Inf., 66(1-2):33-52.
  13. Zhang, Z. and Zhang, C. (2004). Agent-Based Hybrid Intelligent Systems. SpringerVerlag.
  14. Zhang, Z., Z. C. (2004). Agent-Based Hybrid Intelligent Systems, chapter Agent-Based Hybrid Intelligent System for Data mining. In (Zhang and Zhang, 2004).
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Paper Citation


in Harvard Style

Vaculík K. and Popelínský L. (2014). Graph Mining for Automatic Classification of Logical Proofs . In Proceedings of the 6th International Conference on Computer Supported Education - Volume 1: CSEDU, ISBN 978-989-758-020-8, pages 563-568. DOI: 10.5220/0004963405630568


in Bibtex Style

@conference{csedu14,
author={Karel Vaculík and Luboš Popelínský},
title={Graph Mining for Automatic Classification of Logical Proofs},
booktitle={Proceedings of the 6th International Conference on Computer Supported Education - Volume 1: CSEDU,},
year={2014},
pages={563-568},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004963405630568},
isbn={978-989-758-020-8},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 6th International Conference on Computer Supported Education - Volume 1: CSEDU,
TI - Graph Mining for Automatic Classification of Logical Proofs
SN - 978-989-758-020-8
AU - Vaculík K.
AU - Popelínský L.
PY - 2014
SP - 563
EP - 568
DO - 10.5220/0004963405630568