Abstract
Dialogs in formal domains, such as mathematics, are characterized by a mixture of telegraphic natural language text and embedded formal expressions. Analysis methods for this kind of setting are rare and require empirical justification due to a notorious lack of data, as opposed to the richness of presentations found in genre-specific textbooks. In this paper, we focus on dedicated interpretation techniques for major phenomena observed in a recently collected corpus on tutorial dialogs in proving mathematical theorems. We combine analysis techniques for mathematical formulas and for natural language expressions, supported by knowledge about domain-relevant lexical semantics and by representations relating vague lexical to precise domain terms.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Aleven, V., Koedinger, K.: The Need for Tutorial Dialog to Support Self- Explanation. In: Papers from the 2000 AAAI Fall Symposium on Building Dialogue Systems for Tutorial Applications, pp. 65–73. AAAI Press, Menlo Park (2000)
Baldridge, J.: Lexically Specified Derivational Control in Combinatory Categorial Grammar. Ph.D. Thesis, University of Edinburgh, Edinburgh (2002)
Baldridge, J., Kruijff, G.-J.: Coupling CCG with Hybrid Logic Dependency Semantics. In: Proc. of ACL, Philadelphia PA, pp. 319–326 (2002)
Baldridge, J., Kruijff, G.-J.: Multi-Modal Combinatory Categorial Grammar. In: Proc. of EACL 2003, Budapest, pp. 211–218 (2003)
Benzmüller, C., Fiedler, A., Gabsdil, M., Horacek, H., Kruijff-Korbayová, I., Pinkal, M., Siekmann, J., Tsovaltzi, D., Vo, B., Wolska, M.: Tutorial Dialogs on Mathematical Proofs. In: IJCAI Workshop on Knowledge Representation and Automated Reasoning for E-Learning Systems, pp. 12–22 (2003)
Benzmüller, C., Fiedler, A., Gabsdil, M., Horacek, H., Kruijff-Korbayová, I., Pinkal, M., Siekmann, J., Tsovaltzi, D., Vo, B., Wolska, M.: A Wizard-of-Oz Experiment for Tutorial Dialogues in Mathematics. In: AIED2003 — Supplementary Proceedings of the 11th International Conference on Artificial Intelligence in Education, Sidney, Australia, pp. 471–481 (2003)
Fiedler, A., Gabsdil, M.: Supporting Progressive Refinement of Wizard-of-Oz Experiments. In: Proc. of the ITS 2002 – Workshop on Empirical Methods for Tutorial Dialogue, San Sebastian, Spain, pp. 62–69 (2002)
Fiedler, A., Tsovaltzi, D.: Automating Hinting in Mathematical Tutorial Dialogue. In: Proc. of the EACL 2003 Workshop on Dialogue Systems: Interaction, Adaptation and Styles of Management, Budapest, pp. 45–52 (2003)
Hajičová, E., Panevová, J., Sgall, P.: A Manual for Tectogrammatical Tagging of the Prague Dependency Treebank. TR-2000-09, Charles University, Prague (2000)
Horacek, H., Fiedler, A., Franke, A., Moschner, M., Pollet, M., Sorge, V.: Representation of Mathematical Objects for Inferencing and for Presentation Purposes. In: Proc. of EMCSR 2004, Vienna, pp. 683–688 (2004)
Kohlhase, M., Franke, A.: MBase: Representing Knowledge and Context for the Integration of Mathematical Software Systems. Journal of Symbolic Computation 32(4), 365–402 (2000)
Kruijff, G.-J.: A Categorial-Modal Logical Architecture of Informativity: Dependency Grammar Logic & Information Structure. Ph.d. Dissertation, Charles University, Prague (2001)
Melis, E., et al.: ActiveMath: A Generic and Adaptive Web-Based Learning Environment. Artifical Intelligence in Education 12(4), 385–407 (2001)
Moore, J.: What Makes Human Explanations Effective? In: Proc. of the Fifteenth Annual Conference of the Cognitive Science Society, Hillsdale, NJ. Earlbaum (1993)
SFB 378 web-site: http://www.coli.uni-sb.de/sfb378/
Sgall, P., Hajičová, E., Panevová, J.: The Meaning of the Sentence in its Semantic and Pragmatic Aspects. Reidel Publishing Company, Dordrecht (1986)
Siekmann, J., et al.: Proof Development with Ωmega. In: Proceedings of the 18th Conference on Automated Deduction, pp. 144–149. Copenhagen, Denmark (2002)
Trindi project: http://www.ling.gu.se/research/projects/trindi/
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Horacek, H., Wolska, M. (2004). Interpreting Semi-formal Utterances in Dialogs about Mathematical Proofs. In: Meziane, F., Métais, E. (eds) Natural Language Processing and Information Systems. NLDB 2004. Lecture Notes in Computer Science, vol 3136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27779-8_3
Download citation
DOI: https://doi.org/10.1007/978-3-540-27779-8_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22564-5
Online ISBN: 978-3-540-27779-8
eBook Packages: Springer Book Archive