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International Conference on Intelligent Computer Mathematics

CICM 2017: Intelligent Computer Mathematics pp 132–146Cite as

Towards Mathematical AI via a Model of the Content and Process of Mathematical Question and Answer Dialogues

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10383))

Abstract

This paper outlines a strategy for building semantically meaningful representations and carrying out effective reasoning in technical knowledge domains such as mathematics. Our central assertion is that the semi-structured Q&A format, as used on the popular Stack Exchange network of websites, exposes domain knowledge in a form that is already reasonably close to the structured knowledge formats that computers can reason about. The knowledge in question is not only facts – but discursive, dialectical, argument for purposes of proof and pedagogy. We therefore assert that modelling the Q&A process computationally provides a route to domain understanding that is compatible with the day-to-day practices of mathematicians and students. This position is supported by a small case study that analyses one question from Mathoverflow in detail, using concepts from argumentation theory. A programme of future work, including a rigorous evaluation strategy, is then advanced.

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Notes

  1. 1.

    http://stackexchange.com/sites#questions.

  2. 2.

    http://mathoverflow.net/q/12732.

  3. 3.

    http://mathoverflow.net/q/34044.

  4. 4.

    At this point, the discussion becomes multi-threaded, since comments can now attach to the answer as well.

  5. 5.

    Intuitively, upper-triangular \(2\times 2\) matrices have one element that is zero, so the subgroup has one codimension in \(\text {GL}_2(\mathbf C)\), namely, a copy of \(\mathbf C\). The fact that the index is infinite follows (but an algebraic proof is also straightforward). For an example of an infinite group and a subgroup with finite index, consider \(\mathbf Z\) and \(2\mathbf Z\): in this case, the group is equal to the union of cosets.

  6. 6.

    https://www.authorea.com/users/5713/articles/51708-understanding-a-dataset- arxiv-org/_show_article.

  7. 7.

    https://research.googleblog.com/2017/05/coarse-discourse-dataset-for.html.

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Acknowledgements

Martin and Corneli were support by Martin’s EPSRC fellowship award “The Social Machine of Mathematics” (EP/K040251/1); Murray-Rust was supported by “SOCIAM - the theory and practice of Social Machines” (EP/J017728/2).

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Authors and Affiliations

  1. University of Edinburgh, Edinburgh, UK

    Joseph Corneli & Dave Murray-Rust

  2. University of Oxford, Oxford, UK

    Ursula Martin

  3. University of Dundee, Dundee, UK

    Alison Pease

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  1. Joseph Corneli
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  2. Ursula Martin
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  4. Alison Pease
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Correspondence to Joseph Corneli .

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Editors and Affiliations

  1. Radboud University, Nijmegen, The Netherlands

    Herman Geuvers

  2. Coventry University, Coventry, United Kingdom

    Matthew England

  3. National University of Sciences and Technology, Islamabad, Pakistan

    Osman Hasan

  4. Jacobs University Bremen, Bremen, Germany

    Florian Rabe

  5. FIZ Karlsruhe, Berlin, Germany

    Olaf Teschke

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Corneli, J., Martin, U., Murray-Rust, D., Pease, A. (2017). Towards Mathematical AI via a Model of the Content and Process of Mathematical Question and Answer Dialogues. In: Geuvers, H., England, M., Hasan, O., Rabe, F., Teschke, O. (eds) Intelligent Computer Mathematics. CICM 2017. Lecture Notes in Computer Science(), vol 10383. Springer, Cham. https://doi.org/10.1007/978-3-319-62075-6_10

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  • DOI: https://doi.org/10.1007/978-3-319-62075-6_10

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