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Expressing the Notion of a Mathematical Structure in the Formal Language of Mizar

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Man-Machine Interactions 5 (ICMMI 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 659))

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Abstract

In the paper, the problem with the translation of ordinary mathematical structures from the natural language into the formal one is identified. As a concrete example of the system I used the Mizar system, the interactive proof assistant for the formalization of mathematics. Chosen testbed, both for new developments, and for revising old ones, was the theory of \(\mathbb Z\)-modules.

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Authors and Affiliations

  1. Institute of Informatics, University of Białystok, Konstantego Ciołkowskiego 1M, 15-245, Białystok, Poland

    Adam Grabowski

Authors
  1. Adam Grabowski
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Correspondence to Adam Grabowski .

Editor information

Editors and Affiliations

  1. Institute of Informatics, Silesian University of Technology, Gliwice, Poland

    Aleksandra Gruca

  2. Institute of Informatics, Silesian University of Technology, Gliwice, Poland

    Tadeusz Czachórski

  3. Institute of Informatics, Silesian University of Technology, Gliwice, Poland

    Katarzyna Harezlak

  4. Institute of Informatics, Silesian University of Technology, Gliwice, Poland

    Stanisław Kozielski

  5. Institute of Informatics, Silesian University of Technology, Gliwice, Poland

    Agnieszka Piotrowska

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Grabowski, A. (2018). Expressing the Notion of a Mathematical Structure in the Formal Language of Mizar. In: Gruca, A., Czachórski, T., Harezlak, K., Kozielski, S., Piotrowska, A. (eds) Man-Machine Interactions 5. ICMMI 2017. Advances in Intelligent Systems and Computing, vol 659. Springer, Cham. https://doi.org/10.1007/978-3-319-67792-7_26

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  • DOI: https://doi.org/10.1007/978-3-319-67792-7_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67791-0

  • Online ISBN: 978-3-319-67792-7

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