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Building a Framework of Rough Inclusion Functions by Means of Computerized Proof Assistant

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Rough Sets (IJCRS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11499))

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Abstract

The paper describes some of the issues concerning the development of automated formal framework for the reasoning about rough inclusion functions, starting with the classical one, and generalizations thereof. We work with the Mizar system; the viewpoint of the rough set theory, and especially mereology by Leśniewski, can allow for the creation of new foundations for the Mizar Mathematical Library, or at least for fresh branch of this formal database, originally based on Tarski-Grothendieck axioms.

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Notes

  1. 1.

    All items from the Mizar Mathematical Library which are automatically hyperlinked can be browsed online from the page http://mizar.org/version/current/html/.

  2. 2.

    Radix type together with the cluster of attributes makes a new type of an object.

  3. 3.

    http://mizar.uwb.edu.pl/library/roughif1/.

  4. 4.

    The author wishes to thank one of the referees for this valuable remark. Of course, we are interested in the development of quasi RIFs and weak quasi RIFs, so this distinction is important even if it is meaningless in the theory of RIFs.

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Authors and Affiliations

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

    Adam Grabowski

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  1. Adam Grabowski
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Correspondence to Adam Grabowski .

Editor information

Editors and Affiliations

  1. University of Debrecen, Debrecen, Hungary

    Tamás Mihálydeák

  2. Southwest Petroleum University, Chengdu, China

    Fan Min

  3. Chongqing University of Posts and Telecommunications, Chongqing, China

    Guoyin Wang

  4. Indian Institute of Technology Kanpur, Kanpur, India

    Mohua Banerjee

  5. Fujian Normal University, Fuzhou, China

    Ivo Düntsch

  6. University of Rzeszów, Rzeszow, Poland

    Zbigniew Suraj

  7. University of Milano-Bicocca, Milan, Italy

    Davide Ciucci

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Grabowski, A. (2019). Building a Framework of Rough Inclusion Functions by Means of Computerized Proof Assistant. In: Mihálydeák, T., et al. Rough Sets. IJCRS 2019. Lecture Notes in Computer Science(), vol 11499. Springer, Cham. https://doi.org/10.1007/978-3-030-22815-6_18

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  • DOI: https://doi.org/10.1007/978-3-030-22815-6_18

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  • Print ISBN: 978-3-030-22814-9

  • Online ISBN: 978-3-030-22815-6

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