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Enhancement of Mizar Texts with Transitivity Property of Predicates

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Book cover Intelligent Computer Mathematics (CICM 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9791))

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Abstract

A typical proof step in mathematical reasoning consists of two parts – a formula to be proven and a list of references used to justify the formula. In addition, computer proof-assistants can use specialized procedures and algorithms to strengthen their computational power to verify the correctness of reasonings.

The Mizar system supports several mechanisms to increase automation of some reasoning steps. One of them is registration of chosen properties of predicates and functors when they are defined. We propose strengthening of the Mizar system by processing another common property used in mathematics – transitivity.

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Notes

  1. 1.

    Total numbers are not simply sums of columns, because errors occurring after removing different registrations could occur in the same articles.

  2. 2.

    Other such automations are, for example, processing of adjectives [7] and definitional expansions [8].

  3. 3.

    Computations were carried out at the Computer Center of University of Białystok http://uco.uwb.edu.pl.

  4. 4.

    The full list is accessible at http://alioth.uwb.edu.pl/~artur/transitivity/th2trans.txt.

  5. 5.

    The full list of non-zero numbers of references is accessible at http://alioth.uwb.edu.pl/~artur/transitivity/references.txt.

  6. 6.

    http://mizar.uwb.edu.pl/version/current/html/osalg_1.html.

References

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Authors and Affiliations

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

    Artur Korniłowicz

Authors
  1. Artur Korniłowicz
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Correspondence to Artur Korniłowicz .

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Editors and Affiliations

  1. Jacobs University Bremen, Bremen, Germany

    Michael Kohlhase

  2. Chalmers University, Göteborg, Sweden

    Moa Johansson

  3. National Institute of Standards and Technology, Gaithersburg, Maryland, USA

    Bruce Miller

  4. Microsoft Research, Redmond, Washington, USA

    Leonardo de Moura

  5. University of Waterloo, Waterloo, Ontario, Canada

    Frank Tompa

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Korniłowicz, A. (2016). Enhancement of Mizar Texts with Transitivity Property of Predicates. In: Kohlhase, M., Johansson, M., Miller, B., de Moura, L., Tompa, F. (eds) Intelligent Computer Mathematics. CICM 2016. Lecture Notes in Computer Science(), vol 9791. Springer, Cham. https://doi.org/10.1007/978-3-319-42547-4_12

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  • DOI: https://doi.org/10.1007/978-3-319-42547-4_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-42546-7

  • Online ISBN: 978-3-319-42547-4

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