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Program-Oriented Logics of Renominative Level with Extended Renomination and Equality

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Book cover Information and Communication Technologies in Education, Research, and Industrial Applications (ICTERI 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1175))

Abstract

The formalism of program logics is the main instrument for software verification. Such logics are based on formal program models and reflect main program properties. Among various program logics, Floyd-Hoare logic and its variants take a special place because of its naturalness and simplicity. But such logics are oriented on total pre- and post-conditions, and in the case of partial conditions they become unsound. Different methods to overcome this problem were proposed in our previous works. One of the methods involves extension of program algebras with the composition of predicate complement. This permits to modify rules of the logic making them sound. Such modification requires introduction of undefinedness conditions into logic rules. To work with such conditions, an underlying predicate logic should become more expressive. In this paper we continue our research of such logics. We investigate a special program-oriented predicate logic called logic of renominative (quantifier-free) level with the composition of predicate complement, extended renomination, and equality predicate. This logic is a constituent part of the program logic. We introduce a special consequence relation for this logic, construct a sequent calculus, and prove its soundness and completeness.

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Authors and Affiliations

  1. Taras Shevchenko National University of Kyiv, 60 Volodymyrska Street, City of Kyiv, 01033, Ukraine

    Mykola Nikitchenko, Oksana Shkilniak & Stepan Shkilniak

Authors
  1. Mykola Nikitchenko
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  2. Oksana Shkilniak
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  3. Stepan Shkilniak
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Correspondence to Mykola Nikitchenko .

Editor information

Editors and Affiliations

  1. Zaporizhzhia National University, Zaporizhzhia, Ukraine

    Vadim Ermolayev

  2. Université Cote d’Azur, Nice, France

    Frédéric Mallet

  3. University of Warmia and Mazury in Olsztyn, Olsztyn, Poland

    Vitaliy Yakovyna

  4. University of Klagenfurt, Klagenfurt am Wörthersee, Austria

    Heinrich C. Mayr

  5. Kherson State University, Kherson, Ukraine

    Aleksander Spivakovsky

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Nikitchenko, M., Shkilniak, O., Shkilniak, S. (2020). Program-Oriented Logics of Renominative Level with Extended Renomination and Equality. In: Ermolayev, V., Mallet, F., Yakovyna, V., Mayr, H., Spivakovsky, A. (eds) Information and Communication Technologies in Education, Research, and Industrial Applications. ICTERI 2019. Communications in Computer and Information Science, vol 1175. Springer, Cham. https://doi.org/10.1007/978-3-030-39459-2_4

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  • DOI: https://doi.org/10.1007/978-3-030-39459-2_4

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  • Print ISBN: 978-3-030-39458-5

  • Online ISBN: 978-3-030-39459-2

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