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Satisfiability and Validity Problems in Many-Sorted Composition-Nominative Pure Predicate Logics

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ICT in Education, Research, and Industrial Applications (ICTERI 2012)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 347))

Abstract

We propose methods for solving the satisfiability and validity problems in many-sorted composition-nominative pure predicate logics (without functions and with equality). These logics are algebra-based logics of many-sorted partial predicates constructed in a semantic-syntactic style on the methodological basis that is common with programming; they can be considered as generalizations of traditional many-sorted logics on classes of partial predicates that do not have fixed arity. We show the reduction of the satisfiability problem to the same problem for many-sorted classical first-order pure predicate logic with equality. As validity is dual to satisfiability, the method proposed can be adopted to the validity problem. This enables us to use existent satisfiability and validity checking procedures developed for classical logic also for solving these problems in composition-nominative pure predicate logics with equality.

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Author information

Authors and Affiliations

  1. Department of Theory and Technology of Programming, Taras Shevchenko National University of Kyiv, 64, Volodymyrska Street, 01601, Kyiv, Ukraine

    Mykola S. Nikitchenko & Valentyn G. Tymofieiev

Authors
  1. Mykola S. Nikitchenko
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  2. Valentyn G. Tymofieiev
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Editor information

Editors and Affiliations

  1. Department of Information Technologies, Zaporozhye National University, 66 Zhukovskogo st, 69600, Zaporozhye, Ukraine

    Vadim Ermolayev

  2. Mayr Application Engineering, Alpen-Adria University Klagenfurt, Universitätsstrasse 65, 9020, Klagenfurt, Austria

    Heinrich C. Mayr

  3. Department of Theory and Technology of Programming, National Taras Shevchenko University of Kyiv, 64, Volodymyrska Street, 01033, Kyiv, Ukraine

    Mykola Nikitchenko

  4. Kherson State University, 40-rokiv, Zhovtnya st. 27, 73000, Kherson, Ukraine

    Aleksander Spivakovsky

  5. School of Mathematics and Mechanics, Karazin Kharkiv National University, 4 Svobody Sqr, 61022, Kharkov, Ukraine

    Grygoriy Zholtkevych

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Nikitchenko, M.S., Tymofieiev, V.G. (2013). Satisfiability and Validity Problems in Many-Sorted Composition-Nominative Pure Predicate Logics. In: Ermolayev, V., Mayr, H.C., Nikitchenko, M., Spivakovsky, A., Zholtkevych, G. (eds) ICT in Education, Research, and Industrial Applications. ICTERI 2012. Communications in Computer and Information Science, vol 347. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35737-4_6

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  • DOI: https://doi.org/10.1007/978-3-642-35737-4_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35736-7

  • Online ISBN: 978-3-642-35737-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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