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

  • Mykola S. Nikitchenko
  • Valentyn G. Tymofieiev
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 347)


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.


many-sorted logic composition-nominative logic partial predicate quasiary predicate partial logic first-order logic satisfiability validity 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Mykola S. Nikitchenko
    • 1
  • Valentyn G. Tymofieiev
    • 1
  1. 1.Department of Theory and Technology of ProgrammingTaras Shevchenko National University of KyivKyivUkraine

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