Advertisement

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)

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.

Keywords

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Mendelson, E.: Introduction to Mathematical Logic, 4th edn. Chapman & Hall, London (1997)zbMATHGoogle Scholar
  2. 2.
    Kroening, D., Strichman, O.: Decision Procedures – an Algorithmic Point of View. Springer, Heidelberg (2008)zbMATHGoogle Scholar
  3. 3.
    Marques-Silva, J.: Practical Applications of Boolean Satisfiability. In: Workshop on Discrete Event Systems, Goteborg, Sweden, May 28-30, pp. 74–80 (2008)Google Scholar
  4. 4.
    Nieuwenhuis, R., Oliveras, A., Tinelli, C.: Solving SAT and SAT modulo theories: from an abstract Davis-Putnam-Logemann-Loveland procedure to DPLL(T). J. ACM 53, 937–977 (2006)MathSciNetCrossRefGoogle Scholar
  5. 5.
    de Moura, L., Bjørner, N.: Satisfiability Modulo Theories: Introduction and Applications. Comm. ACM 54(9), 69–77 (2011)CrossRefGoogle Scholar
  6. 6.
    Nikitchenko, N.S.: A Composition Nominative Approach to Program Semantics. Technical Report IT, TR 1998-020, Technical University of Denmark (1998)Google Scholar
  7. 7.
    Basarab, I.A., Gubsky, B.V., Nikitchenko, N.S., Red’ko, V.N.: Composition Models of Databases. In: Eder, J., Kalinichenko, L.A. (eds.) East-West Database Workshop. Workshops in Computing Series, pp. 221–231. Springer, London (1995)Google Scholar
  8. 8.
    Nielson, H.R., Nielson, F.: Semantics with Applications: A Formal Introduction. John Wiley & Sons Inc. (1992)Google Scholar
  9. 9.
    Nikitchenko, M.S.: Composition-Nominative Aspects of Address Programming. Kibernetika I Sistemnyi Analiz 6, 24–35 (2009) (in Russian)Google Scholar
  10. 10.
    Nikitchenko, M.S., Shkilnyak, S.S.: Mathematical Logic and Theory of Algorithms. Publishing House of Taras Shevchenko National University of Kyiv, Kyiv (2008) (in Ukrainian)Google Scholar
  11. 11.
    Nikitchenko, M.S., Tymofieiev, V.G.: Satisfiability Problem in Composition-Nominative Logics. In: Proceedings of the Eleventh International Conference on Informatics INFORMATICS 2011, Roznava, Slovakia, November 16-18, pp. 75–80 (2011)Google Scholar
  12. 12.
    Nikitchenko, M.S., Tymofieiev, V.G.: Satisfiability in Composition-Nominative Logics. Central European Journal of Computer Science (to appear)Google Scholar
  13. 13.
    Nikitchenko, M.S., Tymofieiev, V.G.: Satisfiability Problem in Composition-Nominative Logics of Quantifier-Equational Level. In: Proc. 8th Int. Conf. ICTERI 2012, Kherson, Ukraine, June 6-10, vol. 848. CEUR-WS.org (2012), http://ceur-ws.org/Vol-848/ICTERI-2012-CEUR-WS-paper-38-p-56-70.pdf
  14. 14.
    Winskel, G.: The Formal Semantics of Programming Languages. MIT Press (1993)Google Scholar
  15. 15.
    Blamey, S.: Partial Logic. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, vol. III. D. Reidel Publishing Company (1986)Google Scholar
  16. 16.
    Jones, C.B.: Reasoning About Partial Functions in the Formal Development of Programs. ENTCS 145, 3–25 (2006)Google Scholar
  17. 17.
    Owe, O.: Partial Logics Reconsidered: A Conservative Approach. Form Asp. Comput. 5, 208–223 (1997)CrossRefGoogle Scholar
  18. 18.
    Janssen, T.M.V.: Compositionality. In: van Benthem, J., ter Meulen, A. (eds.) Handbook of Logic and Language, pp. 417–473. Elsevier and MIT Press (1997)Google Scholar
  19. 19.
    Pitts, A.M.: Nominal Logic, A First Order Theory of Names and Binding. Inform Comput. 186, 165–193 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Barrett, C., Sebastiani, R., Seshia, S.A., Tinelli, C.: Satisfiability Modulo Theories. In: Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.) Handbook of Satisfiability. IOS Press (2009)Google Scholar

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

Personalised recommendations