Skip to main content

Composition-Nominative Logics as Institutions

Logica Universalis volume 12, pages 221–238 (2018)Cite this article

Abstract

Composition-nominative logics (CNL) are program-oriented logics. They are based on algebras of partial predicates which do not have fixed arity. The aim of this work is to present CNL as institutions. Homomorphisms of first-order CNL are introduced, satisfaction condition is proved. Relations with institutions for classical first-order logic are considered. Directions for further investigation are outlined.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

References

  1. Nikitchenko, M., Shkilniak, S.: Mathematical logic and theory of algorithms. Publishing house of Taras Shevchenko National University of Kyiv, Kyiv. In Ukrainian (2008)

  2. Nikitchenko, M., Chentsov, A.: Basics of intensionalized data: presets, sets, and nominats. Comput. Sci. J. Moldova, vol. 20, no. 3(60), pp. 334–365 (2012)

  3. Nikitchenko, M., Tymofieiev, V.: Satisfiability in composition-nominative logics. Cent. Eur. J. Comput. Sci. 2(3), 194–213 (2012)

    MATH  Google Scholar 

  4. Ivanov, I., Nikitchenko, M., Abraham, U.: Event-based proof of the mutual exclusion property of Peterson’s algorithm. Formaliz. Math. 23(4), 325–331 (2015). https://doi.org/10.1515/forma-2015-0026

    Article  MATH  Google Scholar 

  5. Nikitchenko, M., Ivanov, I., Kornilowicz, A., Kryvolap, A.: Extended Floyd–Hoare logic over relational nominative data. CCIS, vol. 826, pp. 41–64, Springer, Cham. (2018)

  6. Béziau, J.-Y.: 13 questions about universal logic. Bull. Sect. Logic 35(2/3), 133–150 (2006)

    MathSciNet  MATH  Google Scholar 

  7. Béziau, J.-Y. (ed.): Universal Logic: an Anthology. Studies in Universal Logic, Springer Basel (2012)

  8. Mossakowski, T., Goguen, J., Diaconescu, R., Tarlecki, A.: What is a logic? In: Béziau, J.-Y. (ed.) Logica Universalis: Towards a General Theory of Logic, pp. 111–133. Basel, Birkhäuser (2007)

    Chapter  Google Scholar 

  9. Diaconescu, R.: Institution-Independent Model Theory. Birkhäuser, Basel (2008)

    MATH  Google Scholar 

  10. Pierce, B.: Types and Programming Languages. MIT Press, Cambridge (2002)

    MATH  Google Scholar 

  11. Rydeheard, D., Burstall, R.: Computational Category Theory. Prentice Hall, New York (1988)

    MATH  Google Scholar 

  12. Chentsov, A.: Many-sorted first-order composition-nominative logic as institution, Comput. Sci. J. Mold., vol. 24, no. 1(70), pp. 27–54 (2016) [Online]. http://www.math.md/publications/csjm/issues/v24-n1/12089/

  13. Mossakowski, T., Diaconescu, R., Tarlecki, A.: What is a logic translation? Log. Univ. 3, 95–124 (2009). https://doi.org/10.1007/s11787-009-0005-2

    Article  MathSciNet  MATH  Google Scholar 

  14. Fernandes, D.: Translations: generalizing relative expressiveness between logics. arXiv:1706.08481 (2017)

  15. Goguen, J., Rosu, G.: Institution morphisms, Formal Asp. Comput., vol. 13, no. 3–5, pp. 274–306 (2002) [Online]. https://doi.org/10.1007/s001650200013

  16. Sannella, D., Tarlecki, A.: Foundations of algebraic specification and formal software development, ser. monographs in theoretical computer science. An EATCS Series. Springer-Verlag, Berlin Heidelberg (2012)

  17. Nikitchenko, M., Shkilniak, S.: Towards representation of classical logic as quasiary logic. In: Proceedings of Conference on Mathematical Foundations of Informatics (MFOI-2017), pp. 133–138 (2017) [Online]. http://mfoi2017.math.md/MFOI2017_Proceedings.pdf

  18. Charguéraud, A.: The locally nameless representation. J. Autom. Reason., vol. 49, no. 3, pp. 363–408 (2012) [Online]. https://doi.org/10.1007/s10817-011-9225-2

  19. Kryvolap, A., Nikitchenko, M., Schreiner, W.: Extending Floyd–Hoare logic for partial pre- and postconditions. CCIS 412, 355–378 (2013)

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Alexey Chentsov & Mykola Nikitchenko

Authors
  1. Alexey Chentsov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mykola Nikitchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mykola Nikitchenko.

Additional information

We thank Dr. Valentyn Tymofieiev and anonymous reviewers for helpful comments.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Chentsov, A., Nikitchenko, M. Composition-Nominative Logics as Institutions. Log. Univers. 12, 221–238 (2018). https://doi.org/10.1007/s11787-018-0191-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11787-018-0191-x

Keywords

  • Institution
  • first-order logic
  • partial predicate
  • quasiary predicate
  • composition-nominative logic

Mathematics Subject Classification

  • Primary 03B70
  • Secondary 03B10
  • 03C95
  • 03G25