Logica Universalis

, Volume 12, Issue 1–2, pp 221–238 | Cite as

Composition-Nominative Logics as Institutions

  • Alexey Chentsov
  • Mykola NikitchenkoEmail author


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.


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

Mathematics Subject Classification

Primary 03B70 Secondary 03B10 03C95 03G25 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Nikitchenko, M., Shkilniak, S.: Mathematical logic and theory of algorithms. Publishing house of Taras Shevchenko National University of Kyiv, Kyiv. In Ukrainian (2008)Google Scholar
  2. 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)Google Scholar
  3. 3.
    Nikitchenko, M., Tymofieiev, V.: Satisfiability in composition-nominative logics. Cent. Eur. J. Comput. Sci. 2(3), 194–213 (2012)zbMATHGoogle Scholar
  4. 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). CrossRefzbMATHGoogle Scholar
  5. 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)Google Scholar
  6. 6.
    Béziau, J.-Y.: 13 questions about universal logic. Bull. Sect. Logic 35(2/3), 133–150 (2006)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Béziau, J.-Y. (ed.): Universal Logic: an Anthology. Studies in Universal Logic, Springer Basel (2012)Google Scholar
  8. 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)CrossRefGoogle Scholar
  9. 9.
    Diaconescu, R.: Institution-Independent Model Theory. Birkhäuser, Basel (2008)zbMATHGoogle Scholar
  10. 10.
    Pierce, B.: Types and Programming Languages. MIT Press, Cambridge (2002)zbMATHGoogle Scholar
  11. 11.
    Rydeheard, D., Burstall, R.: Computational Category Theory. Prentice Hall, New York (1988)zbMATHGoogle Scholar
  12. 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].
  13. 13.
    Mossakowski, T., Diaconescu, R., Tarlecki, A.: What is a logic translation? Log. Univ. 3, 95–124 (2009). MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Fernandes, D.: Translations: generalizing relative expressiveness between logics. arXiv:1706.08481 (2017)
  15. 15.
    Goguen, J., Rosu, G.: Institution morphisms, Formal Asp. Comput., vol. 13, no. 3–5, pp. 274–306 (2002) [Online].
  16. 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)Google Scholar
  17. 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].
  18. 18.
    Charguéraud, A.: The locally nameless representation. J. Autom. Reason., vol. 49, no. 3, pp. 363–408 (2012) [Online].
  19. 19.
    Kryvolap, A., Nikitchenko, M., Schreiner, W.: Extending Floyd–Hoare logic for partial pre- and postconditions. CCIS 412, 355–378 (2013)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Taras Shevchenko National University of KyivKyivUkraine

Personalised recommendations