On Strongly First-Order Dependencies

  • Pietro GallianiEmail author


We prove that the expressive power of first-order logic with team semantics plus contradictory negation does not rise beyond that of first-order logic (with respect to sentences), and that the totality atoms of arity k + 1 are not definable in terms of the totality atoms of arity k. We furthermore prove that all first-order nullary and unary dependencies are strongly first-order, in the sense that they do not increase the expressive power of first-order logic if added to it.


Expressive Power Logic Sentence Negation Normal Form Constancy Atom Weak Extension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This research was supported by the Deutsche Forschungsgemeinschaft (project number DI 561/6-1). The author thanks an anonymous reviewer for a number of useful corrections and suggestions.


  1. 1.
    Abramsky, S., Väänänen, J.: From IF to BI. Synthese 167, 207–230 (2009). 10.1007/s11229-008-9415-6Google Scholar
  2. 2.
    Abramsky, S., Väänänen, J.: Dependence logic, social choice and quantum physics (2013, in preparation)Google Scholar
  3. 3.
    Durand, A., Kontinen, J.: Hierarchies in dependence logic. CoRR abs/1105.3324 (2011)Google Scholar
  4. 4.
    Engström, F.: Generalized quantifiers in dependence logic. J. Log. Lang. Inf. 21 (3), 299–324 (2012). doi: 10.1007/s10849-012-9162-4
  5. 5.
    Engström, F., Kontinen, J.: Characterizing quantifier extensions of dependence logic. J. Symb. Log. 78 (01), 307–316 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Galliani, P.: Inclusion and exclusion dependencies in team semantics: on some logics of imperfect information. Ann. Pure Appl. Log. 163 (1), 68–84 (2012). doi: 10.1016/j.apal.2011.08.005
  7. 7.
    Galliani, P.: The dynamics of imperfect information. Ph.D. thesis, University of Amsterdam (2012).
  8. 8.
    Galliani, P.: Upwards closed dependencies in team semantics. In: Puppis, G., Villa, T. (eds.) Proceedings Fourth International Symposium on Games, Automata, Logics and Formal Verification. EPTCS, vol. 119, pp. 93–106 (2013). doi:
  9. 9.
    Galliani, P., Hella, L.: Inclusion logic and fixed point logic. In: Rocca, S.R.D. (ed.) Computer Science Logic 2013 (CSL 2013). Leibniz International Proceedings in Informatics (LIPIcs), vol. 23, pp. 281–295. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany (2013). doi:
  10. 10.
    Galliani, P.: The doxastic interpretation of team semantics. In: Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics, vol. 5, p. 167. de Gruyter, New York (2015)Google Scholar
  11. 11.
    Galliani, P., Hannula, M., Kontinen, J.: Hierarchies in independence logic. In: Rocca, S.R.D. (ed.) Computer Science Logic 2013 (CSL 2013). Leibniz International Proceedings in Informatics (LIPIcs), vol. 23, pp. 263–280. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany (2013). doi:
  12. 12.
    Grädel, E., Väänänen, J.: Dependence and independence. Stud. Logica 101 (2), 399–410 (2013). doi: 10.1007/s11225-013-9479-2
  13. 13.
    Hannula, M.: Hierarchies in inclusion logic with lax semantics. In: Logic and Its Applications, pp. 100–118. Springer, Berlin (2015)Google Scholar
  14. 14.
    Hodges, W.: Compositional semantics for a language of imperfect information. J. Interest Group Pure Appl. Log. 5 (4), 539–563 (1997). doi: 10.1093/jigpal/5.4.539
  15. 15.
    Kontinen, J., Nurmi, V.: Team logic and second-order logic. In: Ono, H., Kanazawa, M., de Queiroz, R. (eds.) Logic, Language, Information and Computation. Lecture Notes in Computer Science, vol. 5514, pp. 230–241. Springer, Berlin/Heidelberg (2009). doi: 10.1007/978-3-642-02261-6_19
  16. 16.
    Kontinen, J., Link, S., Väänänen, J.: Independence in database relations. In: Logic, Language, Information, and Computation, pp. 179–193. Springer, Berlin (2013)Google Scholar
  17. 17.
    Kuusisto, A.: A double team semantics for generalized quantifiers. J. Logic Lang. Inf. 24 (2), 149–191 (2015)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Väänänen, J.: Dependence Logic. Cambridge University Press, Cambridge (2007). doi: 10.1017/CBO9780511611193
  19. 19.
    Väänänen, J.: Team logic. In: van Benthem, J., Gabbay, D., Löwe, B. (eds.) Interactive Logic. Selected Papers from the 7th Augustus de Morgan Workshop, pp. 281–302. Amsterdam University Press, Amsterdam (2007)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.School of Engineering and InformaticsUniversity of SussexFalmerUK

Personalised recommendations