Probabilistic Team Semantics

  • Arnaud Durand
  • Miika Hannula
  • Juha Kontinen
  • Arne Meier
  • Jonni VirtemaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10833)


Team semantics is a semantical framework for the study of dependence and independence concepts ubiquitous in many areas such as databases and statistics. In recent works team semantics has been generalised to accommodate also multisets and probabilistic dependencies. In this article we study a variant of probabilistic team semantics and relate this framework to a Tarskian two-sorted logic. We also show that very simple quantifier-free formulae of our logic give rise to \(\mathrm {NP} \)-hard model checking problems.



The second author was supported by grant 3711702 of the Marsden Fund. The third author was supported by grant 308712 of the Academy of Finland. This work was supported in part by the joint grant by the DAAD (57348395) and the Academy of Finland (308099). We also thank the anonymous referees for their helpful suggestions.


  1. 1.
    Corander, J., Hyttinen, A., Kontinen, J., Pensar, J., Väänänen, J.: A logical approach to context-specific independence. In: Väänänen, J., Hirvonen, Å., de Queiroz, R. (eds.) WoLLIC 2016. LNCS, vol. 9803, pp. 165–182. Springer, Heidelberg (2016). Scholar
  2. 2.
    Durand, A., Kontinen, J., de Rugy-Altherre, N., Väänänen, J.: Tractability frontier of data complexity in team semantics. In: Proceedings of GandALF 2015 (2015)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Durand, A., Hannula, M., Kontinen, J., Meier, A., Virtema, J.: Approximation and dependence via multiteam semantics. In: Gyssens, M., Simari, G. (eds.) FoIKS 2016. LNCS, vol. 9616, pp. 271–291. Springer, Cham (2016). Scholar
  4. 4.
    Durand, A., Kontinen, J., Vollmer, H.: Expressivity and complexity of dependence logic. In: Abramsky, S., Kontinen, J., Väänänen, J., Vollmer, H. (eds.) Dependence Logic: Theory and Applications, pp. 5–32. Springer, Cham (2016). Scholar
  5. 5.
    Galliani, P.: Probabilistic dependence logic. Manuscript (2008)Google 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)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Galliani, P., Hella, L.: Inclusion logic and fixed point logic. In: Proceedings of the CSL, pp. 281–295 (2013)Google Scholar
  8. 8.
    Galliani, P., Mann, A.L.: Lottery semantics: a compositional semantics for probabilistic first-order logic with imperfect information. Stud. Log. 101(2), 293–322 (2013)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Garey, M.R., Johnson, D.S.: Computers and Intractability; A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1990)zbMATHGoogle Scholar
  10. 10.
    Grädel, E., Väänänen, J.A.: Dependence and independence. Stud. Log. 101(2), 399–410 (2013)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Gyssens, M., Niepert, M., Gucht, D.V.: On the completeness of the semigraphoid axioms for deriving arbitrary from saturated conditional independence statements. Inf. Process. Lett. 114(11), 628–633 (2014)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Hannula, M., Kontinen, J.: A finite axiomatization of conditional independence and inclusion dependencies. Inf. Comput. 249, 121–137 (2016)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Hannula, M., Kontinen, J., Link, S.: On the finite and general implication problems of independence atoms and keys. J. Comput. Syst. Sci. 82(5), 856–877 (2016)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Hodges, W.: Compositional semantics for a language of imperfect information. Log. J. IGPL 5(4), 539–563 (1997). ElectronicMathSciNetCrossRefGoogle Scholar
  15. 15.
    Hyttinen, T., Paolini, G., Väänänen, J.: Quantum team logic and Bell’s inequalities. Rev. Symb. Log., 1–21 (2015). FirstViewGoogle Scholar
  16. 16.
    Hyttinen, T., Paolini, G., Väänänen, J.: A logic for arguing about probabilities in measure teams. Arch. Math. Log. 56(5–6), 475–489 (2017)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Kontinen, J.: Coherence and computational complexity of quantifier-free dependence logic formulas. Stud. Log. 101(2), 267–291 (2013)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Kontinen, J., Link, S., Väänänen, J.: Independence in database relations. In: Libkin, L., Kohlenbach, U., de Queiroz, R. (eds.) WoLLIC 2013. LNCS, vol. 8071, pp. 179–193. Springer, Heidelberg (2013). Scholar
  19. 19.
    Sevenster, M., Sandu, G.: Equilibrium semantics of languages of imperfect information. Ann. Pure Appl. Log. 161(5), 618–631 (2010)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Väänänen, J.: Dependence Logic - A New Approach to Independence Friendly Logic. London Mathematical Society Student Texts, vol. 70. Cambridge University Press, Cambridge (2007)CrossRefGoogle Scholar
  21. 21.
    Wong, S.K.M., Butz, C.J., Wu, D.: On the implication problem for probabilistic conditional independency. IEEE Trans. Syst. Man Cybern. Part A Syst. Hum. 30(6), 785–805 (2000)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Arnaud Durand
    • 1
  • Miika Hannula
    • 2
  • Juha Kontinen
    • 3
  • Arne Meier
    • 4
  • Jonni Virtema
    • 5
    Email author
  1. 1.Institut de Mathématiques de Jussieu - Paris Rive Gauche, CNRS UMR 7586, Université Paris DiderotParisFrance
  2. 2.Department of Computer ScienceUniversity of AucklandAucklandNew Zealand
  3. 3.Department of Mathematics and StatisticsUniversity of HelsinkiHelsinkiFinland
  4. 4.Institut für Theoretische InformatikLeibniz Universität HannoverHanoverGermany
  5. 5.Databases and Theoretical Computer ScienceHasselt UniversityHasseltBelgium

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