Complexity of Propositional Independence and Inclusion Logic

  • Miika Hannula
  • Juha Kontinen
  • Jonni VirtemaEmail author
  • Heribert Vollmer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9234)


We classify the computational complexity of the satisfiability, validity and model-checking problems for propositional independence and inclusion logic and their extensions by the classical negation.


Propositional logic Team semantics Dependence Independence Inclusion Satisfiability Validity Model-checking 


  1. 1.
    Buss, S.: The Boolean formula value problem is in ALOGTIME. In: Proceedings of the Nineteenth Annual ACM Symposium on Theory of Computing, STOC 1987, pp. 123–131, ACM, New York (1987)Google Scholar
  2. 2.
    Chandra, A.K., Kozen, D.C., Larry, S.J.: Alternation. J. ACM 28(1), 114–133 (1981)CrossRefzbMATHGoogle Scholar
  3. 3.
    Cook, S.A.: The complexity of theorem-proving procedures. In: Proceedings of the Third Annual ACM Symposium on Theory of Computing, STOC 1971, pp. 151–158. ACM, New York (1971)Google Scholar
  4. 4.
    Ebbing, J., Lohmann, P.: Complexity of model checking for modal dependence logic. In: Bieliková, M., Friedrich, G., Gottlob, G., Katzenbeisser, S., Turán, G. (eds.) SOFSEM 2012. LNCS, vol. 7147, pp. 226–237. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  5. 5.
    Galliani, P.: Inclusion and exclusion dependencies in team semantics: on some logics of imperfect information. Ann. Pure Appl. Logic 163(1), 68–84 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Grädel, E., Väänänen, J.: Dependence and independence. Stud. Logica 101(2), 399–410 (2013)CrossRefzbMATHGoogle Scholar
  7. 7.
    Hannula, M., Kontinen, J.: A finite axiomatization of conditional independence and inclusion dependencies. In: Beierle, C., Meghini, C. (eds.) FoIKS 2014. LNCS, vol. 8367, pp. 211–229. Springer, Heidelberg (2014) CrossRefGoogle Scholar
  8. 8.
    Hannula, M., Kontinen, J., Virtema, J., Vollmer, H.: Complexity of propositional independence and inclusion logic. In: CoRR, (2015). abs/1504.06135
  9. 9.
    Hella, L.: Private communicationGoogle Scholar
  10. 10.
    Hella, L., Kuusisto, A., Meier, A., Vollmer, H.: Modal inclusion logic: Being lax is simpler than being strict. In: Italiano, G.F., et al. (eds.) MFCS 2015, Part I, LNCS, vol. 9234, pp. 281–292. Springer, Heidelberg (2015)Google Scholar
  11. 11.
    Kontinen, J., Müller, J.-S., Schnoor, H., Vollmer, H.: A van Benthem theorem for modal team semantics. In: CoRR (2014). abs/1410.6648
  12. 12.
    Kontinen, J., Nurmi, V.: Team logic and second-order logic. Fundam. Inform. 106(2–4), 259–272 (2011)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Levin, L.A.: Universal search problems. Probl. Inf. Transm. 9(3), 265–266 (1973)Google Scholar
  14. 14.
    Lohmann, P., Vollmer, H.: Complexity results for modal dependence logic. Stud. Logica 101(2), 343–366 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Orponen, P.: Complexity classes of alternating machines with oracles. In: Diaz, J. (ed.) Automata, Languages and Programming. LNCS, vol. 154, pp. 573–584. Springer, Heidelberg (1983)CrossRefGoogle Scholar
  16. 16.
    Sano, K., Virtema, J.: Axiomatizing propositional dependence logics. In: CoRR (2014). abs/1410.5038
  17. 17.
    Väänänen, J.: Dependence Logic. Cambridge University Press, Cambridge (2007)CrossRefzbMATHGoogle Scholar
  18. 18.
    Virtema, J.: Complexity of validity for propositional dependence logics. In: Peron, A., Piazza, C. (eds.) Proceedings Fifth International Symposium on Games, Automata, Logics and Formal Verification, GandALF 2014, Verona, Italy. EPTCS, vol. 161, pp. 18–31, 10–12 September 2014Google Scholar
  19. 19.
    Yang, F.: On extensions and variants of dependence logic. Ph.D. thesis, University of Helsinki (2014)Google Scholar
  20. 20.
    Yang, F., Väänänen, J.: Propositional logics of dependence and independence. In: Part I. CoRR (2014). abs/1412.7998

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Miika Hannula
    • 1
  • Juha Kontinen
    • 1
  • Jonni Virtema
    • 2
    Email author
  • Heribert Vollmer
    • 2
  1. 1.University of HelsinkiDepartment of Mathematics and StatisticsHelsinkiFinland
  2. 2.Leibniz Universität HannoverInstitut für Theoretische Informatik, Fakultät für Elektrotechnik und InformatikHanoverGermany

Personalised recommendations