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Facets of Distribution Identities in Probabilistic Team Semantics

  • Miika Hannula
  • Åsa Hirvonen
  • Juha Kontinen
  • Vadim Kulikov
  • Jonni VirtemaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11468)

Abstract

We study probabilistic team semantics which is a semantical framework allowing the study of logical and probabilistic dependencies simultaneously. We examine and classify the expressive power of logical formalisms arising by different probabilistic atoms such as conditional independence and different variants of marginal distribution equivalences. We also relate the framework to the first-order theory of the reals and apply our methods to the open question on the complexity of the implication problem of conditional independence.

Keywords

Team semantics Probabilistic logic Conditional independence 

References

  1. 1.
    Abramsky, S.: Relational hidden variables and non-locality. Studia Logica 101(2), 411–452 (2013)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Barbero, F., Sandu, G.: Interventionist counterfactuals on causal teams. In: Finkbeiner, B., Kleinberg, S. (eds.) Proceedings 3rd Workshop on Formal Reasoning About Causation, Responsibility, and Explanations in Science and Technology, Thessaloniki, Greece, 21st April 2018. Electronic Proceedings in Theoretical Computer Science, vol. 286, pp. 16–30. Open Publishing Association (2019).  https://doi.org/10.4204/EPTCS.286.2CrossRefGoogle Scholar
  3. 3.
    Ben-Or, M., Kozen, D., Reif, J.: The complexity of elementary algebra and geometry. J. Comput. Syst. Sci. 32(2), 251–264 (1986)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Berman, L.: The complexity of logical theories. Theoret. Comput. Sci. 11(1), 71–77 (1980)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Canny, J.: Some algebraic and geometric computations in PSPACE. In: Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing, STOC 1988, pp. 460–467. ACM, New York (1988)Google Scholar
  6. 6.
    Cavallo, R., Pittarelli, M.: The theory of probabilistic databases. In: Proceedings of the 13th International Conference on Very Large Data Bases, VLDB 1987, pp. 71–81. Morgan Kaufmann Publishers Inc., San Francisco (1987)Google Scholar
  7. 7.
    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).  https://doi.org/10.1007/978-3-662-52921-8_11CrossRefGoogle Scholar
  8. 8.
    Durand, A., Hannula, M., Kontinen, J., Meier, A., Virtema, J.: Approximation and dependence via multiteam semantics. Ann. Math. Artif. Intell. 83(3–4), 297–320 (2018). https://doi.org/10.1007/s10472-017-9568-4MathSciNetCrossRefGoogle Scholar
  9. 9.
    Durand, A., Hannula, M., Kontinen, J., Meier, A., Virtema, J.: Probabilistic team semantics. In: Ferrarotti, F., Woltran, S. (eds.) FoIKS 2018. LNCS, vol. 10833, pp. 186–206. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-90050-6_11CrossRefzbMATHGoogle Scholar
  10. 10.
    Ferrante, J., Rackoff, C.: A decision procedure for the first order theory of real addition with order. SIAM J. Comput. 4(1), 69–76 (1975).  https://doi.org/10.1137/0204006MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Galliani, P.: Game values and equilibria for undetermined sentences of dependence logic. MSc thesis. ILLC Publications, MoL-2008-08 (2008)Google Scholar
  12. 12.
    Galliani, P.: Inclusion and exclusion dependencies in team semantics: on some logics of imperfect information. Ann. Pure Appl. Logic 163(1), 68–84 (2012)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Galliani, P., Väänänen, J.: On dependence logic. In: Baltag, A., Smets, S. (eds.) Johan van Benthem on Logic and Information Dynamics. OCL, vol. 5, pp. 101–119. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-06025-5_4CrossRefzbMATHGoogle Scholar
  14. 14.
    Grädel, E., Gurevich, Y.: Metafinite model theory. Inf. Comput. 140(1), 26–81 (1998).  https://doi.org/10.1006/inco.1997.2675MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Grädel, E., Väänänen, J.: Dependence and independence. Studia Logica 101(2), 399–410 (2013).  https://doi.org/10.1007/s11225-013-9479-2MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Hannula, M., Hirvonen, Å., Kontinen, J., Kulikov, V., Virtema, J.: Facets of distribution identities in probabilistic team semantics. CoRR abs/1812.05873 (2018). http://arxiv.org/abs/1812.05873
  17. 17.
    Hannula, M., Kontinen, J.: A finite axiomatization of conditional independence and inclusion dependencies. Inf. Comput. 249, 121–137 (2016).  https://doi.org/10.1016/j.ic.2016.04.001MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Hannula, M., Kontinen, J., Lück, M., Virtema, J.: On quantified propositional logics and the exponential time hierarchy. In: GandALF. EPTCS, vol. 226, pp. 198–212 (2016)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Hannula, M., Kontinen, J., Virtema, J.: Polyteam semantics. In: Artemov, S., Nerode, A. (eds.) LFCS 2018. LNCS, vol. 10703, pp. 190–210. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-72056-2_12CrossRefGoogle Scholar
  20. 20.
    Hannula, M., Kontinen, J., Virtema, J., Vollmer, H.: Complexity of propositional logics in team semantic. ACM Trans. Comput. Log. 19(1), 2:1–2:14 (2018).  https://doi.org/10.1145/3157054MathSciNetCrossRefGoogle Scholar
  21. 21.
    Hodges, W.: Compositional semantics for a language of imperfect information. J. Interest Group Pure Appl. Logics 5(4), 539–563 (1997)MathSciNetzbMATHGoogle Scholar
  22. 22.
    Hyttinen, T., Paolini, G., Väänänen, J.: A logic for arguing about probabilities in measure teams. Arch. Math. Logic 56(5-6), 475–489 (2017).  https://doi.org/10.1007/s00153-017-0535-xMathSciNetCrossRefGoogle Scholar
  23. 23.
    Krebs, A., Meier, A., Virtema, J., Zimmermann, M.: Team semantics for the specification and verification of hyperproperties. In: Potapov, I., Spirakis, P., Worrell, J. (eds.) 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), vol. 117, pp. 10:1–10:16. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Dagstuhl (2018).  https://doi.org/10.4230/LIPIcs.MFCS.2018.10
  24. 24.
    Lück, M.: Canonical models and the complexity of modal team logic. In: 27th EACSL Annual Conference on Computer Science Logic, CSL 2018, 4–7 September 2018, Birmingham, UK, pp. 30:1–30:23 (2018).  https://doi.org/10.4230/LIPIcs.CSL.2018.30
  25. 25.
    Niepert, M., Gyssens, M., Sayrafi, B., Gucht, D.V.: On the conditional independence implication problem: a lattice-theoretic approach. Artif. Intell. 202, 29–51 (2013).  https://doi.org/10.1016/j.artint.2013.06.005MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Väänänen, J.: Dependence Logic. Cambridge University Press, Cambridge (2007)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.University of HelsinkiHelsinkiFinland
  2. 2.Aalto UniversityEspooFinland
  3. 3.Hasselt UniversityHasseltBelgium

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