On Dependence Logic

Chapter
Part of the Outstanding Contributions to Logic book series (OCTR, volume 5)

Abstract

Dependence logic extends the language of first order logic by means of dependence atoms and aims to establish a basic theory of dependence and independence underlying such seemingly unrelated subjects as causality, random variables, bound variables in logic, database theory, the theory of social choice, and even quantum physics. In this work we summarize the setting of dependence logic and recall the main results of this rapidly developing area of research.

Keywords

Dependence logic Independence Team semantics Database theory Belief representation 

References

  1. 1.
    Abramsky S, Väänänen J (2009) From IF to BI. Synthese 167(2):207–230. doi:10.1007/s11229-008-9415-6
  2. 2.
    Armstrong WW (1974) Dependency structures of data base relationships. Inf Process 74Google Scholar
  3. 3.
    van Benthem J (1997) Modal foundations for predicate logic. Log J IGPL 5(2):259–286 (electronic). doi:10.1093/jigpal/5.2.259
  4. 4.
    Casanova MA, Fagin R, Papadimitriou CH (1982) Inclusion dependencies and their interaction with functional dependencies. In: Proceedings of the 1st ACM SIGACT-SIGMOD symposium on principles of database systems, PODS’82. ACM, New York, NY, USA, pp 171–176. doi:10.1145/588111.588141
  5. 5.
    Casanova MA, Vidal VMP (1983) Towards a sound view integration methodology. In: Proceedings of the 2nd ACM SIGACT-SIGMOD symposium on principles of database systems, PODS’83. ACM, New York, NY, USA, pp 36–47. doi:10.1145/588058.588065
  6. 6.
    Durand A, Kontinen J (2012) Hierarchies in dependence logic. ACM Trans Comput Log (TOCL) 13(4):31. doi:http://dx.doi.org/10.1145/2362355.2362359
  7. 7.
    Ebbing J, Kontinen J, Müller J-S, Vollmer H (2012) A fragment of dependence logic capturing polynomial time. arXiv:1210.3321. URL: http://arxiv.org/abs/1210.3321
  8. 8.
    Enderton HB (1970) Finite partially-ordered quantifiers. Math Log Q 16(8):393–397. doi:10.1002/malq.19700160802
  9. 9.
    Fagin R (1981) A normal form for relational databases that is based on domains and keys. ACM Trans Database Syst 6:387–415. doi:10.1145/319587.319592
  10. 10.
    Galliani P (2012) Inclusion and exclusion dependencies in team semantics: on some logics of imperfect information. Ann Pure Appl Log 163(1):68–84. doi:10.1016/j.apal.2011.08.005
  11. 11.
    Galliani P (2012) The dynamics of imperfect information. PhD thesis, University of Amsterdam, September 2012. URL: http://dare.uva.nl/record/425951
  12. 12.
    Galliani P (2013) Upwards closed dependencies in team semantics. In: Puppis G, Villa T (eds) Proceedings fourth international symposium on games, automata, logics and formal verification, vol 119 of EPTCS, pp 93–106. doi:http://dx.doi.org/10.4204/EPTCS.119
  13. 13.
    Galliani P, Hannula M, Kontinen J (2012) Hierarchies in independence logic. In: Rocca SRD (ed) Computer science logic 2013 (CSL 2013), Leibniz international proceedings in informatics (LIPIcs), vol 23. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, pp 263–280. doi:http://dx.doi.org/10.4230/LIPIcs.CSL.2013.263
  14. 14.
    Galliani P, Hella L (2013) Inclusion logic and fixed point logic. In: Rocca SRD (ed) Computer science logic 2013 (CSL 2013), Leibniz international proceedings in informatics (LIPIcs), vol 23. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, pp 281–295. doi:http://dx.doi.org/10.4230/LIPIcs.CSL.2013.281
  15. 15.
    Grädel E, Väänänen J (2013) Dependence and independence. Studia Logica 101(2):399–410. doi:10.1007/s11225-013-9479-2
  16. 16.
    Herrmann C (1995) Corrigendum: corrigendum to “on the undecidability of implications between embedded multivalued database dependencies” [Inf Comput 122:221–235 (1995)]. Inf Comput 204(12):1847–1851. doi:10.1016/j.ic.2006.09.002
  17. 17.
    Herrmann C (1995) On the undecidability of implications between embedded multivalued database dependencies. Inf Comput 122(2):221–235. doi:10.1006/inco.1995.1148
  18. 18.
    Hintikka J, Sandu G (1989) Informational independence as a semantic phenomenon. In: Fenstad JE, Frolov IT, Hilpinen R (eds) Logic, methodology and philosophy of science, pp. 571–589. Elsevier, Amsterdam. doi:10.1016/S0049-237X(08)70066-1
  19. 19.
    Hodges W (1997) Compositional semantics for a language of imperfect information. Log J IGPL 5(4):539–563 (electronic). doi:10.1093/jigpal/5.4.539
  20. 20.
    Hodges W (1997) Some strange quantifiers. In: Structures in logic and computer science, Lecture Notes in Computer Science, vol 1261. Springer, Berlin, pp 51–65. doi:10.1007/3-540-63246-8_4
  21. 21.
    Immerman N (1986) Relational queries computable in polynomial time. Inf Control 68(1):86–104Google Scholar
  22. 22.
    Kontinen J, Link S, Väänänen J (2013) Independence in database relations. In: Proceedings of the 20th International workshop (WOLLIC) on logic, language, information, and computation. Lecture notes in computer science, vol 8071. Springer, pp 152–156Google Scholar
  23. 23.
    Kontinen J, Väänänen J (2009) On definability in dependence logic. J Log Lang Inf 18(3):317–332. doi:10.1007/s10849-009-9082-0
  24. 24.
    Kontinen J, Väänänen J (2013) Axiomatizing first order consequences in dependence logic. Ann Pure Appl Log 164:1101–1117. URL: http://arxiv.org/abs/1208.0176
  25. 25.
    Mann AL, Sandu G, Sevenster M (2011) Independence-friendly logic: A game-theoretic approach. In: London Mathematical Society lecture note series, vol 386. Cambridge University Press, Cambridge. doi:10.1017/CBO9780511981418
  26. 26.
    Mannila H, Räihä KJ (1992) The design of relational databases. Addison-Wesley, CambridgeGoogle Scholar
  27. 27.
    Naumov P, Nicholls B (2013) Re axiomatization of conditional independence. In: TARK, 2013. http://www2.mcdaniel.edu/pnaumov/papers/2013.tark.nn.pdf
  28. 28.
    Parker D Jr, Parsaye-Ghomi K (1980) Inferences involving embedded multivalued dependencies and transitive dependencies. In: Proceedings of the 1980 ACM SIGMOD international conference on management of data, ACM, pp 52–57. doi:10.1145/582250.582259
  29. 29.
    Väänänen J (2007) Dependence logic. In: London Mathematical Society student texts, vol 70. Cambridge University Press, Cambridge. doi:10.1017/CBO9780511611193
  30. 30.
    Vardi MY (1982) The complexity of relational query languages. In: Proceedings of the fourteenth annual ACM symposium on theory of computing. ACM, pp 137–146Google Scholar
  31. 31.
    Walkoe WJ Jr (1970) Finite partially-ordered quantification. J Symbolic Log 35:535–555. doi:10.2307/2271440

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of HelsinkiHelsinkiFinland
  2. 2.Department of Mathematics and StatisticsUniversity of HelsinkiHelsinkiFinland
  3. 3.Institute for Logic, Language and ComputationUniversity of AmsterdamAmsterdamThe Netherlands

Personalised recommendations