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Foundations for a Fourth Normal Form over SQL-Like Databases

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Part of the Lecture Notes in Computer Science book series (LNISA,volume 7260)

Abstract

In the relational model of data the Fourth Normal Form condition guarantees the elimination of data redundancy in terms of functional and multivalued dependencies. For efficient means of data processing the industry standard SQL permits partial data and duplicate rows of data to occur in database systems. Here, the combined class of uniqueness constraints, functional and multivalued dependencies is more expressive than the class of functional and multivalued dependencies itself. Consequently, the Fourth Normal Form condition is not suitable for SQL databases. We characterize the associated implication problem of the combined class in the presence of NOT NULL constraints axiomatically, algorithmically and logically. Based on these results we are able to establish a suitable Fourth Normal Form condition for SQL.

Keywords

  • Functional Dependency
  • Inference Rule
  • Uniqueness Constraint
  • Relation Schema
  • Propositional Variable

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.

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References

  1. Arenas, M., Libkin, L.: An information-theoretic approach to normal forms for relational and XML data. J. ACM 52(2), 246–283 (2005)

    CrossRef  MATH  MathSciNet  Google Scholar 

  2. Atzeni, P., Morfuni, N.: Functional dependencies and constraints on null values in database relations. Information and Control 70(1), 1–31 (1986)

    CrossRef  MATH  MathSciNet  Google Scholar 

  3. Beeri, C., Fagin, R., Howard, J.H.: A complete axiomatization for fds and mvds in database relations. In: SIGMOD, pp. 47–61. ACM (1977)

    Google Scholar 

  4. Codd, E.F.: A relational model of data for large shared data banks. Commun. ACM 13(6), 377–387 (1970)

    CrossRef  MATH  Google Scholar 

  5. Date, C., Darwen, H.: A guide to the SQL standard. Addison-Wesley Professional, Reading (1997)

    Google Scholar 

  6. Demetrovics, J., Katona, G., Miklós, D., Seleznjev, O., Thalheim, B.: Asymptotic properties of keys and functional dependencies in random databases. Theor. Comput. Sci. 190(2), 151–166 (1998)

    CrossRef  MATH  MathSciNet  Google Scholar 

  7. Demetrovics, J., Katona, G.O.H., Miklós, D., Thalheim, B.: On the Number of Independent Functional Dependencies. In: Dix, J., Hegner, S.J. (eds.) FoIKS 2006. LNCS, vol. 3861, pp. 83–91. Springer, Heidelberg (2006)

    CrossRef  Google Scholar 

  8. Demetrovics, J., Molnár, A., Thalheim, B.: Graphical Reasoning for Sets of Functional Dependencies. In: Atzeni, P., Chu, W., Lu, H., Zhou, S., Ling, T.-W. (eds.) ER 2004. LNCS, vol. 3288, pp. 166–179. Springer, Heidelberg (2004)

    CrossRef  Google Scholar 

  9. Demetrovics, J., Molnár, A., Thalheim, B.: Relationship Design Using Spreadsheet Reasoning for Sets of Functional Dependencies. In: Manolopoulos, Y., Pokorný, J., Sellis, T.K. (eds.) ADBIS 2006. LNCS, vol. 4152, pp. 108–123. Springer, Heidelberg (2006)

    CrossRef  Google Scholar 

  10. Fagin, R.: Multivalued dependencies and a new normal form for relational databases. ACM Trans. Database Syst. 2(3), 262–278 (1977)

    CrossRef  Google Scholar 

  11. Galil, Z.: An almost linear-time algorithm for computing a dependency basis in a relational database. J. ACM 29(1), 96–102 (1982)

    CrossRef  MATH  MathSciNet  Google Scholar 

  12. Hartmann, S., Kirchberg, M., Link, S.: Design by example for SQL table definitions with functional dependencies. The VLDB Journal (2011), doi:10.1007/s00778-011-0239-5

    Google Scholar 

  13. Hartmann, S., Leck, U., Link, S.: On Codd families of keys over incomplete relations. Comput. J. 54(7), 1166–1180 (2011)

    CrossRef  Google Scholar 

  14. Hartmann, S., Link, S.: Efficient reasoning about a robust XML key fragment. ACM Trans. Database Syst. 34(2) (2009)

    Google Scholar 

  15. Hartmann, S., Link, S.: Numerical constraints on XML data. Inf. Comput. 208(5), 521–544 (2010)

    CrossRef  MATH  MathSciNet  Google Scholar 

  16. Hartmann, S., Link, S.: When data dependencies over SQL tables meet the Logics of Paradox and \(\mathcal{S}\)-3. In: PODS, pp. 317–326 (2010)

    Google Scholar 

  17. Hartmann, S., Link, S., Schewe, K.-D.: Weak Functional Dependencies in Higher-Order Datamodels. In: Seipel, D., Turull-Torres, J.M. (eds.) FoIKS 2004. LNCS, vol. 2942, pp. 116–133. Springer, Heidelberg (2004)

    CrossRef  Google Scholar 

  18. Imielinski, T., Lipski Jr., W.: Incomplete information in relational databases. J. ACM 31(4), 761–791 (1984)

    CrossRef  MATH  MathSciNet  Google Scholar 

  19. Köhler, H., Link, S.: Armstrong axioms and Boyce-Codd-Heath normal form under bag semantics. Inf. Process. Lett. 110(16), 717–724 (2010)

    CrossRef  MATH  MathSciNet  Google Scholar 

  20. Lien, E.: On the equivalence of database models. J. ACM 29(2), 333–362 (1982)

    CrossRef  MATH  Google Scholar 

  21. Link, S.: Consistency Enforcement in Databases. In: Bertossi, L., Katona, G.O.H., Schewe, K.-D., Thalheim, B. (eds.) Semantics in Databases 2001. LNCS, vol. 2582, pp. 139–159. Springer, Heidelberg (2003)

    CrossRef  Google Scholar 

  22. Link, S., Schewe, K.-D.: An arithmetic theory of consistency enforcement. Acta Cybern. 15(3), 379–416 (2002)

    MATH  MathSciNet  Google Scholar 

  23. Paredaens, J., De Bra, P., Gyssens, M., Van Gucht, D.: The Structure of the Relational Database Model. Springer, Heidelberg (1989)

    CrossRef  MATH  Google Scholar 

  24. Sagiv, Y., Delobel, C., Parker Jr., D.S., Fagin, R.: An equivalence between relational database dependencies and a fragment of propositional logic. J. ACM 28(3), 435–453 (1981)

    CrossRef  MATH  MathSciNet  Google Scholar 

  25. Schaerf, M., Cadoli, M.: Tractable reasoning via approximation. Artif. Intell. 74, 249–310 (1995)

    CrossRef  MATH  MathSciNet  Google Scholar 

  26. Schewe, K.-D., Thalheim, B.: Limitations of rule triggering systems for integrity maintenance in the context of transition specifications. Acta Cybern. 13(3), 277–304 (1998)

    MATH  MathSciNet  Google Scholar 

  27. Schewe, K.-D., Thalheim, B.: Towards a theory of consistency enforcement. Acta Inf. 36(2), 97–141 (1999)

    CrossRef  MATH  MathSciNet  Google Scholar 

  28. Selesnjev, O., Thalheim, B.: On the numbers of shortes keys in relational databases on non-uniform domains. Acta Cybern. 8, 267–271 (1988)

    Google Scholar 

  29. Seleznjev, O., Thalheim, B.: Behavior of keys in random databases. In: SCCC, pp. 171–183 (1998)

    Google Scholar 

  30. Thalheim, B.: A compelte axiomatization for full join dependencies in relations. Bulletin of the EATCS 24, 109–114 (1984)

    Google Scholar 

  31. Thalheim, B.: Deductive normal forms of relations. In: Mathematical Methods of Specification and Synthesis of Software Systems, pp. 226–230 (1985)

    Google Scholar 

  32. Thalheim, B.: Design Tools for Large Relational Database Systems. In: Biskup, J., Demetrovics, J., Paredaens, J., Thalheim, B. (eds.) MFDBS 1987. LNCS, vol. 305, pp. 210–224. Springer, Heidelberg (1988)

    CrossRef  Google Scholar 

  33. Thalheim, B.: Open Problems in Database Theory. In: Biskup, J., Demetrovics, J., Paredaens, J., Thalheim, B. (eds.) MFDBS 1987. LNCS, vol. 305, pp. 241–247. Springer, Heidelberg (1988)

    CrossRef  Google Scholar 

  34. Thalheim, B.: The Higher-Order Entity-Relationship model and (DB)2. In: Demetrovics, J., Thalheim, B. (eds.) MFDBS 1989. LNCS, vol. 364, pp. 382–397. Springer, Heidelberg (1989)

    CrossRef  Google Scholar 

  35. Thalheim, B.: On semantic issues connected with keys in relational databases permitting null values. Elektronische Informationsverarbeitung und Kybernetik 25(1-2), 11–20 (1989)

    MathSciNet  Google Scholar 

  36. Thalheim, B.: Dependencies in relational databases. Teubner (1991)

    Google Scholar 

  37. Thalheim, B.: Fundamentals of Cardinality Constraints. In: Pernul, G., Tjoa, A.M. (eds.) ER 1992. LNCS, vol. 645, pp. 7–23. Springer, Heidelberg (1992)

    CrossRef  Google Scholar 

  38. Thalheim, B.: The number of keys in relational and nested relational databases. Discrete Applied Mathematics 40(2) (1992)

    Google Scholar 

  39. Thalheim, B.: An overview on database theory. Datenbank Rundbrief 10, 2–13 (1992)

    Google Scholar 

  40. Thalheim, B.: Database design strategies. In: CISM, pp. 267–285 (1993)

    Google Scholar 

  41. Thalheim, B.: Foundations of Entity - Relationship Modeling. Ann. Math. Artif. Intell. 7(1-4), 197–256 (1993)

    CrossRef  MATH  MathSciNet  Google Scholar 

  42. Thalheim, B.: Entity-Relationship modeling. Springer, Heidelberg (2000)

    CrossRef  MATH  Google Scholar 

  43. Thalheim, B.: Conceptual Treatment of Multivalued Dependencies. In: Song, I.-Y., Liddle, S.W., Ling, T.-W., Scheuermann, P. (eds.) ER 2003. LNCS, vol. 2813, pp. 363–375. Springer, Heidelberg (2003)

    CrossRef  Google Scholar 

  44. Thalheim, B.: Component development and construction for database design. Data Knowl. Eng. 54(1), 77–95 (2005)

    CrossRef  Google Scholar 

  45. Vincent, M.: Semantic foundation of 4NF in relational database design. Acta Inf. 36, 1–41 (1999)

    CrossRef  MathSciNet  Google Scholar 

  46. Vincent, M., Liu, J., Liu, C.: Strong FDs and their application to normal forms in XML. ACM Trans. Database Syst. 29(3), 445–462 (2004)

    CrossRef  Google Scholar 

  47. Zaniolo, C.: Database relations with null values. J. Comput. Syst. Sci. 28(1), 142–166 (1984)

    CrossRef  MATH  MathSciNet  Google Scholar 

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Ferrarotti, F., Hartmann, S., Köhler, H., Link, S., Vincent, M.W. (2012). Foundations for a Fourth Normal Form over SQL-Like Databases. In: Düsterhöft, A., Klettke, M., Schewe, KD. (eds) Conceptual Modelling and Its Theoretical Foundations. Lecture Notes in Computer Science, vol 7260. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28279-9_8

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  • DOI: https://doi.org/10.1007/978-3-642-28279-9_8

  • Publisher Name: Springer, Berlin, Heidelberg

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