Summary
The desire to extend the applicability of the relational model beyond traditional data-processing applications has stimulated interest in nested or non-first normal form relations in which the attributes of a relation can take on values which are sets or even relations themselves. In this paper, we study the role of null values in the nested relational model using an open world assumption. We extend the traditional theory and study the properties of extended operators for nested relations containing nulls. The no-information, unknown, and non-existent interpretation of nulls are discussed and the meaning of “empty set” is clarified. Finally, contrary to several previous results, we determine that the traditional axiomatization of functional and multivalued dependencies is valid in the presence of nulls.
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Abiteboul, S., Bidoit, N.: Non first normal form relations to represent hierarchically organized data. In: Proceedings of the Third ACM SIGACT-SIGMOD Symposium on Principles of Database Systems, pp. 191–200. Waterloo, 1984
Atzeni, P., Morfuni, N.M.: Functional dependencies in relations with null values. Inf. Process. Lett. 18, 233–238 (1984)
Biskup, J.: A formal approach to null values in database relations. In: Gallaire, H., Minker, J., Nicolas, J. (eds.) Advances in Database Theory, Volume 1, pp. 299–341. New York: Plenum Press 1981
Codd, E.F.: Extending the database relational model to capture more meaning. ACM Trans. Database Syst. 4, 397–434 (1979)
Fagin, R., Mendelzon, A.O., Ullman, J.D.: A simplified universal relation assumption and its properties. ACM Trans. Database Syst. 7, 343–360 (1982)
Fischer, P.C., Van Gucht, D.: Determining when a structure is a nested relation. In: Proceedings of the Eleventh International Conference on Very Large Databases, pp. 171–180. Stockholm, 1985
Fischer, P.C., Van Gucht, D.: Weak multivalued dependencies. In: Proceedings of the Third ACM SIGACT-SIGMOD Symposium on Principles of Database Systems, pp. 266–274. Waterloo, 1984
Güting, R.H., Zicari, R., Choy, D.M.: An Algebra for Structured Office Documents. Technical Report RJ 5559 (56648), IBM Almaden Research Center, 650 Harry Road, San Jose, CA 95120, 1987
Grant, J.: Null values in a relational data base. Inf. Process. Lett. 6, 156–157 (1977)
Jaeschke, G.: Nonrecursive Algebra for Relations with Relation Valued Attributes. Technical Report 84.12.001, Heidelberg Scientific Center. IBM Germany 1984
Jaeschke, G.: Recursive Algebra for Relations with Relation Valued Attributes. Technical Report 84.01.003, Heidelberg Scientific Center, IBM Germany 1984
Jaeschke, G., Schek, H.-J.: Remarks on the algebra of non first normal form relations. In: Proceedings of the ACM SIGACT-SIGMOD Symposium on Principles of Database Systems, pp. 124–138. Los Angeles, 1982
Kambayashi, Y., Tanaka, K., Takeda, K.: Synthesis of unnormalized relations incorporating more meaning. Inf. Sci. 29, 201–247 (1983)
Keller, A., Winslett Wilkins, M.: On the use of an extended relational model to handle changing incomplete information. IEEE Trans. Software Eng. 11, 620–633 (1985)
Korth, H.F., Silberschatz, A.: Database System Concepts. New York: McGraw-Hill 1986
Lien, Y.E.: Multivalued dependencies with null values in relational data bases. In: Proceedings of the Fifth International Conference on Very Large Databases, pp. 61–66. Rio De Janeiro 1979
Lien, Y.E.: On the equivalence of database models. J. ACM 29, pp. 333–362 (1982)
Lipski, W. Jr.: On databases with incomplete information. J. ACM 28, 41–70 (1981)
Lipski, W. Jr.: On semantic issues connected with incomplete information databases. ACM Trans. Database Syst. 4, 262–296 (1979)
Maier, D.: Discarding the universal relation assumption: Preliminary results. In: Proceedings of the XP1 Workshop on Relational Database Theory. New York 1980
Maier, D.: The Theory of Relational Databases. Rockville, MD: Computer Science Press 1983
Makinouchi, A.: A consideration on normal form of not-necessarily-normalized relation in the relational data model. In: Proceedings of the Third International Conference on Very Large Databases, pp. 447–453. Tokyo 1977
Imieliński, T., Lipski, W. Jr.: Incomplete information and dependencies in relational databases. In: Proceedings of ACM-SIGMOD 1983 International Conference on Management of Data, pp. 178–184. San Jose 1983
Imieliński, T., Lipski, W. Jr.: Incomplete information in relational databases. J. ACM 31, 761–791 (1984)
Imieliński, T., Lipski, W., Jr.: On representing incomplete information in a relational database. In: Proceedings of the Seventh International Conference on Very Large Databases, pp. 388–397. Cannes 1981
Ozsoyoğlu, G., Ozsoyoğlu, Z.M.: An extension of relational algebra for summary tables. In: Proceedings of the 2nd International (LBL) Conference on Statistical Database Management, pp. 202–211. Los Angeles 1983
Ozsoyoğlu, Z.M., Yuan, L.-Y.: A new normal form for nested relations. ACM Trans. Database Syst. 12, 111–136 (1987)
Pistor, P., Traunmüller, R.: A data base language for sets, lists, and tables. Inf. Syst. 11, 323–336 (1986)
Roth, M.A.: Theory of Non-First Normal Form Relational Databases. PhD thesis, The University of Texas at Austin, Austin, Texas, May 1986
Roth, M.A., Kirkpatrick, J.E.: Algebras for nested relations. Data Eng. 11, 39–47 (1988)
Roth, M.A., Korth, H.F., Batory, D.S.: SQL/NF: A query language for l1NF relational databases. Inf. Syst. 12, 99–114 (1987)
Roth, M.A., Korth, H.F., Silberschatz, A.: Extended algebra and calculus for ⌝1NF relational databases. ACM Trans. Database Syst. 13, 389–417 (1988)
Schek, H.-J.: Towards a basic relational NF2 algebra processor. In: Proceedings of the International Conference on Foundations of Data Organization, pp. 173–182. Kyoto 1985
Schek, H.-J., Scholl, M.H.: An Algebra for the Relational Model with Relation-Valued Attributes. Technical Report DVSI-1984-T1. Technical University of Darmstadt, Darmstadt, FRG 1984
Schek, H.-J., Scholl, M.H.: Die NF2-relationenalgebra zur einheitlichen Manipulation externer, konzeptueller und interner Datenstrukturen. In: Schmidt, J. (ed.) Sprachen für Datenbanken. Informatik Fachberichte Nr. 72. Berlin Heidelberg New York Tokyo: Springer 1983
Scholl, M.H.: Theoretical foundation of algebraic optimization utilizing unnormalized relations. In: International Conference on Database Theory, Rome. Lect. Notes Comput. Sci. 243, 380–396 (1986)
Sciore, E.: Null Values, Updates, and Normalization in Relational Databases. Technical Report, Department of Electrical Engineering and Computer Science, Princeton University 1979
Thomas, S.J., Fischer, P.C.: Nested relational structures. In: Kanellakis, P.C. (ed.) Advances in Computing Research, Vol. 3. The Theory of Databases, pp. 269–307. Greenwich, CT: JAI Press 1985
Vassiliou, Y.: Functional dependencies and incomplete information. In: Proceedings of the Sixth International Conference on Very Large Databases, pp. 260–269. Montreal 1980
Vassiliou, Y.: Null values in data base management: A denotational semantics approach. In: Proceedings of ACM-SIGMOD International Conference on Management of Data, pp. 162–169. Boston 1979
Wong, E.: A statistical approach to incomplete information in database systems. ACM Trans. Database Syst. 7, 470–488 (1982)
Zaniolo, C.: Database relations with null values. J. Comput. Syst. Sci. 28, 142–166 (1984)
Zaniolo, C.: tA Formal Treatment of Nonexistent Values in Database Relations. Technical Report, Bell Laboratories, Holmdel, NJ, 1983
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Currently with the Air Force Institute of Technology, AFIT/ENG, Wright-Patterson AFB, OH 45433, USA
Research partially supported by an IBM Faculty Development A ward and NSF grant DCR-8507224
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Roth, M.A., Korth, H.F. & Silberschatz, A. Null values in nested relational databases. Acta Informatica 26, 615–642 (1989). https://doi.org/10.1007/BF00288974
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DOI: https://doi.org/10.1007/BF00288974