On the Role of the Complementation Rule for Data Dependencies over Incomplete Relations

Recently, an axiomatization for functional dependencies (FDs) and multivalued dependencies (MVDs) has been established where arbitrary attributes can be specified as NOT NULL. That is, the information stored over such attributes must not be incomplete. The axiomatization subsumes previous axiomatizations of FDs and MVDs where every attribute is declared to be NOT NULL, and where no attribute is declared to be NOT NULL. We establish axiomatizations which underpin formally the intuition that the complementation rule is a mere means of database normalization. The results unburden the existing theory of the strong assumption that all attributes are known at the time when the dependencies are specified. The findings extend and unify previous results for the special cases above.

[1]  Thomas Lukasiewicz Proceedings of the 7th International Symposium on the Foundations of Information and Knowledge Systems‚ FoIKS 2012‚ Kiel‚ Germany‚ March 5−9‚ 2012 , 2000 .

[2]  Y. Edmund Lien,et al.  On the Equivalence of Database Models , 1982, JACM.

[3]  Sebastian Link On the Implication of Multivalued Dependencies in Partial Database Relations , 2008, Int. J. Found. Comput. Sci..

[4]  Sebastian Link,et al.  Empirical evidence for the usefulness of Armstrong relations in the acquisition of meaningful functional dependencies , 2010, Inf. Syst..

[5]  Chen Zhan-sheng,et al.  Strong functional dependencies and their application to normal forms in XML , 2005 .

[6]  Claude Delobel,et al.  Relational database systems , 1985 .

[7]  Carlo Zaniolo,et al.  Database relations with null values , 1982, J. Comput. Syst. Sci..

[8]  Sebastian Link,et al.  Appropriate Reasoning about Data Dependencies in Fixed and Undetermined Universes , 2008, FoIKS.

[9]  Serge Abiteboul,et al.  Foundations of Databases , 1994 .

[10]  Grant E. Weddell,et al.  Reasoning about functional dependencies generalized for semantic data models , 1992, TODS.

[11]  E. F. Codd,et al.  Extending the database relational model to capture more meaning , 1979, ACM Trans. Database Syst..

[12]  Sven Hartmann,et al.  Efficient reasoning about a robust XML key fragment , 2009, TODS.

[13]  Bernhard Thalheim,et al.  Semantics in Data and Knowledge Bases , 2008, SDKB.

[14]  John Grant,et al.  Null Values in a Relational Data Base , 1977, Inf. Process. Lett..

[15]  Akifumi Makinouchi,et al.  A Consideration on Normal Form of Not-Necessarily-Normalized Relation in the Relational Data Model , 1977, VLDB.

[16]  Sven Hartmann,et al.  Characterising nested database dependencies by fragments of propositional logic , 2008, Ann. Pure Appl. Log..

[17]  Mark Levene,et al.  Axiomatisation of Functional Dependencies in Incomplete Relations , 1998, Theor. Comput. Sci..

[18]  Marco Schaerf,et al.  Tractable Reasoning via Approximation , 1995, Artif. Intell..

[19]  Catriel Beeri,et al.  A complete axiomatization for functional and multivalued dependencies in database relations , 1977, SIGMOD '77.

[20]  Jing Wang,et al.  On the Notion of an XML Key , 2008, SDKB.

[21]  David Toman,et al.  On Keys and Functional Dependencies as First-Class Citizens in Description Logics , 2006, IJCAR.

[22]  Paolo Atzeni,et al.  Functional Dependencies and Constraints on Null Values in Database Relations , 1986, Inf. Control..

[23]  Sven Hartmann,et al.  Numerical constraints on XML data , 2010, Inf. Comput..

[24]  E. F. CODD,et al.  A relational model of data for large shared data banks , 1970, CACM.

[25]  Mark Levene,et al.  Database design for incomplete relations , 1999, TODS.

[26]  Margaret S. Wu,et al.  The practical need for fourth normal form , 1992, SIGCSE '92.

[27]  Philip A. Bernstein,et al.  Synthesizing third normal form relations from functional dependencies , 1976, TODS.

[28]  Sven Hartmann,et al.  When data dependencies over SQL tables meet the logics of paradox and S-3 , 2010, PODS '10.

[29]  Philip A. Bernstein,et al.  Computational problems related to the design of normal form relational schemas , 1979, TODS.

[30]  Sebastian Link Charting the completeness frontier of inference systems for multivalued dependencies , 2008, Acta Informatica.

[31]  Georg Gottlob,et al.  Closed World Databases Opened Through Null Values , 1988, VLDB.

[32]  Joachim Biskup Inferences of Multivalued Dependencies in Fixed and Undetermined Universes , 1980, Theor. Comput. Sci..

[33]  Klaus-Dieter Schewe,et al.  Reasoning about Functional and Multi-valued Dependencies in the Presence of Lists , 2004, FoIKS.

[34]  Tomasz Imielinski,et al.  Incomplete Information in Relational Databases , 1984, JACM.

[35]  Klaus-Dieter Schewe,et al.  Weak Functional Dependencies in Higher-Order Datamodels , 2004, FoIKS.

[36]  Jef Wijsen,et al.  Temporal FDs on complex objects , 1999, TODS.

[37]  Marcelo Arenas,et al.  A normal form for XML documents , 2002, PODS '02.

[38]  Ronald Fagin,et al.  Multivalued dependencies and a new normal form for relational databases , 1977, TODS.

[39]  Bernhard Thalheim,et al.  Semantics in Databases , 2001, Semantics in Databases.

[40]  Sebastian Link Consistency Enforcement in Databases , 2001, Semantics in Databases.