On Interactions of Cardinality Constraints, Key, and Functional Dependencies

Cardinality constraints as well as key dependencies and functional dependencies are among the most popular classes of constraints in database models. While the formal properties of each of the constraint classes are now well understood, little is known about their interaction. The objective of this paper is to discuss how constraints from these classes go together. We propose methods for reasoning about a set of cardinality constraints, key and certain functional dependencies. Moreover, we construct Armstrong databases for these constraints, which are of special interest for example-based deduction in database design.

[1]  Zoltán Füredi,et al.  Minimum matrix representation of closure operations , 1985, Discret. Appl. Math..

[2]  Heikki Mannila,et al.  Design by Example: An Application of Armstrong Relations , 1986, J. Comput. Syst. Sci..

[3]  Joachim Biskup,et al.  Decomposition of Relationships through Pivoting , 1996, ER.

[4]  Bolyai János Matematikai Társulat,et al.  Combinatorial theory and its applications , 1970 .

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

[6]  Bernhard Thalheim,et al.  Fundamentals of Cardinality Constraints , 1992, ER.

[7]  David W. Embley,et al.  Cardinality Constraints in Semantic Data Models , 1993, Data Knowl. Eng..

[8]  Jef Wijsen,et al.  Functional Dependencies Generalized for Temporal Databases that Include Object-Identity , 1993, ER.

[9]  János Demetrovics,et al.  Some results about functional dependencies , 1988, Acta Cybern..

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

[11]  Maurizio Lenzerini,et al.  On The Satisfiability of Dependency Constraints in Entity-Relationship Schemata , 1987, VLDB.

[12]  Bernhard Thalheim,et al.  Dependencies in relational databases , 1991, Teubner-Texte zur Mathematik.

[13]  Hanfried Lenz,et al.  Design theory , 1985 .

[14]  Marc Gyssens,et al.  The Structure of the Relational Database Model , 1989, EATCS Monographs on Theoretical Computer Science.

[15]  Peter P. Chen.  The entity-relationship model: toward a unified view of data , 1975, VLDB '75.

[16]  Sven Hartmann.  Graph-Theoretical Methods to Construct Entity-Relationship Databases , 1995, WG.

[17]  Dimitri Theodoratos.  Deductive Object Oriented Schemas , 1996, ER.

[18]  Philip A. Bernstein,et al.  Decomposition of a Data Base and the Theory of Boolean Switching Functions , 1973, IBM J. Res. Dev..

[19]  Richard Statman,et al.  On the Structure of Armstrong Relations for Functional Dependencies , 1984, JACM.

[20]  Peter P. Chen.  The entity-relationship approach , 1993 .

[21]  Sven Hartmann.  On the Consistency of Int-cardinality Constraints , 1998, ER.

[22]  Bernhard Thalheim,et al.  Foundations of entity-relationship modeling , 1993, Annals of Mathematics and Artificial Intelligence.

[23]  David Maier,et al.  The Theory of Relational Databases , 1983 .