Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
W.W. Armstrong, Dependency structures of database relationship, Information Processing 74 (1974) 580–583.
C. Beeri, M. Dowd, R. Fagin and R. Statman, On the structure of Armstrong relations for functional dependencies, J. ACM 31 (1984) 30–46.
J. Biskup, R. Menzel, T. Polle and Y. Sagiv, Decomposition of relationships through pivoting, in: B. Thalheim (ed.), Conceptual Modeling (Springer, Berlin, 1996) 28–41.
P.P. Chen, The Entity-Relationship Model: Towards a unified view of data, ACM Trans. Database Syst. 1 (1984) 9–36.
E.F. Codd, A relation model of data for large shared data banks, Commun. ACM 13 (1970) 377–387.
C. Delobel and R.G. Casey, Decompositions of a database and the theory of Boolean switching functions, IBM J. Res. Dev. 17 (1973) 374–386.
J. Demetrovics, Z. Füredi and G.O.H. Katona, Minimum matrix representation of closure operations, Discrete Appl. Math. 11 (1985) 115–128.
J. Demetrovics and V.D. Thi, Some results about functional dependencies, Acta Cybern. 8 (1988) 273–278.
A. Hajnal and E. Szemeredi, Proof of a conjecture of Erdős, in: P. Erdős, A. Renyi and V.T. Sos (eds.), Combinatorial theory and its applications, Colloq. Math. Soc. Jáanos Bolyai 4 (North-Holland, Amsterdam, 1970) 601–623.
S. Hartmann, Graph-theoretic methods to construct entity-relationship databases, in: M. Nagl (ed.), Graph-theoretic concepts in computer science, LNCS 1017 (Springer, Berlin, 1995) 131–145.
S. Hartmann, On the consistency of int-cardinality constraints, in: T.W. Ling, S. Ram and M.L. Lee (eds.), Conceptual Modeling, LNCS 1507 (Springer, Berlin, 1998) 150–163.
D. Jungnickel, T. Beth and H. Lenz, Design Theory (BI, Mannheim, 1985).
M. Lenzerini and P. Nobili, On the satisfiability of dependency constraints in Entity-Relationship schemata, Inf. Syst. 15 (1990) 453–461.
S.W. Liddle, D.W. Embley and S.N. Woodfield, Cardinality constraints in semantic data models, Data Knowl. Eng. 11 (1993) 235–270.
D. Maier, The theory of relational databases (Computer Science Press, Rockville, 1983).
H. Mannila and K. Räihä, Design by example: an application of Armstrong relations, J. Comput. Syst. Sci. 33 (1986) 126–141.
J. Paredaens, P. De Bra, M. Gyssens and D. Van Gucht, The structure of the relational database model (Springer, Berlin, 1989).
B. Thalheim, Dependencies in Relational Databases (Teubner, Stuttgart, 1991).
B. Thalheim, Foundations of Entity-Relationship Modeling, Ann. Math. Artif. Intell. 6 (1992) 197–256.
B. Thalheim, Fundamentals of cardinality constraints, in: G. Pernul and A.M. Tjoa (eds.), Entity-relationship approach, LNCS 645 (Springer, Berlin, 1992) 7–23.
D. Theodorates, Deductive object oriented schemas, in: B. Thalheim (ed.), Conceptual modeling, LNCS 1157 (Springer, Berlin, 1996) 58–72.
G.E. Weddell, Reasoning about functional dependencies generalized for semantic data models, ACM Trans. Database Syst. 17 (1992) 32–64.
J. Wijsen, J. Vandenbulcke and H. Olivie, Functional dependencies generalized for temporal databases, in: R. Elmasri, V. Kouramajian and B. Thalheim (eds.), Entity-Relationship approach, LNCS 823 (Springer, Berlin, 1994) 99–109.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hartmann, S. (2000). On Interactions of Cardinality Constraints, Key, and Functional Dependencies. In: Schewe, KD., Thalheim, B. (eds) Foundations of Information and Knowledge Systems. FoIKS 2000. Lecture Notes in Computer Science, vol 1762. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46564-2_9
Download citation
DOI: https://doi.org/10.1007/3-540-46564-2_9
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67100-8
Online ISBN: 978-3-540-46564-5
eBook Packages: Springer Book Archive