Abstract
We introduce a new point of view into database schemes by applying systematically an old logical technique: translation schemes, and their induced formula and structure transformations. This allows us to re-examine the notion of dependency preserving decomposition and its generalization refinement.
The most important aspect of this approach lies in laying the groundwork for a formulation of the Fundamental Problem of Database Design, namely to exhibit desirable differences between translation-equivalent presentations of data and to examine refinements of data presentations in a systematic way. The emphasis in this paper is not on results. The main line of thought is an exploration of the use of an old logical tool in addressing the Fundamental Problem.
Translation schemes allow us to have a new look at normal forms of database schemes and to suggest a new line of search for other normal forms. Furthermore we give a characterization of the embedded implicational dependencies (EID's) using FD's and inclusion dependencies (ID's) and a basic class of refinements consisting of projections and natural joins.
Partially supported by a Grant of the German-Israel Foundation and by the Fund for Promotion of Research of the Technion-Israeli Institute of Technology
Partially supported by a Grant of the German-Israeli Foundation
Preview
Unable to display preview. Download preview PDF.
References
S. Abiteboul, R. Hull, and V. Vianu. Foundations of Database. Addison Wesley, 1994.
F. Bancilhon and N. Spyratos. Update semantics of relational views. ACM Transactions on Database Systems, 6(4):557–575, 1981.
C. Beeri and M. Vardi. Formal systems for tuple and equality generating dependencies. SIAM Journal on Computing, 13(1):76–98, 1984.
K.J. Compton and C.W. Henson. A uniform method for proving lower bounds on the computational complexity of logical theories. Annals of Pure and Applied Logic, 48:1–79, 1990.
A. Chandra, H. Lewis, and J.A. Makowsky. Embedded implicational dependencies and their implication problem. In ACM Symposium on the Theory of Computing 1981, pages 342–354. ACM, 1981.
B. Courcelle. Monadic second order graph transductions: A survey. Theoretical Computer Science, 126:53–75, 1994.
E. Dahlhaus. Reductions to NP-complete problems by interpretations. In E. Börger et. al., editor, Logic and Machines: Decision Problems and Complexity, volume 171, pages 357–365. Springer Verlag, 1983.
A. Dawar. Feasible Computation Through Model Theory. PhD thesis, Department of Computer Science, University of Maryland, 1993.
H.D. Ebbinghaus, J. Flum, and W. Thomas. Mathematical Logic, 2nd edition. Undergraduate Texts in Mathematics. Springer-Verlag, 1994.
R. Fagin and M. Vardi. The theory of data dependencies. In M. Anshel and W. Gewirtz, editors, Proceedings of Symposia in Applied Mathematics, volume 34 of American Mathematical Society, pages 19–71. RI, 1986.
D. Hilbert and P. Bernays. Grundlagen der Mathematik, I, volume 40 of Die Grundleheren der mathematischen Wissenschaften in Einzeldarstellungn. Springer Verlag, Heidelberg, 2nd edition, 1970.
C. Herrmann. On the ubdecidability of implication between embedded multivalued database dependencies. Information and Computation, 122:221–235, 1995.
N. Immerman. Languages that capture complexity classes. SIAM Journal on Computing, 16(4):760–778, Aug 1987.
P.G. Kolaitis. Implicit definability on finite structures and unambiguous computations. In FOCS'90, pages 168–180. IEEE, 1990.
A. Keller and J.D. Ullman. On complementary and independent mappings. Proc. ACM SIGMOD Symp. on the Management of Data, pages 145–148, 1984.
J.A. Makowsky. Capturing complexity classes with Lindström quantifiers. In MFCS'94, volume 841 of Lecture Notes in Computer Science, pages 68–71. Springer Verlag, 1994.
J. Mycielski, P. Pudlák, and A.S. Stern. A Lattice of Chapters of Mathematics, volume 426 of Memoirs of the American Mathematical Society. American Mathematical Society, 1990.
H. Mannila and K.J. RÄihÄ. The Design of Relational Databases. Addison-Wesley, 1992.
J.A. Makowsky and E. Ravve. Dependency preserving refinment of database schemes. Technical Report, April 1996, Department of Computer Science, Technion-Israel Institute of Technology, Haifa, Israel, 1996.
J.A. Makowsky and M. Vardi. On the expressive power of data dependencies. Acta Informatica, 23.3:231–244, 1986.
J. Paredaens, P. De Bra, M. Gyssens, and D. Van Gucht, editors. The Structure of the Relational Database Model, volume 17 of EATCS Monographs on Theeoretical Computer Science. Springer Verlag, Heidelberg, 1989.
M.A. Rabin. A simple method for undecidability proofs and some applications. In Y. Bar Hillel, editor, Logic, Methodology and Philosophy of Science II, Studies in Logic, pages 58–68. North Holland, 1965.
B. Thalheim. Dependencies in Relational Databses, volume 126 of Teubner-Texte zur Mathematik. B.G. Teubner Verlagsgesellschaft, Leipzig, 1991.
B. Thalheim. Foundation of entity-relationship modeling. Annals of Mathematics and Artificial Intelligence, 7:197–256, 1993.
B. Thalheim. A survey on database constraints. Reine Informatik I-8/1994, FakultÄt für Mathematik, Naturwissenschaften und Informatik, 1994.
J.D. Ullman. Principles of Database Systems. Principles of Computer Science Series. Computer Science Press, 2nd edition, 1982.
M. Vardi. Fundamentals of dependency theory. In Trends in Theoretical Computer Science, pages 171–224. Computer Science Press, 1987.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Makowsky, J.A., Ravve, E.V. (1996). Translation schemes and the fundamental problem of database design. In: Thalheim, B. (eds) Conceptual Modeling — ER '96. ER 1996. Lecture Notes in Computer Science, vol 1157. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0019911
Download citation
DOI: https://doi.org/10.1007/BFb0019911
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61784-6
Online ISBN: 978-3-540-70685-4
eBook Packages: Springer Book Archive