This Article 
 Bibliographic References 
 Add to: 
Reasoning about Uniqueness Constraints in Object Relational Databases
September/October 2003 (vol. 15 no. 5)
pp. 1295-1306

Abstract—Uniqueness constraints such as keys and functional dependencies in the relational model are a core concept in information systems technology. In this paper, we consider uniqueness constraints suitable for object relational data models and identify a boundary between tractable and intractable varieties. The subclass that is tractable is still a strict generalization of both keys and relational functional dependencies. We present an efficient decision procedure for the logical implication problem of this subclass. The problem itself is formulated as an implication problem for a simple dialect of description logic (DL). DLs are a family of languages for knowledge representation that have many applications in information systems technology and for which model building procedures have been developed that can decide implication problems for dialects that are very expressive. Our own procedure complements this approach and can be integrated with these earlier procedures. Finally, to motivate our results, we review some applications of our procedure in query optimization.

[1] A.V. Aho, Y. Sagiv, and J.D. Ullman, Efficient Optimization of a Class of Relational Expressions ACM Trans. Database Systems, vol. 4, no. 4, pp. 435-454, Dec. 1979.
[2] C. Beeri and P.A. Bernstein, Computation Problems Related to the Design of Normal Form Relational Schemas ACM Trans. Database Systems, vol. 4, no. 1, pp. 30-59, Mar. 1979.
[3] J. Biskup, U. Dayal, and P.A. Bernstein, Synthesizing Independent Database Schemas Proc. ACM SIGMOD Int'l Conf. Management of Data, pp. 143-151, 1979.
[4] M. Buchheit et al., Refining the Structure of Terminological Systems: Terminology = Schema + Views Proc. 12th Nat'l Conf. Artificial Intelligence, pp. 199-204, 1994.
[5] P.A. Bernstein, Synthesizing Third Normal Form Relations from Functional Dependencies ACM Trans. Database Systems, vol. 1, no. 4, pp. 277-298, Dec. 1976.
[6] H.W. Beck, S.K. Gala, and S.B. Navathe, Classification as a Query Processing Technique in the CANDIDE Semantic Data Model Proc. First Int'l Conf. Data Eng., pp. 572-581, 1989.
[7] J. Biskup, Boyce-Codd Normal Form and Object Normal Forms Information Processing Letters, vol. 32, no. 1, pp. 29-33, July 1989.
[8] M. Buchheit et al., Subsumption between Queries to Object-Oriented Databases Information Systems, vol. 9, no. 1, pp. 33-54, 1994.
[9] A. Borgida, Description Logics in Data Management IEEE Trans. Knowledge and Data Eng., vol. 7, no. 5, pp. 671-682, 1995.
[10] A. Borgida and P.F. Patel-Schneider, A Semantics and Complete Algorithm for Subsumption in the CLASSIC Description Logic J. Artificial Intelligence Research, pp. 277-308, 1994.
[11] S. Bergamaschi and C. Sartoni, “On Taxonomic Reasoning in Conceptual Design,” ACM Trans. Database Systems, vol. 17, no. 3, pp. 385-422, 1992.
[12] M.F. van Bommel and G.E. Weddell, Reasoning about Equations and Functional Dependencies on Complex Objects IEEE Trans. Knowledge and Data Eng., vol. 6, no. 3, pp. 455-469, 1994.
[13] A. Borgida and G.E. Weddell, Adding Uniqueness Constraints to Description Logics (Preliminary Report) Proc. Fifth Int'l Conf. Deductive and Object-Oriented Databases, pp. 85-102, Dec. 1997.
[14] D. Calvanese et al., Description Logic Framework for Information Integration Proc. Sixth Int'l Conf. Principles of Knowledge Representation and Reasoning, pp. 2-13, 1998.
[15] D. Calvanese, G. De Giacomo, and M. Lenzerini, Keys for Free in Description Logics Proc. 2000 Description Logic Workshop, 2000.
[16] D. Calvanese, G. De Giacomo, and M. Lenzerini, Identification Constraints and Functional Dependencies in Description Logics Proc. Int'l Joint Conf. Artificial Intellignece, 2001.
[17] S.S. Cosmadakis and P.C. Kanellakis, Equational Theories and Database Constraints Proc. 17th Ann. Symp. Theory of Computing, pp. 273-284, 1985.
[18] S.S. Cosmadakis, P.C. Kanellakis, and M.Y. Vardi, Polynomial-Time Implication problems for Unary Inclusion Dependencies J. ACM, vol. 37, no. 1, pp. 15-46, Jan. 1990.
[19] E.F. Codd, Further Normalization of the Data Base Relational Model Data Base Systems, 1972.
[20] M.A. Casanova and V.M.P. Vidal, Towards a Sound View Integration Methology Proc. Second ACM SIGACT-SIGMOD Symp. Principles of Database Systems, pp. 36-47, 1983.
[21] S. Chaudhuri and M. Vardi, Optimization of Real Conjunctive Queries Proc. 12th ACM SIGACT-SIGMOD-SIGART Symp. Principles of Database Systems, pp. 59-70, 1993.
[22] S.K. Debray and D.S. Warren, Functional Computations in Logic Programs ACM Trans. Programming Languages Systems, vol. 11, no. 3, pp. 451-481, July 1989.
[23] R. Fagin, "A Normal Form for Relational Databases that is Based on Domains and Keys," ACM Trans. Database Systems, vol. 6, no. 3, pp. 387-415, Sept. 1981.
[24] R. Godin and R. Missaoui, Semantic Query Optimization Using Inter-Relational Functional Dependencies Proc. 24th Ann. Hawaii Int'l Conf System Sciences, vol. 3, pp. 368-375, 1991.
[25] I. Horrocks et al., How to Decide Query Containment under Constraints Using a Description Logic Proc. Seventh Int'l Workshop Knowledge Representation Meets Databases, no. 29, pp. 59-72, 2000.
[26] M. Hammer and S.B. Zdonik, Knowledge-Based Query Processing Proc. Sixth Int'l Conf. Very Large Data Bases, pp. 137-147, Oct. 1980.
[27] M. Ito and G.E. Weddell, Implication Problems for Functional Constraints on Databases Supporting Complex Objects J. Computer and System Sciences, vol. 49, no. 3, pp. 726-768, Dec. 1994.
[28] V.L. Khizder, Uniqueness Constraints in Object-Relational Databases and Description Logics PhD thesis, Dept. of Computer Science, Univ. of Waterloo, Waterloo, Ontario, Canada, 1997.
[29] J.J. King, QUIST: A System for Semantic Query Optimization in Relational Databases Proc. Seventh Int'l Conf. Very Large Data Bases, pp. 510-517, Sept. 1981.
[30] V.L. Khizder, D. Toman, and G.E. Weddell, Reasoning about Duplicate Elimination with Description Logics Proc. First Int'l Conf. Computational Logic, pp. 1017-1032, July 2000.
[31] V.L. Khizder, D. Toman, and G.E. Weddell, On Decidability and Complexity of Description Logics with Uniqueness Constraints Proc. Eighth Int'l Conf. Database Theory, pp. 54-67, 2001.
[32] V.L. Khizder and G.E. Weddell, Reasoning about Uniqueness Constraints in Object Relational Databases Technical Report CS-98-13, Computer Science Dept., Univ. of Waterloo, 1998.
[33] A.Y. Levy, D. Srivastava, and T. Kirk, “Data Model and Query Evaluation in Global Information Systems,” J. Intelligent Information Systems, special issue on networked information discovery and retrieval, vol. 5, no. 2, 1995.
[34] A.O. Mendelzon, Functional Dependencies in Logic Programs Proc. 11th Int'l Conf. Very Large Data Bases, pp. 324-330, Aug. 1985.
[35] A.O. Mendelzon and P.T. Wood, Functional Dependencies in Horn Clause Queries ACM Trans. Database Systems, vol. 16, no. 1, pp. 31-55, Mar. 1991.
[36] D. Simmen, E. Shekita, and T. Malkemus, Fundamental Techniques for Order Optimization Proc. ACM SIGMOD Int'l Conf. Management of Data, pp. 57-67, 1996.
[37] D.-M. Tsou and P.C. Fischer, Decomposition of a Relation Scheme into Boyce-Codd Normal Form SIGACT News, vol. 14, no. 3, pp. 23-29, 1982.
[38] J.D. Ullman, Principles of Database Systems.Rockville, Md.: Computer Science Press, 1982.
[39] G.E. Weddell, A Theory of Functional Dependencies for Object-Oriented Data Models Proc. First Int'l Conf. Deductive and Object-Oriented Databases, pp. 165-184, Dec. 1989.
[40] G.E. Weddell, Reasoning about Functional Dependencies Generalized for Semantic Data Models ACM Trans. Database Systems, vol. 17, no. 1, pp. 32-64, Mar. 1992.
[41] J. Wright et al., A Knowledge-Based Configurator that Supports Sales, Engineering, and Manufacturing at AT&T Network Systems Proc. Conf. Industrial Applications of Artificial Intelligence, pp. 183-193, 1993.

Index Terms:
Complex objects, uniqueness constraints, object relational databases, semantic query optimization, description logics, subsumption algorithms.
Vitaliy L. Khizder, Grant E. Weddell, "Reasoning about Uniqueness Constraints in Object Relational Databases," IEEE Transactions on Knowledge and Data Engineering, vol. 15, no. 5, pp. 1295-1306, Sept.-Oct. 2003, doi:10.1109/TKDE.2003.1232279
Usage of this product signifies your acceptance of the Terms of Use.