A Proof Procedure for Data Dependencies

Journal of the ACM (JACM)

Volumn 31, Issue 4, 1984, Pages 718-741

  Beeri, Catriel ^a   Vardi, Moshe Y ^b  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

^b STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DATA DEPENDENCIES; PROOF PROCEDURE; RELATIONAL DATABASES;

DATABASE SYSTEMS;

EID: 0021508773     PISSN: 00045411     EISSN: 1557735X     Source Type: Journal    
DOI: 10.1145/1634.1636     Document Type: Article

References (55)

1. Abiteboul, S., and Vardi, M. Y. Formal systems for untyped data dependencies. To appear.
2. Aho, A. V., Beeri, C., and Ullman, J. D. The theory of joins in relational databases. ACM Trans Database Syst 4, 3 (Sept. 1979), 297-314.
3. Aho, A. V., Sagiv, Y., and Ullman, J. D. Equivalence among relational expressions. SIAM J Comput. 8 (1979), 218-246.
4. Armstrong, W. W., Dependency structure in data base relationships. In Proceedings of IFIP 74, Elsevier North-Holland, New York, 1974, pp. 580-583.
5. Armstrong, W. W., and Delobel, C. Decompositions and functional dependencies in relations. ACM Trans. Database Syst. 5, 4 (Dec. 1980), 404-430.
6. Beeri, C. On the membership problem for functional and multivalued dependencies in relational databases. ACM Trans Database Syst 5, 3 (Sept. 1980), 241-259.
7. Beeri, G, and Bernstein, P. A. Computational problems related to the design of normal form relational schemas. ACM Trans Database Syst 4, 1 (Mar. 1979), 30-59.
8. Beeri, C., Bernstein, P. A., and Goodman, N. A sophisticate's introduction to database normalization theory. In Proceedings of the 4th International Conference on Very Large Data Bases (West Berlin, Germany, Sept. 13-15). ACM, New York, 1978, pp. 113-124.
9. Beeri, C., Fagin, R., and Howard, J. H. A complete axiomatization for functional and multivalued dependencies in database relations. In Proceedings of the 3rd ACM-SIGMOD International Conference on Management of Data (Toronto, Ontario, Canada, Aug. 3-5). ACM, New York, 1977, pp. 47-61.
10. Berri, C., Mendelzon, A. O., Sagiv, Y., and Ullman, J. D. Equivalence of relational database schemes. SIAM J Comput 10 (1981), 647-656.
11. Beeri, C., and Rissanen, J. Faithful representation of relational database schemes. IBM Res. Rep. IBM, San Jose, 1980.
12. Beeri, G, and Vardi, M. Y. On the complexity of testing implication of data dependencies. Res. Rep. Dept. Computer Science, The Hebrew University of Jerusalem, Jerusalem, Israel, 1980.
13. Beeri, C., and Vardi, M. Y. The implication problem for data dependencies. In Proceedings of the 8th International Colloquium for Automata Languages and Programming (Acre, Israel, July 13-17). Lecture Notes in Computer Science, vol. 115. Springer-Verlag, New York, 1981, pp. 73-85.
14. Beeri, C., and Vardi, M. Y. On the properties of join dependencies. In Advances in Database Theory, H. Gallaire, J. Minker, and J. M. Nicolas, Eds. Plenum Press, New York, 1981, pp. 25-72.
15. Beeri, C., and Vardi, M. Y. Formal system for tuple and equality generating dependencies. SIAM] Comput 13 (1984), 76-98.
16. Bernstein, P. A. Synthesizing third normal form relations from functional dependencies. ACM Trans Database Syst, 4 (Dec. 1976), 277-298.
17. Biskup, J. On the complementation rule for multivalued dependencies in data base relations. Acta Inf /(/(1978), 297-305.
18. Biskup, J. Inferences of multivalued dependencies in fixed and undetermined universe. Theor Comput Sci 10 (1980), 93-105.
19. Chandra, A. K., Lewis, H. R., and Makowsky, J. A. Embedded implicational dependencies and their inference problem. In Proceedings of the 13th Annual ACM Symposium on the Theory of Computing (Milwaukee, Wise., May 11-13). ACM, New York, 1981, pp. 342-354.
20. Chang, C. L., and Lee, C. R. T. Symbolic Logic and Mechanical Theorem Proving, Academic Press, New York, 1973.
21. Codd, E.F. Further normalization of the data base relational model. In Data Base Systems (R. Rustin, Ed.). Prentice-Hall, Englewood Cliffs, N.J., 1972, pp. 33-64.
22. Delobel, C. Normalization and hierarchal dependencies in the relational data model. ACM Trans Database Syst 3, 3 (Sept. 1978), 201-222.
23. Fagin, R. Multivalued dependencies and a new normal form for relational databases. ACM Trans. Database Syst 2, 2 (June 1977), 262-278.
24. Fagin, R. A normal form for relational databases that is based on domains and keys. ACM Trans. Database Syst. 6,3 (Sept. 1981), 387-415.
25. Fagin, R. Horn clauses and database dependencies. J. ACM 29,4 (Oct. 1982), 952-985.
26. Fagin, R., Maier,D., Ullman, J. D., and Yannakakis, M. Tools for template dependencies. SIAM J. Comput. 12 (1983), 36-59.
27. Graham, M. H. A new proof that the chase is a Church-Rosser replacement system. In Proceedings of the XP1 Workshop on Relational Database Theory (Stony Brook, June) 1980.
28. Grant, J., and Jacobs, B. E. On the family of generalized dependency constraints. J. ACM 29, 2 (Oct. 1982), 986-997.
29. Gurevich, Y., and Lewis, H. R. The inference problem for template dependencies. In Proceedings of the ACM Symposium on Principles of Database Systems (Los Angeles). ACM, New York, 1982, pp. 221-229.
30. Ito, M., Taniguchi, K., and Kasami, T. Membership problem for embedded multivalued dependencies under some restricted conditions. Theor. Comput. Sci. 23 (1983), 175-194.
31. Kanellakis, P. C. On the computational complexity of cardinality constraints in relational databases. Inf. Proc. Lett. II (1980), 98-101.
32. Maier, D., Mendelzon, A. O., Sadri, F., and Ullman, J. D. Adequacy of decompositions of relational databases. In Advances in Database Theory, H. Gallaire, J. Minker, and J. M. Nicolas, Eds. Plenum Press, New York, 1981, pp. 101-114.
33. Maier, D., Mendelzon, A. O., and Sagiv, Y. Testing implications of data dependencies. ACM Trans. Database Syst. 4,4 (Dec. 1979), 455-469.
34. Maier, D., Sagiv, Y., and Yannakakis, M. On the complexity of testing implications of functional and join dependencies. J ACM 28,4 (Oct. 1981), 680-695.
35. Mendelzon, A. O. On axiomatizing multivalued dependencies in relational databases. J. ACM 26, 1 (Jan. 1979), 37-44.
36. Nicolas, J. M. First order logic formalization for functional, multivalued and mutual dependent cies. In Proceedings of the ACM-SIGMOD International Conference on Management of Data (Austin, Tex,, May 31-June 2). ACM, New York, 1978, pp. 40-46.
37. Nicolas, J. M. Mutual dependencies and some results on undecomposable relations. In Proceedings of the 4th International Conference on Very Large Data Bases (West Berlin, Germany, Sept. 13-15). ACM, New York, 1978, pp. 360-367.
38. Paredaens,J. Transitive dependencies in a database scheme. RAIRO Inf/Comput Sci /-/(1980), 149-164.
39. Paredaens, J. The interaction of integrity constraints in an information system. J. Comput Syst. Sci. 20(1980), 310-329.
40. Paredaens, J. A universal formalism to express decomposition, functional dependencies and other constraints in a relational database. Theor. Comput. Sci. 19 (1982), 143-160.
41. Paredaens, J., and Janssens, D. Decompositions of relations-A comprehensive approach. In Advances in Database Theory, H. Gallaire, J. Minker, and J. M. Nicolas, Eds. Plenum Press, New York, 1981, pp. 73-100.
42. Rissanen, J. Theory of relations for databases-A tutorial survey. In Proceedings of the 7th Symposium on Mathematical Foundations of Computer Science (Zakopane, Poland, Sept. 4-8) Lecture Notes in Computer Science, vol. 64. Springer-Verlag, New York, 1978, pp. 537-551.
43. Sadri, F., and Ullman, J. D. Template dependencies: A large class of dependencies in relational databases and its complete axiomatization. J. ACM 29, 2 (Apr. (982), 363-372.
44. Sadri, F., and Ullman, J. D. The theory of functional and template dependencies. Theor Comput. Sci. / 7 (1982), 317-332.
45. Sagiv, Y., Delobel, G, Parker, D. S., and Fagin, R. An equivalence between relational database dependencies and a fragment of propositional calculus. J. ACM 28, 3 (July 1981), 435-453.
46. Sagiv, Y., and Walecka, S. F. Subset dependencies and a completeness result for a subclass of embedded multivalued dependencies. J. ACM 29,1 (Jan. 1982), 103-117.
47. Sciore, E. A complete axiomatization of full join dependencies. J. ACM 29, 2 (Apr. 1982), 373-393.
48. Vardi, M. Y. Axiomatization of functional and join dependencies in the relational model. M.Sc. Thesis, Dept. Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel, 1980.
49. Vardi, M. Y. The implication problem for data dependencies in relational databases. Ph.D. Thesis (in Hebrew), The Hebrew University of Jerusalem, Jerusalem, Israel, 1981.
50. Vardi, M. Y. The implication and the finite implication problems for typed template dependencies. J. Comput System Sci. 28, 1 (Feb. 1984), 3-28.
51. Vard[, M. Y. On the decomposition of relational databases. In Proceedings of the 23rd IEEE Symposium on the Foundations of Computer Science, (Chicago, Nov. 3-5). IEEE, New York, 1982, pp. 176-187.
52. Vardi, M. Y. Inferring multivalued dependencies from functional and join dependencies. Acta Inf. 19 (1983), 305-324.
53. Vardi, M. Y. Inferring multivalued dependencies from tuple and equality generating dependencies. To appear.
54. Yannakakis, M., and Papdimitriou, C. Algebraic dependencies. J. Comput. System Sci. 21 (1982), 2-41.
55. Zaniolo, C. Analysis and design of relational schemata for database systems. Tech. Rep. UCLA-ENG-7769, Dept. Computer Science, UCLA, Los Angeles, July 1976.