Abstract
Codd tables are databases that can carry Codd’s null “value unknown at present” in columns that are specified as NULL. Under Levene and Loizou’s possible world semantics we investigate the combined class of uniqueness constraints and functional dependencies over Codd tables. We characterize the implication problem of this class axiomatically, logically and algorithmically. Since the interaction of members in this class is intricate data engineers can benefit from concise sample tables. Therefore, we investigate structural and computational properties of Armstrong tables. These are Codd tables that satisfy the consequences of a given set of elements in our class and violate all those elements that are not consequences. We characterize when a given Codd table is an Armstrong table for any given set of our class. From this result we establish an algorithm that computes an Armstrong table in time that is at most quadratic in the number of rows in a minimum-sized Armstrong table. Data engineers can use our Armstrong tables to judge, justify, convey and test their understanding of the application domain.
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References
Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley, Reading (1995)
Alexe, B., Kolaitis, P., Tan, W.-C.: Characterizing schema mappings via data examples. In: Proceedings to the Twenty-Ninth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems (PODS), pp. 261–271 (2010)
Armstrong, W.W.: Dependency structures of database relationships. Information Processing 74, 580–583 (1974)
Atzeni, P., Morfuni, N.: Functional dependencies and constraints on null values in database relations. Information and Control 70(1), 1–31 (1986)
Beeri, C., Dowd, M., Fagin, R., Statman, R.: On the structure of Armstrong relations for functional dependencies. J. ACM 31(1), 30–46 (1984)
Codd, E.F.: A relational model of data for large shared data banks. Commun. ACM 13(6), 377–387 (1970)
Codd, E.F.: Extending the database relational model to capture more meaning. ACM Trans. Database Syst. 4(4), 397–434 (1979)
Date, C., Darwen, H.: A guide to the SQL standard. Addison-Wesley Professional, Reading (1997)
De Marchi, F., Petit, J.-M.: Semantic sampling of existing databases through informative Armstrong databases. Inf. Syst. 32(3), 446–457 (2007)
Demetrovics, J.: On the equivalence of candidate keys with Sperner systems. Acta Cybern. 4, 247–252 (1980)
Diederich, J., Milton, J.: New methods and fast algorithms for database normalization. ACM Trans. Database Syst. 13(3), 339–365 (1988)
Fagin, R.: Functional dependencies in a relational data base and propositional logic. IBM Journal of Research and Development 21(6), 543–544 (1977)
Fagin, R.: Armstrong databases. Technical Report RJ3440(40926), IBM Research Laboratory, San Jose, California, USA (1982)
Gottlob, G., Pichler, R., Wei, F.: Tractable database design through bounded treewidth. Inf. Syst. 35(3), 278–298 (2010)
Hartmann, S., Link, S.: When data dependencies over SQL tables meet the Logics of Paradox and S-3. In: PODS Conference (2010)
Imielinski, T., Lipski Jr., W.: Incomplete information in relational databases. J. ACM 31(4), 761–791 (1984)
Langeveldt, W.-D., Link, S.: Empirical evidence for the usefulness of Armstrong relations in the acquisition of meaningful functional dependencies. Inf. Syst. 35(3), 352–374 (2010)
Levene, M., Loizou, G.: Axiomatisation of functional dependencies in incomplete relations. Theor. Comput. Sci. 206(1-2), 283–300 (1998)
Mannila, H., Räihä, K.-J.: Design by example: An application of Armstrong relations. J. Comput. Syst. Sci. 33(2), 126–141 (1986)
Schaerf, M., Cadoli, M.: Tractable reasoning via approximation. Artif. Intell. 74, 249–310 (1995)
Thalheim, B.: Entity-Relationship modeling. Springer, Heidelberg (2000)
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Ferrarotti, F., Hartmann, S., Le, V.B.T., Link, S. (2011). Codd Table Representations under Weak Possible World Semantics. In: Hameurlain, A., Liddle, S.W., Schewe, KD., Zhou, X. (eds) Database and Expert Systems Applications. DEXA 2011. Lecture Notes in Computer Science, vol 6860. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23088-2_9
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DOI: https://doi.org/10.1007/978-3-642-23088-2_9
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