![]() We develop a foundation for the systematic investigation of data examples and obtain a number of results on both the capabilities and the limitations of data examples in explaining and understanding schema mappings. A promising approach to this effect is to use "good" data examples that illustrate the schema mapping at hand. Since in real-life applications schema mappings can be quite complex, it is important to develop methods and tools for understanding, explaining, and refining schema mappings. Schema mappings are high-level specifications that describe the relationship between two database schemas they are considered to be the essential building blocks in data exchange and data integration, and have been the object of extensive research investigations. They also control the degree by which the implication of data dependencies over total relations is soundly approximated in SQL table definitions. Our findings establish NOT NULL constraints as an effective mechanism to balance not only the certainty in database relations but also the expressiveness with the efficiency of entailment relations. We show that our results also apply to Codd's null interpretation “value unknown at present”, but not to Imielinski's or-relations utilizing Levene and Loizou's weak possible world semantics. These dualities allow us to transfer several findings from the propositional fragments to the corresponding classes of data dependencies, and vice versa. We also show how our equivalences for multivalued dependencies can be extended to Delobel's class of full first-order hierarchical decompositions, and the equivalences for functional dependencies can be extended to arbitrary Boolean dependencies. In particular, S is the set of variables that correspond to attributes declared NOT NULL. We further show that the implication problem of this class is equivalent to that in a propositional fragment of Schaerf and Cadoli's family of para-consistent S-3 logics. ![]() The resulting theory subsumes three previously orthogonal frameworks. Under Zaniolo's “no information” interpretation of null markers we establish an axiomatization and algorithms to decide the implication problem for the combined class of functional and multivalued dependencies in the presence of NOT NULL constraints. We investigate the implication problem for classes of data dependencies over SQL table definitions. These results can be utilized to consolidate and communicate the understanding of the application domain between different stake-holders of a database. Finally, we investigate structural and computational properties of Armstrong databases for the class of data dependencies under consideration. These findings have important applications in database design and data processing. We establish an axiomatic and an algorithmic characterization of the implication problem. In this paper, we study the implication problem of the combined class of functional dependencies and cardinality constraints over partial bags. However, data dependencies interact differently over partial bags than over the idealized special case of relations. To make data processing more efficient in practice, partial bags are permitted as database instances to accommodate partial and duplicate information. The theory of data dependencies is largely a theory over relations. Certain keys are therefore semantically well founded and able to meet Codd’s entity integrity rule while handling high volumes of incomplete data from different formats.ĭata dependencies capture meaningful information about an application domain within the target database. ![]() Our experiments show that certain keys with NULLs occur in real-world data, and related computational problems can be solved efficiently. In addition to basic characterization, axiomatization, discovery, and extremal combinatorics problems, we investigate the existence and construction of Armstrong tables, and describe an indexing scheme for enforcing certain keys. ![]() Certain keys extend primary keys to include NULL columns and can uniquely identify entities whenever feasible, while primary keys may not. Possible keys coincide with UNIQUE, thus providing a semantics for their syntactic definition in the SQL standard. We investigate the notions of possible and certain keys, which are keys that hold in some or all possible worlds that originate from an SQL table, respectively. In SQL, primary key columns are NOT NULL, and UNIQUE constraints guarantee uniqueness only for tuples without NULL. Driven by the dominance of the relational model and the requirements of modern applications, we revisit the fundamental notion of a key in relational databases with NULL. ![]()
0 Comments
Leave a Reply. |