Principles of Database Systems
Principles of Database Systems
Incomplete information and dependencies in relational databases
SIGMOD '83 Proceedings of the 1983 ACM SIGMOD international conference on Management of data
A Sound and Sometimes Complete Query Evaluation Algorithm for Relational Databases with Null Values
A Sound and Sometimes Complete Query Evaluation Algorithm for Relational Databases with Null Values
Theory of Relational Databases
Theory of Relational Databases
Incomplete Information in Relational Databases
Journal of the ACM (JACM)
Abstraction in query processing
Journal of the ACM (JACM)
A Hybrid Representation of Vague Collections for Distributed Object Management Systems
IEEE Transactions on Knowledge and Data Engineering
A Closed Approach to Vague Collections in Partly Inaccessible Distributed Databases
ADBIS '99 Proceedings of the Third East European Conference on Advances in Databases and Information Systems
Towards an algebraic theory of information integration
Information and Computation - Special issue: Commemorating the 50th birthday anniversary of Paris C. Kanellakis
Towards an algebraic theory of information integration
Information and Computation
Treating incomplete knowledge in formal concept analysis
Formal Concept Analysis
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We formulate some natural conditions which should be satisfied in an extension of the relational algebra from the usual relations to tables with null values, and we explain the motivation behind these conditions. Roughly speaking, our conditions say that the extended algebra makes it possible to correctly compute the "true tuples" in the result of applying a relational expression (query) to tables with nulls (database state), and that the computation can be carried out recursively, following the structure of the expression. We prove that these conditions are exactly equivalent to other conditions proposed earlier by the author and T. Imieliński. We give a simple proof of the correctness of the "naive" extension of the relational algebra to tables with marked nulls, where the nulls are treated as if they were regular values, and which supports the operations of projection, positive selection, union, join and renaming of attributes. We also show that the result of the naive evaluation of such an expression (query) is equal to the response to the query as defined --- in a proof-theoretic framework --- by Reiter.