Incomplete Information in Relational Databases
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Notions of dependency satisfaction
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Interactions between dependencies and nested relational structures
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Denotational semantics: a methodology for language development
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The relational model with relation-valued attributes
Information Systems
Non first normal form relations: An algebra allowing data restructuring
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Functional dependencies and constraints on Null values in database relations
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A new normal form for nested relations
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On bounded database schemes and bounded Horn-clause programs
SIAM Journal on Computing
Completeness issues for join dependencies derived from the universal relation join dependency
Information Processing Letters
Extended algebra and calculus for nested relational databases
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Optimization of object-retrieval queries
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A recursive algebra and query optimization for nested relations
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Null values in nested relational databases
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Nested relations and complex objects in databases
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On the uniqueness of nested relations
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Remarks on the algebra of non first normal form relations
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Theory of Relational Databases
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A nested relational approach to processing SQL subqueries
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Functional and multivalued dependencies in nested databases generated by record and list constructor
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On the logical implication of multivalued dependencies with null values
CATS '06 Proceedings of the 12th Computing: The Australasian Theroy Symposium - Volume 51
Deciding implication for functional dependencies in complex-value databases
Theoretical Computer Science - Logic, language, information and computation
SQL query optimization through nested relational algebra
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Lossless decompositions in complex-valued databases
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Incomplete information and certain answers in general data models
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On the logical implication of multivalued dependencies with null values
CATS '06 Proceedings of the Twelfth Computing: The Australasian Theory Symposium - Volume 51
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The nested relational model extends the flat relational model by relaxing the first normal form assumption in order to allow the modeling of complex objects. Much of the previous work on the nested relational model has concentrated on defining the data structures and query language for the model. The work done on integrity constraints in nested relations has mainly focused on characterizing subclasses of nested relations and defining normal forms for nested relations with certain desirable properties.In this paper we define the semantics of nested relations, which may contain null values, in terms of integrity constraints, called null extended data dependencies, which extend functional dependencies and join dependencies encountered in flat relational database theory. We formalize incomplete information in nested relations by allowing only one unmarked generic null value, whose semantics we do not further specify. The motivation for the choice of a generic null is our desire to investigate only fundamental semantics which are common to all unmarked null types. This lead us to define a preorder on nested relations, which allows us to measure the relative information content of nested relations. We also define a procedure, called the extended chase procedure, for testing satisfaction of null extended data dependencies and for making inferences by using these null extended data dependencies. The extended chase procedure is shown to generalize the classical chase procedure, which is of major importance in flat relational database theory. As a consequence of our approach we are able to capture the novel notion of losslessness in nested relations, called herein null extended lossless decomposition. Finally, we show that the semantics of nested relations are a natural extension of the semantics of flat relations.