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Multivalued Dependencies and a New Normal Form for Relational Databases
 ACM Transactions on Database Systems
, 1977
"... A new type of dependency, which includes the wellknown functional dependencies as a special case, is defined for relational databases. By using this concept, a new (“fourth”) normal form for relation schemata is defined. This fourth normal form is strictly stronger than Codd’s “improved third norm ..."
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Cited by 116 (5 self)
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A new type of dependency, which includes the wellknown functional dependencies as a special case, is defined for relational databases. By using this concept, a new (“fourth”) normal form for relation schemata is defined. This fourth normal form is strictly stronger than Codd’s “improved third normal form ” (or “BoyceCodd normal form”). It is shown that, every relation schema can be decomposed into a family of relation schemata in fourth normal form without loss of information (that is, the original relation can be obtained from the new relations by taking joins). Key words and phrases: database design, multivalued dependency, functional dependency, fourth normal form, 4NF, third normal form, 3NF, BoyceCodd normal form, normalization, decomposition, relational database
Testing implications of data dependencies
 ACM Transactions on Database Systems
, 1979
"... Presented is a computation methodthe chasefor testing implication of data dependencies by a set of data dependencies. The chase operates on tableaux similar to those of Aho, Sagiv, and Ullman. The chase includes previous tableau computation methods as special cases. By interpreting tableaux altern ..."
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Cited by 110 (3 self)
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Presented is a computation methodthe chasefor testing implication of data dependencies by a set of data dependencies. The chase operates on tableaux similar to those of Aho, Sagiv, and Ullman. The chase includes previous tableau computation methods as special cases. By interpreting tableaux alternately as mappings or as templates for relations, it is possible to test implication of join dependencies (including multivalued dependencies) and functional dependencies by a set of dependencies.
Fuzzy functional dependencies and lossless join decomposition of fuzzy relational database systems
 ACM Transactions on Database Systems
, 1988
"... This paper deals with the application of fuzzy logic in a relational database environment with the objective of capturing more meaning of the data. It is shown that with suitable interpretations for the fuzzy membership functions, a fuzzy relational data model can be used to represent ambiguities in ..."
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Cited by 73 (0 self)
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This paper deals with the application of fuzzy logic in a relational database environment with the objective of capturing more meaning of the data. It is shown that with suitable interpretations for the fuzzy membership functions, a fuzzy relational data model can be used to represent ambiguities in data values as well as impreciseness in the association among them. Relational operators for fuzzy relations have been studied, and applicability of fuzzy logic in capturing integrity constraints has been investigated. By introducing a fuzzy resemblance measure EQUAL for comparing domain values, the definition of classical functional dependency has been generalized to fuzzy functional dependency (ffd). The implication problem of ffds has been examined and a set of sound and complete inference axioms has been proposed. Next, the problem of lossless join decomposition of fuzzy relations for a given set of fuzzy functional dependencies is investigated. It is proved that with a suitable restriction on EQUAL, the design theory of a classical relational database with functional dependencies can be extended to fuzzy relations satisfying fuzzy functional dependencies.
A simplified universal relation assumption and its properties
 ACM Transactions on Database Systems
, 1982
"... One problem concerning the universal relation assumption is the inability of known methods to obtain a database scheme design in the general case, where the realworld constraints are given by a set of dependencies that includes embedded multivalued dependencies. We propose a simpler method of descr ..."
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Cited by 56 (0 self)
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One problem concerning the universal relation assumption is the inability of known methods to obtain a database scheme design in the general case, where the realworld constraints are given by a set of dependencies that includes embedded multivalued dependencies. We propose a simpler method of describing the real world, where constraints are given by functional dependencies and a single join dependency. The relationship between this method of defining the real world and the classical methods is exposed. We characterize in terms of hypergrapbs those multivalued dependencies that are the consequence of a given join dependency. Also characterized in terms of hypergraphs are those join dependencies that are equivalent to a set of multivalued dependencies.
Conditional Independence Relations Have No Finite Complete Characterization
, 1990
"... The hypothesis of existence of a finite characterization of conditionalindependence relations (CIRs) is refused. This result is shown to be equivalent with the nonexistence of a simple deductive system describing relationships among CIstatements (it is certain type of syntactic description). H ..."
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Cited by 43 (6 self)
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The hypothesis of existence of a finite characterization of conditionalindependence relations (CIRs) is refused. This result is shown to be equivalent with the nonexistence of a simple deductive system describing relationships among CIstatements (it is certain type of syntactic description). However, under the assumption that CIRs are grasped the existence of a countable characterization of CIRs is shown. Finally, the problem of characterization of CIRs is shown to be diverse from an analogical problem of axiomatization EMVDs arising in the theory of relational databases. INTRODUCTION Let [¸ i ] i2N be a random vector (2 card N ! 1) and let us suppose for simplicity that its components are finitevalued random variables. Then we can define a ternary disjoint relation I on expN (disjoint means that its domain is the set of triplets of pairwise disjoint subsets of N ): I(A; BjC) holds iff [¸ i ] i2A is conditionally independent of [¸ i ] i2B given [¸ i ] i2C . We shall ca...
On the structure of Armstrong relations for functional dependencies
 Journal of the ACM
, 1984
"... Abstract. An Armstrong relation for a set of functional dependencies (FDs) is a relation that satisfies each FD implied by the set but no FD that is not implied by it. The structure and size (number of tuples) of Armstrong relatsons are investigated. Upper and lower bounds on the size of minimalsiz ..."
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Cited by 42 (3 self)
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Abstract. An Armstrong relation for a set of functional dependencies (FDs) is a relation that satisfies each FD implied by the set but no FD that is not implied by it. The structure and size (number of tuples) of Armstrong relatsons are investigated. Upper and lower bounds on the size of minimalsized Armstrong relations are derived, and upper and lower bounds on the number of distinct entries that must appear m an Armstrong relation are given. It is shown that the time complexity of finding an Armstrong relation, gwen a set of functional dependencies, is precisely exponential in the number of attributes. Also shown,s the falsity of a natural conjecture which says that almost all relations obeying a given set of FDs are Armstrong relations for that set of FDs. Finally, Armstrong relations are used to generahze a result, obtained by Demetrovics using quite complicated methods, about the possible sets of keys for a relauon.
On the Implication Problem for Probabilistic Conditional Independency
, 2000
"... The implication problem is to test whether a given set of independencies logically implies another independency. This problem is crucial in the design of a probabilistic reasoning system. We advocate that Bayesian networks are a generalization of standard relational databases. On the contrary, it ha ..."
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Cited by 35 (30 self)
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The implication problem is to test whether a given set of independencies logically implies another independency. This problem is crucial in the design of a probabilistic reasoning system. We advocate that Bayesian networks are a generalization of standard relational databases. On the contrary, it has been suggested that Bayesian networks are different from the relational databases because the implication problem of these two systems does not coincide for some classes of probabilistic independencies. This remark, however, does not take into consideration one important issue, namely, the solvability of the implication problem.
Multistructural databases
 In Proc. 24th ACM Symposium on Principles of Database Systems
, 2005
"... This report has been submitted for publication outside of IBM and will Probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its coctents. In view of the transfer of copyright tti the outside publisher, its distribution Cutside of IBM ..."
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Cited by 21 (6 self)
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This report has been submitted for publication outside of IBM and will Probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its coctents. In view of the transfer of copyright tti the outside publisher, its distribution Cutside of IBM prior to publication should be limited to peer communications and specific requests. After outside publication, requests should be filled only by reprints or legally obtained copies of the article (e.g., payment of royalties).
A New Definition of Fuzzy Functional Dependency in Fuzzy Relational Databases
 International Journal of Intelligent Systems
, 1994
"... The need to incorporate and treat information given in fuzzy terms in Relational Databases has concentrated a great effort in the last years. This paper focuses on the treatment of functional dependencies (f.d.) between attributes of a relation scheme. We review other approaches to this problem and ..."
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Cited by 19 (11 self)
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The need to incorporate and treat information given in fuzzy terms in Relational Databases has concentrated a great effort in the last years. This paper focuses on the treatment of functional dependencies (f.d.) between attributes of a relation scheme. We review other approaches to this problem and present some of its missfunctions concerning intuitive properties a fuzzy extension of f.d. should verify. Then we introduce a fuzzy extension of this concept to overcome the previous anomalous behaviors and study its properties. Of primary interest is the completeness of our fuzzy version of Armstrong axioms in order to derive all the fuzzy functional dependencies logically implied by a set of f.f.d. just using these axioms. 1 1 The Crisp Relational Model Relational Databases ([Codd 70]) constitute the main approach to the treatment of databases. It is considered a set of Attributes fA h g h=1:::n and an instance r of a relation scheme R(A 1 ; : : : ; A n ). The database contain several
Purely Relational FLWORs
 In <XIMEP
, 2005
"... We report on a compilation procedure that derives relational algebra plans from arbitrarily nested XQuery FLWOR blocks. While recent research was able to develop relational encodings of trees which may turn RDBMSs into highly efficient XPath and XML Schema processors, here we describe relational enc ..."
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Cited by 15 (10 self)
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We report on a compilation procedure that derives relational algebra plans from arbitrarily nested XQuery FLWOR blocks. While recent research was able to develop relational encodings of trees which may turn RDBMSs into highly efficient XPath and XML Schema processors, here we describe relational encodings of nested iteration, variables, andthe item sequences to which variables are bound. The developed techniques are purely relational in more than one sense: (a) we rely on a standard (or rather: classical) algebra that is readily supported by relational engines, and (b) we use relational concepts like functional and multivalued dependencies to significantly simplify the emitted plans. This work blends well with the mentioned tree encodings and thus contributes a further important building block to investigations into XQuery processors based on relational database technology. 1.