Armstrong axioms and Boyce–Codd–Heath Normal Form under bag semantics

Köehler, Henning; Link, Sebastian

doi:10.1016/j.ipl.2010.06.002

Cited by 13 publications

(4 citation statements)

References 13 publications

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“…Is is also worth noting that the passage from set to multisets has interesting consequences also for the study of implication problems of database dependencies. For example, while key constraints can be expressed by functional dependencies under team semantics, this is no longer true under multiteam semantics [23].…”

Section: ⊓ ⊔mentioning

confidence: 99%

Approximation and dependence via multiteam semantics

Durand

Hannula

Kontinen

et al. 2018

Ann Math Artif Intell

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Section: ⊓ ⊔mentioning

confidence: 99%

Approximation and dependence via multiteam semantics

Durand

Hannula

Kontinen

et al. 2018

Ann Math Artif Intell

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“…Applications comprise almost the full range of database topics including normalization [Biskup et al 1979;Fagin 1977b;Köhler and Link 2010;Kolahi and Libkin 2010;Vincent 1999], requirements engineering and schema validation [Mannila and Räihä 1986], data mining [Mannila and Räihä 1994], database security ], view maintenance [Klug and Price 1982], and query optimization [Deutsch et al 2007]. They have received considerable attention in other data models [Arenas et al 2008;Atzeni and Morfuni 1986;Bojanczyk et al 2009;Gottlob et al 2010;Hartmann and Link 2008;2009;2010a;Jensen et al 1996;Kolahi 2007;Levene and Loizou 1998;Tari et al 1997;Toman and Weddell 2008;Wijsen 1999].…”

Section: Related Workmentioning

confidence: 99%

“…In terms of data dependencies the problem is to decide whether for an arbitrarily given set ∪ {ϕ} of data dependencies in C, implies ϕ, that is, whether every relation that satisfies all the elements of also satisfies ϕ. For databases specifically, solutions to the implication problem are essential for their modeling and design [Abiteboul et al 1995;Thalheim 2000], and can advance many data processing tasks such as updates [Arenas and Libkin 2005;Köhler and Link 2010;Kolahi and Libkin 2010;Vincent 1999], queries [Deutsch et al 2006], security [Biskup 2009], maintenance [Klug and Price 1982], cleaning , integration [Cali et al 2004], and exchange [Fagin et al 2005]. According to [Delobel and Adiba 1985] the class of functional dependencies (FDs) captures around two-thirds, and the class of multivalued dependencies (MVDs) around one-quarter of all unirelational dependencies (those defined over a single relation schema) that arise in practice.…”

Section: Introductionmentioning

confidence: 99%

The implication problem of data dependencies over SQL table definitions

Hartmann

Link

2012

ACM Trans. Database Syst.

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We investigate the implication problem for classes of data dependencies over SQL table definitions. 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. The resulting theory subsumes three previously orthogonal frameworks. We further show that the implication problem of this class is equivalent to that in a propositional fragment of Schaerf and Cadoli's [1995] family of para-consistent S-3 logics. In particular, S is the set of variables that correspond to attributes declared NOT NULL. 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. These dualities allow us to transfer several findings from the propositional fragments to the corresponding classes of data dependencies, and vice versa. We show that our results also apply to Codd's null interpretation "value unknown at present", but not to Imielinski's [1989] or-relations utilizing Levene and Loizou's weak possible world semantics [Levene and Loizou 1998]. 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. They also control the degree by which the implication of data dependencies over total relations is soundly approximated in SQL table definitions. ACM Reference Format:Hartmann, S., and Link, S. 2012. The implication problem of data dependencies over SQL table definitions: Axiomatic, algorithmic and logical characterizations.

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“…At the end, the authors do not allow any bags that contain any data redundancy or duplication on normal form condition that characterizes that schema. The output start to bridge the gap between the theories based knowledge of dependencies and the reality of database instances in which redundant tuples commonly occur [10].…”

Section: Review Of Previous Approachesmentioning

confidence: 99%

Relational Database Design: A Review

Kumar¹,

Azad²

2017

IJCA

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Relational Database Designing and Normalization approach is an essential work for the designing of relation up to higher normal form in the field of Database designer. Database Relation stored information into two dimensional matrix form i.e. rows and column. The task of Normalization is to remove data redundancy, data inconstancy and maintain atomicity within the database relation. Key is an attribute of a relation that indentifies the tuple within a database relation, uniquely. This key attribute is generated by applying the closure operations on a given set of functional dependency. Functional dependency of a relation shows the various relations between the attributes and entity relationship diagram shows the prototype of the relation from which designer derived the functional dependency. Relational Database Designing has been spaciously studied and reviewed by many researchers previously; still the works is going on in this area. This paper review the various researches works done earlier in this field and also explain the various applications of Database normalization.

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Armstrong axioms and Boyce–Codd–Heath Normal Form under bag semantics

Cited by 13 publications

References 13 publications

Approximation and dependence via multiteam semantics

Approximation and dependence via multiteam semantics

The implication problem of data dependencies over SQL table definitions

Relational Database Design: A Review

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