Deciding implication for functional dependencies in complex-value databases

Hartmann, Sven; Link, Sebastian

doi:10.1016/j.tcs.2006.08.005

Cited by 9 publications

(3 citation statements)

References 68 publications

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“…In case of other constructors, such as for set or multiset type, Lemma 2.2 fails, and an extension of the Equivalence theorem [11] for FDs alone becomes already sophisticated, see [15]. The papers [11,21] provide alternative proofs for the original equivalence results for FDs and MVDs.…”

Section: Related and Future Workmentioning

confidence: 99%

An Equivalence between Dependencies in Nested Databases and a Fragment of Propositional Logic

Hartmann

Link

2006

Electronic Notes in Theoretical Computer Science

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We extend the result on the equivalence between functional and multivalued dependencies in relational databases and a fragment of propositional logic. It is shown that this equivalence still holds for functional and multivalued dependencies in databases that support complex values via nesting of records and lists. The equivalence has several implications. Firstly, it extends a well-known result from relational databases to databases which are not in first normal form. Secondly, it characterises the implication of functional and multivalued dependencies in complex-value databases in purely logical terms. The database designer can take advantage of this equivalence to reduce database design problems to simpler problems in propositional logic. Furthermore, relational database design tools can be reused to solve problems for complex-value databases.

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Section: Related and Future Workmentioning

confidence: 99%

An Equivalence between Dependencies in Nested Databases and a Fragment of Propositional Logic

Hartmann

Link

2006

Electronic Notes in Theoretical Computer Science

Self Cite

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“…On the other hand, other authors use a practical framework. Hartmann and Link [9] present polynomial-time algorithms to determine non-redundant covers of sets of FDs, and to decide whether a given set of subattributes forms a superkey. Similar to this paper, their work flows from theory to practice, as it is based on a representation theorem for Brouwerian algebras.…”

Section: Introductionmentioning

confidence: 99%

Ideal non-deterministic operators as a formal framework to reduce the key finding problem

Mora

Guzmán

Enciso

2011

International Journal of Computer Mathematics

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A formal development in the framework of the lattice theory for functional dependencies and minimal keys is presented. Beyond this theoretical study, a technique to prune the key finding problem, named scheme pruning transformation, is proposed in this work. This transformation is founded on theoretical results and has linear cost in the worst case. Moreover, this approach has provided a better size reduction than the usual techniques existing in the literature.

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“…The main result of [4] is the following extension of Fagin's Equivalence Theorem from [3]. Theorem 4 allows to convert the implication problem of FDs in complex-value databases into the well-studied problem of satisfiability of propositional Horn clauses.…”

Section: Fds and Horn Clausesmentioning

confidence: 99%

Functional Dependencies on Nested Attributes: Algebraic, Logical and Topological Perspective

Hartmann

16th International Workshop on Database and Expert Systems Applications (DEXA'05)

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We summarise recent results on functional dependencies in nested databases that are generated by record, list, set and multiset constructor. There are three different perspectives from which functional dependencies can be viewed. The algebraic perspective is based on a Brouwerian algebra which is more general than the Boolean powerset algebra from the relational data model. The logical perspective shows that the implication of functional dependencies is equivalent to the implication of Horn clauses. The topological perspective results in an axiomatisation of functional dependencies that is reminiscent of Armstrong's original axiomatisation for relational databases.

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Deciding implication for functional dependencies in complex-value databases

Cited by 9 publications

References 68 publications

An Equivalence between Dependencies in Nested Databases and a Fragment of Propositional Logic

An Equivalence between Dependencies in Nested Databases and a Fragment of Propositional Logic

Ideal non-deterministic operators as a formal framework to reduce the key finding problem

Functional Dependencies on Nested Attributes: Algebraic, Logical and Topological Perspective

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