Normal forms and syntactic completeness proofs for functional independencies

Duminda Wijesekera; M. Ganesh; Jaideep Srivastava; Anil Nerode

doi:10.1016/S0304-3975(00)00195-X

Normal forms and syntactic completeness proofs for functional independencies

Duminda Wijesekera, M. Ganesh, Jaideep Srivastava, Anil Nerode

Computer Science and Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

We prove normal form theorems of a complete axiom system for the inference of functional dependencies and independencies in relational databases. We also show that all proofs in our system have a normal form where the application of independency rules is limited to three levels. Our normal form results in a faster proof-search engine in deriving consequences of functional independencies. As a result, we get a new construction of an Armstrong relation for a given set of functional dependencies. It is also shown that an Armstrong relation for a set of functional dependencies and independencies do not exist in general, and this generalizes the same result valid under the closed-world assumption.

Original language	English (US)
Pages (from-to)	365-405
Number of pages	41
Journal	Theoretical Computer Science
Volume	266
Issue number	1-2
DOIs	https://doi.org/10.1016/S0304-3975(00)00195-X
State	Published - Sep 6 2001

Bibliographical note

Funding Information:
This work was partially supported by DoD MURI grant DAAH04-96-10341. ∗Corresponding author. E-mail addresses: duminda@isse.gmu.edu (D. Wijesekera), ganesh@genelogic.com srivasta@cs.umn.edu (J. Srivastava), anil@math.cornell.edu (A. Nerode).

Keywords

Completeness proofs
Data mining
Functional dependencies
Integrity constraints

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title = "Normal forms and syntactic completeness proofs for functional independencies",

abstract = "We prove normal form theorems of a complete axiom system for the inference of functional dependencies and independencies in relational databases. We also show that all proofs in our system have a normal form where the application of independency rules is limited to three levels. Our normal form results in a faster proof-search engine in deriving consequences of functional independencies. As a result, we get a new construction of an Armstrong relation for a given set of functional dependencies. It is also shown that an Armstrong relation for a set of functional dependencies and independencies do not exist in general, and this generalizes the same result valid under the closed-world assumption.",

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AU - Wijesekera, Duminda

AU - Ganesh, M.

AU - Srivastava, Jaideep

AU - Nerode, Anil

N1 - Funding Information: This work was partially supported by DoD MURI grant DAAH04-96-10341. ∗Corresponding author. E-mail addresses: duminda@isse.gmu.edu (D. Wijesekera), ganesh@genelogic.com srivasta@cs.umn.edu (J. Srivastava), anil@math.cornell.edu (A. Nerode).

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N2 - We prove normal form theorems of a complete axiom system for the inference of functional dependencies and independencies in relational databases. We also show that all proofs in our system have a normal form where the application of independency rules is limited to three levels. Our normal form results in a faster proof-search engine in deriving consequences of functional independencies. As a result, we get a new construction of an Armstrong relation for a given set of functional dependencies. It is also shown that an Armstrong relation for a set of functional dependencies and independencies do not exist in general, and this generalizes the same result valid under the closed-world assumption.

AB - We prove normal form theorems of a complete axiom system for the inference of functional dependencies and independencies in relational databases. We also show that all proofs in our system have a normal form where the application of independency rules is limited to three levels. Our normal form results in a faster proof-search engine in deriving consequences of functional independencies. As a result, we get a new construction of an Armstrong relation for a given set of functional dependencies. It is also shown that an Armstrong relation for a set of functional dependencies and independencies do not exist in general, and this generalizes the same result valid under the closed-world assumption.

KW - Completeness proofs

KW - Data mining

KW - Functional dependencies

KW - Integrity constraints

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EP - 405

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ER -

Normal forms and syntactic completeness proofs for functional independencies

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Bibliographical note

Keywords

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