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Technical Correspondence: “Differential Dependencies: Reasoning and Discovery” Revisited

Published: 30 June 2015 Publication History

Abstract

To address the frequently occurring situation where data is inexact or imprecise, a number of extensions to the classical notion of a functional dependency (FD) integrity constraint have been proposed in recent years. One of these extensions is the notion of a differential dependency (DD), introduced in the recent article “Differential Dependencies: Reasoning and Discovery” by Song and Chen in the March 2011 edition of this journal. A DD generalises the notion of an FD by requiring only that the values of the attribute from the RHS of the DD satisfy a distance constraint whenever the values of attributes from the LHS of the DD satisfy a distance constraint. In contrast, an FD requires that the values from the attributes in the RHS of an FD be equal whenever the values of the attributes from the LHS of the FD are equal.
The article “Differential Dependencies: Reasoning and Discovery” investigated a number of aspects of DDs, the most important of which, since they form the basis for the other topics investigated, were the consistency problem (determining whether there exists a relation instance that satisfies a set of DDs) and the implication problem (determining whether a set of DDs logically implies another DD). Concerning these problems, a number of results were claimed in “Differential Dependencies: Reasoning and Discovery”. In this article we conduct a detailed analysis of the correctness of these results. The outcomes of our analysis are that, for almost every claimed result, we show there are either fundamental errors in the proof or the result is false. For some of the claimed results we are able to provide corrected proofs, but for other results their correctness remains open.

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Cited By

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  • (2018)A rough set approach for approximating differential dependenciesExpert Systems with Applications10.1016/j.eswa.2018.06.025114(488-502)Online publication date: Dec-2018
  • (2017)Response to “Differential Dependencies Revisited”ACM Transactions on Database Systems10.1145/298360242:1(1-3)Online publication date: 14-Jan-2017
  • (2016)Qualitative Cleaning of Uncertain DataProceedings of the 25th ACM International on Conference on Information and Knowledge Management10.1145/2983323.2983679(2269-2274)Online publication date: 24-Oct-2016

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cover image ACM Transactions on Database Systems
ACM Transactions on Database Systems  Volume 40, Issue 2
June 2015
283 pages
ISSN:0362-5915
EISSN:1557-4644
DOI:10.1145/2799368
Issue’s Table of Contents
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Publication History

Published: 30 June 2015
Accepted: 01 January 2015
Revised: 01 January 2015
Received: 01 February 2014
Published in TODS Volume 40, Issue 2

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Author Tags

  1. Database
  2. consistency
  3. integrity constraint
  4. logical implication

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Cited By

View all
  • (2018)A rough set approach for approximating differential dependenciesExpert Systems with Applications10.1016/j.eswa.2018.06.025114(488-502)Online publication date: Dec-2018
  • (2017)Response to “Differential Dependencies Revisited”ACM Transactions on Database Systems10.1145/298360242:1(1-3)Online publication date: 14-Jan-2017
  • (2016)Qualitative Cleaning of Uncertain DataProceedings of the 25th ACM International on Conference on Information and Knowledge Management10.1145/2983323.2983679(2269-2274)Online publication date: 24-Oct-2016

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