Functional Dependencies in Incomplete Databases with Limited Domains

Alattar, Munqath; Sali, Attila

doi:10.1007/978-3-030-39951-1_1

Cited by 7 publications

(31 citation statements)

References 16 publications

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Section: Contributionsmentioning

confidence: 99%

“…In the present paper, we study spFD's that were earlier introduced in [4,5] as a generalized version of functional dependency constraint using the visible domain concept and we continue the work started in [3]. We provided a graph-theoretical condition for the spFD satisfaction in [4]. We give a list of axioms of weak/strong and certain FD's that are sound for spFD's, as well and describe several possible sound weakenings for those that are not sound.…”

Section: Contributionsmentioning

confidence: 99%

“…Strongly possible worlds were introduced by [3] where strongly possible keys (spKey's) were studied. The natural extension to strongly possible functional dependencies was investigated in [4].…”

Section: Introductionmentioning

confidence: 99%

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Strongly Possible Functional Dependencies for SQL

Al-atar

Sali

2022

Acta Cybern

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Missing data is a large-scale challenge to research and investigate. It reduces the statistical power and produces negative consequences that may introduce selection bias on the data. Many approaches to handle this problem have been introduced. The main approaches suggested are either missing values to be ignored (removed) or imputed (filled in) with new values. This paper uses the second method. Possible worlds and possible and certain keyswere introduced in Köhler et.al., and by Levene et.al. Köhler and Link introduced certain functional dependencies (c-FD) as a natural complement to Lien's class of possible functional dependencies (p-FD). Weak and strong functional dependencies were studied by Levene and Loizou. We introduced the intermediate concept of strongly possible worlds that are obtained by imputing values already existing in the table in a preceding paper. This results in strongly possible keys (spKey's) and strongly possible functional dependencies (spFD's). We give a polynomial algorithm to verify a single spKey and show that in general, it is NP-complete to verify an arbitrary collection of spKeys. We give a graph-theoretical characterization of the validity of a given spFD X →sp Y.We show, that the complexity to verify a single strongly possible functional dependency is NP-complete in general, then we introduce some cases when verifying a single spFD can be done in polynomial time.As a step forward axiomatization of spFD's, the rules given for weak and strong functional dependencies are checked. Appropriate weakenings of those that are not sound for spFD's are listed. The interaction between spFD's and spKey's and certain keys is studied. Furthermore, a graph theoretical characterization of implication between singular attribute spFD's is given.

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Section: Contributionsmentioning

confidence: 99%

Section: Contributionsmentioning

confidence: 99%

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Strongly Possible Functional Dependencies for SQL

Al-atar

Sali

2022

Acta Cybern

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“…We provided a graph-theoretical characterization for spFD satisfaction in Ref. 1. Following are the main contributions of this paper:…”

Section: Contributionsmentioning

confidence: 99%

“…In a preceding paper, 1 we provided some characterization for validating a given (spFD) X! sp Y and the axioms' soundness of weak/strong functional dependencies (FDs) introduced in Ref.…”

Section: Introductionmentioning

confidence: 99%

Toward an Axiomatization of Strongly Possible Functional Dependencies

Alattar

Sali

2020

Vietnam J. Comp. Sci.

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In general, there are two main approaches to handle the missing data values problem in SQL tables. One is to ignore or remove any record with some missing data values. The other approach is to fill or impute the missing data with new values [A. Farhangfar, L. A. Kurgan and W. Pedrycz, A novel framework for imputation of missing values in databases, IEEE Trans. Syst. Man Cybern. A, Syst. Hum. 37(5) (2007) 692–709]. In this paper, the second method is considered. Possible worlds, possible and certain keys, and weak and strong functional dependencies were introduced in Refs. 4 and 2 [H. Köhler, U. Leck, S. Link and X. Zhou, Possible and certain keys for SQL, VLDB J. 25(4) (2016) 571–596; M. Levene and G. Loizou, Axiomatisation of functional dependencies in incomplete relations, Theor. Comput. Sci. 206(1) (1998) 283–300]. We introduced the intermediate concept of strongly possible worlds in a preceding paper, which are obtained by filling missing data values with values already existing in the table. Using strongly possible worlds, strongly possible keys and strongly possible functional dependencies (spFDs) were introduced in Refs. 5 and 1 [M. Alattar and A. Sali, Keys in relational databases with nulls and bounded domains, in ADBIS 2019: Advances in Databases and Information Systems, Lecture Notes in Computer Science, Vol. 11695 (Springer, Cham, 2019), pp. 33–50; Functional dependencies in incomplete databases with limited domains, in FoiKS 2020: Foundations of Information and Knowledge Systems, Lecture Notes in Computer Science, Vol. 12012 (Springer, Cham, 2020), pp. 1–21]. In this paper, some axioms and rules for strongly possible functional dependencies are provided, These axioms and rules form the basis for a possible axiomatization of spFDs. For that, we analyze which weak/strong functional dependency and certain functional dependency axioms remain sound for strongly possible functional dependencies, and for the axioms that are not sound, we give appropriate modifications for soundness.

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Can We Probabilistically Generate Uniformly Distributed Relation Instances Efficiently?

Biskup

Preuß

2020

Lecture Notes in Computer Science

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Functional Dependencies in Incomplete Databases with Limited Domains

Cited by 7 publications

References 16 publications

Strongly Possible Functional Dependencies for SQL

Strongly Possible Functional Dependencies for SQL

Toward an Axiomatization of Strongly Possible Functional Dependencies

Can We Probabilistically Generate Uniformly Distributed Relation Instances Efficiently?

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