Possibilistic Functional Dependencies and Their Relationship to Possibility Theory

Link, Sebastian; Prade, Henri

doi:10.1109/tfuzz.2015.2466074

Cited by 20 publications

(17 citation statements)

References 46 publications

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“…3. Our contributions are based on the following notion of a possibilistic functional dependency that the authors of this article introduced in [39]. Before describing our contributions we first explain this notion and the qualitative model of uncertainty.…”

Section: Overviewmentioning

confidence: 99%

“…We refer to ''degree of possibility'' since the degrees are grading the possibility that the associated tuple belongs to a possible world that is compatible with the uncertain database. A more detailed analysis can be found in [39]. Our p-degrees form a finite, strictly linear chain α 1 > · · · > α k > α k+1 , where α 1 is the top p-degree and α k+1 is the bottom p-degree, reserved for tuples that are regarded as impossible to occur in a given relation.…”

Section: Overviewmentioning

confidence: 99%

“…Hence, the case where k = 1 corresponds to the classical relational model of data, and our data model is therefore a proper extension of this model. In [39], possibilistic functional dependencies (pFDs) were introduced by assigning a degree of certainty (c-degree) to a classical FD. Our c-degrees form a finite, strictly linear chain β 1 > · · · > β k > β k+1 .…”

Section: Overviewmentioning

confidence: 99%

“…The work in [39] also describes the novelty of the notion of a pFD over previous notions. In brief, other work on possibility theory associates attribute values with possibility distributions or c-degree to data, while the model in [39] assigns p-degrees to data and c-degrees to constraints. In the current article we will show that this is a right notion to exploit uncertainty in data for relational database schema design.…”

Section: Overviewmentioning

confidence: 99%

“…We recall the possibilistic data model introduced in [39]. For a discussion related to the possibilistic grounding of our model and its originality in comparison to previous work we refer the interested reader to [39].…”

Section: Uncertain Databasesmentioning

confidence: 99%

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Relational database schema design for uncertain data

Link

Prade

2019

Information Systems

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a b s t r a c tDriven by the dominance of the relational model, we investigate how the requirements of applications on the certainty of functional dependencies can improve the outcomes of relational database schema design. For that purpose, we assume that tuples are assigned a degree of possibility with which they occur in a relation, and that functional dependencies are assigned a dual degree of certainty which says to which tuples they apply. A design theory is developed for functional dependencies with degrees of certainty, including efficient axiomatic and algorithmic characterizations of their implication problem. Naturally, the possibility degrees of tuples bring forward different degrees of data redundancy, caused by functional dependencies with the dual degree of certainty. Variants of the classical syntactic Boyce-Codd and Third Normal Forms are established. They are justified semantically in terms of eliminating data redundancy and update anomalies of given degrees, and minimizing data redundancy of given degrees across all dependency-preserving decompositions, respectively. As a practical outcome of our results, designers can simply fix the degree of certainty they target, and then apply classical decomposition and synthesis to the set of functional dependencies whose associated degree of certainty meets the target. Hence, by fixing the certainty degree a designer controls which integrity requirements will be enforced for the application and which data will be processed by the application. The choice of the certainty degree also balances the classical trade-off between query and update efficiency on future database instances. Our experiments confirm the effectiveness of our control parameter, and provide original insight into classical normalization strategies and their implementations.

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Section: Overviewmentioning

confidence: 99%

Section: Overviewmentioning

confidence: 99%

Section: Overviewmentioning

confidence: 99%

Section: Overviewmentioning

confidence: 99%

Section: Uncertain Databasesmentioning

confidence: 99%

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Relational database schema design for uncertain data

Link

Prade

2019

Information Systems

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Handling Uncertainty in Relational Databases with Possibility Theory - A Survey of Different Modelings

Pivert

Prade

2018

Lecture Notes in Computer Science

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Mainstream approaches to uncertainty modeling in relational databases are probabilistic. Still some researchers persist in proposing representations based on possibility theory. They are motivated by the ability of this latter setting for modeling epistemic uncertainty and by its qualitative nature. Interestingly enough, several possibilistic models have been proposed over time, and have been motivated by different application needs ranging from database querying, to database design and to data cleaning. Thus, one may distinguish between four different frameworks ordered here according to an increasing representation power: databases with (i) layered tuples; (ii) certainty-qualified attribute values; (iii) attribute values restricted by general possibility distributions; (iv) possibilistic c-tables. In each case, we discuss the role of the possibility-necessity duality, the limitations and the benefit of the representation settings, and their suitability with respect to different tasks.

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A Fourth Normal Form for Uncertain Data

Wei

Link

2019

Advanced Information Systems Engineering

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Possibilistic Functional Dependencies and Their Relationship to Possibility Theory

Cited by 20 publications

References 46 publications

Relational database schema design for uncertain data

Relational database schema design for uncertain data

Handling Uncertainty in Relational Databases with Possibility Theory - A Survey of Different Modelings

A Fourth Normal Form for Uncertain Data

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