Logical Foundations of Possibilistic Keys

Köehler, Henning; Leck, Uwe; Link, Sebastian; Prade, Henri

doi:10.1007/978-3-319-11558-0_13

Cited by 22 publications

(11 citation statements)

References 33 publications

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“…The full investigation of these issues, with the study of the weighted counterpart of Armstrong's system of axioms, is the topic of a companion paper [53] and patent application [54]. Moreover, possibilistic keys [55] have been investigated as an important special case of possibilistic FDs and correspond to goal Horn clauses via (11). Besides, rather than starting with a layered database, and computing the certainty levels associated with FDs, one may also think of doing the converse, namely starting with a set of more or less certain FDs that should hold in a classical database, and looking for a stratification of the database which agrees with the certainty levels of the FDs.…”

Section: Discussionmentioning

confidence: 99%

Possibilistic Functional Dependencies and Their Relationship to Possibility Theory

Link

Prade

2016

IEEE Trans. Fuzzy Syst.

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Section: Discussionmentioning

confidence: 99%

Possibilistic Functional Dependencies and Their Relationship to Possibility Theory

Link

Prade

2016

IEEE Trans. Fuzzy Syst.

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“…All application areas of keys deserve new attention in the light of possible and certain keys. It is interesting to combine possible and certain keys with possibilistic or probabilistic keys [8,26].…”

Section: Discussionmentioning

confidence: 99%

Possible and certain SQL keys

KöhlerHenning¹,

LinkSebastian²,

Zhou³

2015

Proc. VLDB Endow.

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Driven by the dominance of the relational model, the requirements of modern applications, and the veracity of data, we revisit the fundamental notion of a key in relational databases with NULLs. In SQL database systems primary key columns are NOT NULL by default. NULL columns may occur in unique constraints which only guarantee uniqueness for tuples which do not feature null markers in any of the columns involved, and therefore serve a different function than primary keys. We investigate the notions of possible and certain keys, which are keys that hold in some or all possible worlds that can originate from an SQL table, respectively. Possible keys coincide with the unique constraint of SQL, and thus provide a semantics for their syntactic definition in the SQL standard. Certain keys extend primary keys to include NULL columns, and thus form a sufficient and necessary condition to identify tuples uniquely, while primary keys are only sufficient for that purpose. In addition to basic characterization, axiomatization, and simple discovery approaches for possible and certain keys, we investigate the existence and construction of Armstrong tables, and describe an indexing scheme for enforcing certain keys. Our experiments show that certain keys with NULLs do occur in real-world databases, and that related computational problems can be solved efficiently. Certain keys are therefore semantically well-founded and able to maintain data quality in the form of Codd's entity integrity rule while handling the requirements of modern applications, that is, higher volumes of incomplete data from different formats.

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“…Reasoning about pFDs and their use for schema design, which is the main practical motivation for this notion of a pFD, are the contributions of the current article. Reasoning about keys and cardinality constraints have also been studied in [31,33] in the context of our possibilistic data model.…”

Section: Related Workmentioning

confidence: 99%

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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Logical Foundations of Possibilistic Keys

Cited by 22 publications

References 33 publications

Possibilistic Functional Dependencies and Their Relationship to Possibility Theory

Possibilistic Functional Dependencies and Their Relationship to Possibility Theory

Possible and certain SQL keys

Relational database schema design for uncertain data

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