On Codd Families of Keys over Incomplete Relations

Hartmann, Sven; Leck, Uwe; Link, Sebastian

doi:10.1093/comjnl/bxq073

Cited by 29 publications

(10 citation statements)

References 82 publications

(116 reference statements)

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“…Other directions include the problems of dependency inference [Mannila and Räihä 1994], data cleaning , and extremal problems [Demetrovics et al 2006;Engel 1997;Hartmann et al 2011] in the presence of null markers.…”

Section: Future Directionsmentioning

confidence: 99%

The implication problem of data dependencies over SQL table definitions

Hartmann

Link

2012

ACM Trans. Database Syst.

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We investigate the implication problem for classes of data dependencies over SQL table definitions. Under Zaniolo's "no information" interpretation of null markers we establish an axiomatization and algorithms to decide the implication problem for the combined class of functional and multivalued dependencies in the presence of NOT NULL constraints. The resulting theory subsumes three previously orthogonal frameworks. We further show that the implication problem of this class is equivalent to that in a propositional fragment of Schaerf and Cadoli's [1995] family of para-consistent S-3 logics. In particular, S is the set of variables that correspond to attributes declared NOT NULL. We also show how our equivalences for multivalued dependencies can be extended to Delobel's class of full first-order hierarchical decompositions, and the equivalences for functional dependencies can be extended to arbitrary Boolean dependencies. These dualities allow us to transfer several findings from the propositional fragments to the corresponding classes of data dependencies, and vice versa. We show that our results also apply to Codd's null interpretation "value unknown at present", but not to Imielinski's [1989] or-relations utilizing Levene and Loizou's weak possible world semantics [Levene and Loizou 1998]. Our findings establish NOT NULL constraints as an effective mechanism to balance not only the certainty in database relations but also the expressiveness with the efficiency of entailment relations. They also control the degree by which the implication of data dependencies over total relations is soundly approximated in SQL table definitions. ACM Reference Format:Hartmann, S., and Link, S. 2012. The implication problem of data dependencies over SQL table definitions: Axiomatic, algorithmic and logical characterizations.

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Section: Future Directionsmentioning

confidence: 99%

The implication problem of data dependencies over SQL table definitions

Hartmann

Link

2012

ACM Trans. Database Syst.

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“…That is, no two different rows have matching total values in each of the key columns. The concept of a key is essential for many other data models, including semantic models [1][2][3][4], object models [5], description logics [6], XML [7][8][9], RDF [10], and OWL [11].…”

Section: Introductionmentioning

confidence: 99%

Schema- and Data-driven Discovery of SQL Keys

Le¹,

Link²,

Memari³

2012

Journal of Computing Science and Engineering

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Keys play a fundamental role in all data models. They allow database systems to uniquely identify data items, and therefore, promote efficient data processing in many applications. Due to this, support is required to discover keys. These include keys that are semantically meaningful for the application domain, or are satisfied by a given database. We study the discovery of keys from SQL tables. We investigate the structural and computational properties of Armstrong tables for sets of SQL keys. Inspections of Armstrong tables enable data engineers to consolidate their understanding of semantically meaningful keys, and to communicate this understanding to other stake-holders. The stake-holders may want to make changes to the tables or provide entirely different tables to communicate their views to the data engineers. For such a purpose, we propose data mining algorithms that discover keys from a given SQL table. We combine the key mining algorithms with Armstrong table computations to generate informative Armstrong tables, that is, key-preserving semantic samples of existing SQL tables. Finally, we define formal measures to assess the distance between sets of SQL keys. The measures can be applied to validate the usefulness of Armstrong tables, and to automate the marking and feedback of non-multiple choice questions in database courses.

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“…These include results on the implication problem [1,11], Armstrong relations [2,18,24,47,64] and the discovery of keys from relations [4,28,40,48,51,52], as well as extremal combinatorics [10,23,34,59]. Keys have also been considered in other data models, including incomplete relations [22,34,39,37,36,25,62,65] and XML data [26,27]. Note that Armstrong relations are also an AI tool to acquire and reason about conditional independencies [19,50].…”

Section: Extending Results From Keys Over Certain Relationsmentioning

confidence: 99%

Possibilistic keys

Balamuralikrishna

Jiang

Köhler

et al. 2019

Fuzzy Sets and Systems

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Possibility theory is applied to introduce and reason about the fundamental notion of a key for uncertain data. Uncertainty is modeled qualitatively by assigning to tuples of data a degree of possibility with which they occur in a relation, and assigning to keys a degree of certainty which says to which tuples the key applies. The associated implication problem is characterized axiomatically and algorithmically. Using extremal combinatorics, we then characterize the families of non-redundant possibilistic keys that attain maximum cardinality. In addition, we show how to compute for any given set of possibilistic keys a possibilistic Armstrong relation, that is, a possibilistic relation that satisfies every key in the given set and violates every possibilistic key not implied by the given set. We also establish an algorithm for the discovery of all possibilistic keys that are satisfied by a given possibilistic relation. It is shown that the computational complexity of computing possibilistic Armstrong relations is precisely exponential in the input, and the decision variant of the discovery problem is NP-complete as well as W[2]-complete in the size of the possibilistic key. Further applications of possibilistic keys in constraint maintenance, data cleaning, and query processing are illustrated by examples. The computation of possibilistic Armstrong relations and discovery of possibilistic keys from possibilistic relations have been implemented as prototypes. Extensive experiments with these prototypes provide insight into the size of possibilistic Armstrong relations and the time to compute them, as well as the time it takes to compute a cover of the possibilistic keys that hold on a possibilistic relation, and the time it takes to remove any redundant possibilistic keys from this cover.

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On Codd Families of Keys over Incomplete Relations

Cited by 29 publications

References 82 publications

The implication problem of data dependencies over SQL table definitions

The implication problem of data dependencies over SQL table definitions

Schema- and Data-driven Discovery of SQL Keys

Possibilistic keys

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