Possibilistic keys

Abstract

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.

Uniqueness Constraints for Object Stores

“…Keys and uniqueness constraints have also been studied in various different data models, including Web models such as XML [23], JSON [37] and RDF [30], models where data is nested using records, lists, sets, or union operators [38,41], description logics [44], temporal models [26,50], objectrelational [28] and object-oriented data models [7], as well as models for uncertain data such as probabilistic databases [9] or possibilistic databases [3].…”

“…(2) We provide real-world examples and use cases that illustrate the benefit of ctUCs for indexing, updating, and optimizing queries. (3) We include experiments that quantify the impact of indices for ctUCs on both query and update operations in object stores, such as graph database systems. In particular, we demonstrate on the example of Neo4j property graphs that the validation of ctUCs achieves perfect scalability under updates by requiring a number of accesses to the ctUC-index that remains constant while the instance size grows.…”