Modeling and Querying Uncertain Relational Databases: A Survey of Approaches Based on the Possible Worlds Semantics

Abstract

In this paper, we give an overview of the most representative approaches aimed at querying databases containing ill-known data, starting from the pioneering works by Codd and Lipski and up to very recent proposals. This study focuses on approaches with a clear and sound semantics, based on the notion of possible worlds. Three types of queries are considered: (i) those about attribute values (in an algebraic or SQL-like framework), (ii) those about the properties satisfied by a given set of worlds (i.e., a set of instances of an imprecise database), and (iii) those about the representation of uncertain data. For the first two types, it is emphasized that a trade-off has to be found between expressivity (of the model) and tractability (of the queries in the context of a given model).

Combining quantifications for flexible query result ranking

“…Often, a set of data exists, each of which could be the intended datum. In those cases, it is said that the datum is subject to uncertainty [1], [2], [5], [8], [12], [21], [24]- [27]. Usually, for a datum subject to uncertainty, an attempt is made to model the available knowledge about the intended datum, by assigning each of the data which could be the intended datum a degree of confidence an agent has that the corresponding datum is the intended datum.…”

“…Such imperfections may take the form of uncertainties [1]- [9], imprecisions [1], [8], [9], vaguenesses [1], [9], contradictions, etc [8]- [10]. To allow the representation of such imperfections or ways to deal with them, many existing approaches propose to extend the data contained in databases to also contain descriptions of the determined intensity levels of such imperfections or such ways of handling imperfections [1], [5], [6], [11]. For example, consider table I, which is the visualization of an example relational database relation containing data representing 3 properties of each of 5 rental cars.…”

A Possibilistic Valid-Time Model

“…Because necessity cannot exceed 0 unless possibility is 1, this gives a natural ranking score. Some authors [5] mentioned before that the possibility and necessity measures result in a total order in the set of events. This e Q time (r) is then rescaled to the unit interval, resulting in e Q time (r).…”

Mapping Data Between Probability Spaces in Probabilistic Databases

“…In addition, several research articles have been published to address different features that need to be supported in probabilistic database systems [2][3][4][5][6][7]. Some of the Prototype systems that have been reported in the literature include Trio [8], MayBMS [9], MystiQ [10], Prob-View [11], Orion system [12], MCDB [13], and BayesStore [14]. Trio, MayBMS, and MystiQ are systems that support discrete forms of uncertainty, in which a finite set of possible instances is represented.…”