From complete to incomplete information and back

Abstract

Incomplete information arises naturally in numerous data management applications. Recently, several researchers have studied query processing in the context of incomplete information. Most work has combined the syntax of a traditional query language like relational algebra with a nonstandard semantics such as certain or ranked possible answers. There are now also languages with special features to deal with uncertainty. However, to the standards of the data management community, to date no language proposal has been made that can be considered a natural analog to SQL or relational algebra for the case of incomplete information.In this paper we propose such a language, World-set Algebra, which satisfies the robustness criteria and analogies to relational algebra that we expect. The language supports the contemplation on alternatives and can thus map from a complete database to an incomplete one comprising several possible worlds. We show that World-set Algebra is conservative over relational algebra in the sense that any query that maps from a complete database to a complete database (a complete-to-complete query) is equivalent to a relational algebra query. Moreover, we give an efficient algorithm for effecting this translation. We then study algebraic query optimization of such queries.We argue that query languages with explicit constructs for handling uncertainty allow for the more natural and simple expression of many real-world decision support queries. The results of this paper not only suggest a language for specifying queries in this way, but also allow for their efficient evaluation in any relational database management system.

Approximating predicates and expressive queries on probabilistic databases

“…2 U A[conf, repair-key] (the maximal language studied in this paper) is a fragment of the query language implemented in the MayBMS system [2,3]. It also seems to be subsumed by the query language of the Trio System [18].…”

“…The Trio project at Stanford has been studying probabilistic databases with a focus on combining uncertainty and data provenance management support [5]. Our own group has had a particular focus on developing more expressive query languages for probabilistic databases that yield new applications [4,2], while at the same time admitting efficient evaluation [1].…”

Efficient recovery of missing events

“…We employ a real data set collected from a train manufacturer 2 . There are 149 process specifications considered with sizes up to 63 transitions and 79 places.…”

“…To capture incompleteness and non-determinism in design, planning and scheduling specifications, data models such as AND/OR trees [15] are proposed by facilitating factorized representations. Antova et al [1] propose world-set decompositions for finite sets of worlds, as well as relational algebra queries on world-sets [2]. However, these two techniques, AND/OR trees [15] and world-set decompositions [1], dedicated to representing finite sets of worlds are not directly applicable to event data studied in this paper, where sequences could be infinite due to the existence of loops.…”

Indexing correlated probabilistic databases

“…In recent years, several approaches have been developed for managing probabilistic data and for answering queries over them (see, e.g., [10,35,1,30,31,3,2,34]). The methods proposed in that work can be used to both manage tuple-or attribute-level uncertainties, and to process a rich class of probabilistic queries over them.…”