Complete Approximations of Incomplete Queries

TL;DR

This paper investigates how to determine the completeness of conjunctive query answers over partially complete databases and proposes methods to approximate incomplete queries using maximal specializations and minimal generalizations.

Contribution

It introduces formal characterizations of complete query approximations and provides algorithms for computing them using fixed-point and recursive techniques.

Findings

MCS can be computed via recursive backward application of rules.

MCG characterized as least fixed-point of a monotonic operator.

Complexity analysis and implementation techniques using ASP and Prolog.

Abstract

This paper studies the completeness of conjunctive queries over a partially complete database and the approximation of incomplete queries. Given a query and a set of completeness rules (a special kind of tuple generating dependencies) that specify which parts of the database are complete, we investigate whether the query can be fully answered, as if all data were available. If not, we explore reformulating the query into either Maximal Complete Specializations (MCSs) or the (unique up to equivalence) Minimal Complete Generalization (MCG) that can be fully answered, that is, the best complete approximations of the query from below or above in the sense of query containment. We show that the MSG can be characterized as the least fixed-point of a monotonic operator in a preorder. Then, we show that an MCS can be computed by recursive backward application of completeness rules. We study the complexity of both problems and discuss implementation techniques that rely on an ASP and Prolog engines, respectively.