Consistent Query Answering for Primary Keys and Conjunctive Queries with Counting

TL;DR

This paper extends consistent query answering to include counting occurrences of values in query answers, introducing a new class of queries, C_parsimony, that precisely characterizes those allowing efficient counting through repairs.

Contribution

It defines the class C_parsimony, proving it exactly captures self-join-free conjunctive queries with parsimonious counting, advancing understanding of query classes for counting in repairs.

Findings

C_parsimony contains all self-join-free conjunctive queries with parsimonious counting

C_forest is a subset of C_parsimony, but not equal

Efficient counting can be characterized by syntactic query classes

Abstract

The problem of consistent query answering for primary keys and self-join-free conjunctive queries has been intensively studied in recent years and is by now well understood. In this paper, we study an extension of this problem with counting. The queries we consider count how many times each value occurs in a designated (possibly composite) column of an answer to a full conjunctive query. In a setting of database repairs, we adopt the semantics of [Arenas et al., ICDT 2001] which computes tight lower and upper bounds on these counts, where the bounds are taken over all repairs. Ariel Fuxman defined in his PhD thesis a syntactic class of queries, called C_forest, for which this computation can be done by executing two first-order queries (one for lower bounds, and one for upper bounds) followed by simple counting steps. We use the term "parsimonious counting" for this computation. A natural question is whether C_forest contains all self-join-free conjunctive queries that admit parsimonious counting. We answer this question negatively. We define a new syntactic class of queries, called C_parsimony, and prove that it contains all (and only) self-join-free conjunctive queries that admit parsimonious counting.