A Simple Algorithm for Consistent Query Answering under Primary Keys

We consider the dichotomy conjecture for consistent query answering under primary key constraints stating that for every fixed Boolean conjunctive query q, testing whether it is certain over all repairs of a given inconsistent database is either polynomial time or coNP-complete. This conjecture has been verified for self-join-free and path queries. We propose a simple inflationary fixpoint algorithm for consistent query answering which, for a given database, naively computes a set $\Delta$ of subsets of database repairs with at most $k$ facts, where $k$ is the size of the query $q$. The algorithm runs in polynomial time and can be formally defined as: 1. Initialize $\Delta$ with all sets $S$ of at most $k$ facts such that $S$ satisfies $q$. 2. Add any set $S$ of at most $k$ facts to $\Delta$ if there exists a block $B$ (ie, a maximal set of facts sharing the same key) such that for every fact $a$ of $B$ there is a set $S' \in \Delta$ contained in $(S \cup \{a\})$. The algorithm answers "$q$ is certain" iff $\Delta$ eventually contains the empty set. The algorithm correctly computes certain answers when the query $q$ falls in the polynomial time cases for self-join-free queries and path queries. For arbitrary queries, the algorithm is an under-approximation: The query is guaranteed to be certain if the algorithm claims so. However, there are polynomial time certain queries (with self-joins) which are not identified as such by the algorithm

A SAT-based System for Consistent Query Answering

An inconsistent database is a database that violates one or more integrity constraints, such as functional dependencies. Consistent Query Answering is a rigorous and principled approach to the semantics of queries posed against inconsistent databases. The consistent answers to a query on an inconsistent database is the intersection of the answers to the query on every repair, i.e., on every consistent database that differs from the given inconsistent one in a minimal way. Computing the consistent answers of a fixed conjunctive query on a given inconsistent database can be a coNP-hard problem, even though every fixed conjunctive query is efficiently computable on a given consistent database. We designed, implemented, and evaluated CAvSAT, a SAT-based system for consistent query answering. CAvSAT leverages a set of natural reductions from the complement of consistent query answering to SAT and to Weighted MaxSAT. The system is capable of handling unions of conjunctive queries and arbitrary denial constraints, which include functional dependencies as a special case. We report results from experiments evaluating CAvSAT on both synthetic and real-world databases. These results provide evidence that a SAT-based approach can give rise to a comprehensive and scalable system for consistent query answering.Comment: 25 pages including appendix, to appear in the 22nd International Conference on Theory and Applications of Satisfiability Testin

Consistent Query Answering for Primary Keys and Conjunctive Queries with Counting

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.Comment: 27 pages, 2 figure

Consistent Query Answering for Primary Keys in Logspace

We study the complexity of consistent query answering on databases that may violate primary key constraints. A repair of such a database is any consistent database that can be obtained by deleting a minimal set of tuples. For every Boolean query q, CERTAINTY(q) is the problem that takes a database as input and asks whether q evaluates to true on every repair. In [Koutris and Wijsen, ACM TODS, 2017], the authors show that for every self-join-free Boolean conjunctive query q, the problem CERTAINTY(q) is either in P or coNP-complete, and it is decidable which of the two cases applies. In this paper, we sharpen this result by showing that for every self-join-free Boolean conjunctive query q, the problem CERTAINTY(q) is either expressible in symmetric stratified Datalog (with some aggregation operator) or coNP-complete. Since symmetric stratified Datalog is in L, we thus obtain a complexity-theoretic dichotomy between L and coNP-complete. Another new finding of practical importance is that CERTAINTY(q) is on the logspace side of the dichotomy for queries q where all join conditions express foreign-to-primary key matches, which is undoubtedly the most common type of join condition

Consistent Query Answering for Primary Keys on Rooted Tree Queries

We study the data complexity of consistent query answering (CQA) on databases that may violate the primary key constraints. A repair is a maximal subset of the database satisfying the primary key constraints. For a Boolean query q, the problem CERTAINTY(q) takes a database as input, and asks whether or not each repair satisfies q. The computational complexity of CERTAINTY(q) has been established whenever q is a self-join-free Boolean conjunctive query, or a (not necessarily self-join-free) Boolean path query. In this paper, we take one more step towards a general classification for all Boolean conjunctive queries by considering the class of rooted tree queries. In particular, we show that for every rooted tree query q, CERTAINTY(q) is in FO, NL-hard $\cap$ LFP, or coNP-complete, and it is decidable (in polynomial time), given q, which of the three cases applies. We also extend our classification to larger classes of queries with simple primary keys. Our classification criteria rely on query homomorphisms and our polynomial-time fixpoint algorithm is based on a novel use of context-free grammar (CFG).Comment: To appear in PODS'2