Rewriting Consistent Answers on Annotated Data
Phokion G. Kolaitis, Nina Pardal, Jonni Virtema, Jef Wijsen
TL;DR
This work advances consistent query answering for databases annotated with values from naturally ordered positive semirings by introducing semiring semantics, repairs, and the minimum-based consistent answers. It generalizes the Koutris–Wijsen rewritability result from ordinary Boolean databases to a broad class of semirings, showing that for self-join free conjunctive queries with one key per relation, consistent answers are expressible in a specialized logic $\mathcal{L}_\mathbb{K}$ if and only if the attack graph is acyclic. The paper provides concrete rewritings for the path query, develops the $\mathcal{L}_\mathbb{K}$ framework, and analyzes the computational complexity via $\mathbb{K}$-circuits, establishing both rewritability results and hardness/approximability results (notably for the bag semiring with strong cycles). These results open avenues for efficient provenance-aware query answering and for extending rewrite-based methods to richer semiring settings.
Abstract
We embark on a study of the consistent answers of queries over databases annotated with values from a naturally ordered positive semiring. In this setting, the consistent answers of a query are defined as the minimum of the semiring values that the query takes over all repairs of an inconsistent database. The main focus is on self-join free conjunctive queries and key constraints, which is the most extensively studied case of consistent query answering over standard databases. We introduce a variant of first-order logic with a limited form of negation, define suitable semiring semantics, and then establish the main result of the paper: the consistent query answers of a self-join free conjunctive query under key constraints are rewritable in this logic if and only if the attack graph of the query contains no cycles. This result generalizes an analogous result of Koutris and Wijsen for ordinary databases, but also yields new results for a multitude of semirings, including the bag semiring, the tropical semiring, and the fuzzy semiring. Further, for the bag semiring, we show that computing the consistent answers of any self-join free conjunctive query whose attack graph has a strong cycle is not only NP-hard but also it is NP-hard to even approximate the consistent answers with a constant relative approximation guarantee.