Rewriting Consistent Answers on Annotated Data

2024-12-16

arXiv.org

AI Summary

This paper investigates consistent query answering (CQA) over inconsistent databases annotated with values from naturally ordered positive semirings, focusing on union-free conjunctive queries under key constraints and the semiring-valued minimization semantics. We propose the first first-order logic characterization supporting restricted negation and establish the first necessary and sufficient condition for rewritability of consistent answers—i.e., equivalence to a standard query: acyclicity of the query attack graph. This condition unifies and generalizes prior results for classical, bag, tropical, and fuzzy semirings. Leveraging semiring semantics, attack graph analysis, and complexity-theoretic reductions, we deliver an exact characterization of rewritability. Moreover, we prove that for bag semirings, computing consistent answers for queries containing strong cycles—and even obtaining constant-factor relative approximations—is NP-hard.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Data Mining & Knowledge Management: Intelligent Query Processing

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Web Mining and Content Analysis: Community question answering
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

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.

Problem

• Study consistent query answers on annotated databases
• Rewrite queries using logic with limited negation
• Analyze complexity of computing consistent answers

Innovation

• Uses first-order logic with limited negation
• Applies semiring semantics for consistent answers
• Generalizes results to multiple semirings