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Computing Consistent Least Upper Bounds in Aggregate Logic

Authors Aziz Amezian El Khalfioui , Jef Wijsen

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Subject Classification

ACM Subject Classification
  • Information systems → Relational database query languages
  • Theory of computation → Incomplete, inconsistent, and uncertain databases
  • Theory of computation → Logic and databases
Keywords
  • Consistent query answering
  • primary key
  • conjunctive query
  • aggregate logic

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Abstract

We consider the problem of answering conjunctive queries with aggregation on database instances that may violate primary key constraints. In SQL, these queries follow the SELECT-FROM-WHERE-GROUP BY format, where the WHERE clause involves a conjunction of equalities, and the SELECT clause can incorporate aggregate operators like MAX, MIN, SUM, AVG, or COUNT. Repairs of a database instance are defined as inclusion-maximal subsets that satisfy all primary keys. The range-consistent answer to a numerical query over an inconsistent database is a pair [glb, lub], where glb and lub are, respectively, the smallest and the greatest results returned by the query over all possible repairs. While previous work has focused on the computation of the glb, the current paper studies the computation of the lub for a numerical domain of non-negative rational numbers. We introduce the notion of κ-acyclicity for self-join-free conjunctive queries. We show that if the body of a SUM-query is κ-acyclic, then the lub can be computed through a rewriting in first-order aggregate logic. Moreover, we show that this result extends to all aggregate operators that are monotone and associative. Importantly, we also prove the inverse: if the body of a SUM-query is not κ-acyclic, then the lub cannot be computed in first-order aggregate logic.

Cite As Get BibTex

Aziz Amezian El Khalfioui and Jef Wijsen. Computing Consistent Least Upper Bounds in Aggregate Logic. In 29th International Conference on Database Theory (ICDT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 365, pp. 4:1-4:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ICDT.2026.4

Author Details

Aziz Amezian El Khalfioui
  • Research fellow FNRS, University of Mons, Mons, Belgium
Jef Wijsen
  • University of Mons, Mons, Belgium

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