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Sufficient Explanations in Databases and their Connections to Necessary Explanations and Repairs

Leopoldo Bertossi, Nina Pardal

TL;DR

The paper tackles how to explain query answers in databases using sufficient explanations and their connections to necessary explanations and repairs. It introduces formal definitions of MSS and sufficiency-degree, and shows how to derive MSS from the database repair core to enable efficient computation for fixed-query sizes. The work establishes a tight link between sufficiency and repairs, and between necessity and sufficiency, providing data-complexity results and algorithmic procedures that avoid enumerating all repairs. It also discusses lineage-based interpretations via circumscription and outlines directions for extending the framework to more general queries and knowledge-assembly contexts. The findings offer a principled, computation-aware framework for quantifying and extracting strong, minimal causes of QA results in relational databases, with potential applications in explainable AI and data governance.

Abstract

The notion of cause, as formalized by Halpern and Pearl, has been recently applied to relational databases, to characterize and compute causal explanations for query answers. In this work we consider the alternative notion of sufficient explanation. We investigate its connections with database repairs as used for dealing with inconsistent databases, and with causality-based necessary explanations. We also obtain some computational results.

Sufficient Explanations in Databases and their Connections to Necessary Explanations and Repairs

TL;DR

The paper tackles how to explain query answers in databases using sufficient explanations and their connections to necessary explanations and repairs. It introduces formal definitions of MSS and sufficiency-degree, and shows how to derive MSS from the database repair core to enable efficient computation for fixed-query sizes. The work establishes a tight link between sufficiency and repairs, and between necessity and sufficiency, providing data-complexity results and algorithmic procedures that avoid enumerating all repairs. It also discusses lineage-based interpretations via circumscription and outlines directions for extending the framework to more general queries and knowledge-assembly contexts. The findings offer a principled, computation-aware framework for quantifying and extracting strong, minimal causes of QA results in relational databases, with potential applications in explainable AI and data governance.

Abstract

The notion of cause, as formalized by Halpern and Pearl, has been recently applied to relational databases, to characterize and compute causal explanations for query answers. In this work we consider the alternative notion of sufficient explanation. We investigate its connections with database repairs as used for dealing with inconsistent databases, and with causality-based necessary explanations. We also obtain some computational results.

Paper Structure

This paper contains 13 sections, 10 theorems, 3 equations, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Relational Databases.
  4. QA-Causality, Responsibility and Repairs.
  5. Related Work.
  6. Necessity for Query Answering
  7. Sufficiency for Query Answering
  8. Sufficient Explanations and Database Repairs
  9. Discussion and Conclusions
  10. 1. Necessity Degree vs Sufficiency Degree.
  11. 2. Sufficiency and Circumscribed Lineage.
  12. 3. Some Additional Research Directions.
  13. Proofs of Results

Key Result

proposition 1

Let $D=D^x \cup D^n$, $\mathcal{ Q}$ be a BMQ with $D \models \mathcal{ Q}$, and $t \in D^n$. It holds: $t$ belongs to some MSS for $\mathcal{ Q}$ iff $t$ is a necessary tuple $\mathcal{ Q}$. $\blacksquare$

Theorems & Definitions (14)

  • definition 1
  • definition 2
  • proposition 1
  • proposition 2
  • definition 3
  • lemma 1
  • corollary 1
  • proposition 3
  • proposition 4
  • theorem 1
  • ...and 4 more