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Querying and Repairing Inconsistent Prioritized Knowledge Bases: Complexity Analysis and Links with Abstract Argumentation

Meghyn Bienvenu, Camille Bourgaux

TL;DR

This work studies querying and repairing inconsistent prioritized knowledge bases (KBs) that integrate an ontology, facts, and a priority relation over conflicting facts. It transfers optimal repair notions from databases to KBs, provides a comprehensive data-complexity analysis for query entailment, uniqueness, and enumeration across DL-Lite dialects, and establishes deep links to abstract argumentation by showing Pareto-optimal repairs correspond to stable extensions and often to preferred extensions in preference-based SETAFs. It further develops a grounded repair semantics inspired by grounded extensions, computable in polynomial time in favorable settings, and demonstrates a practical under-approximation that preserves tractability. By connecting prioritized KBs to PSETAFs, the paper enables cross-fertilization with argumentation theory while offering tractable reasoning primitives for inconsistency-tolerant OMQA (Ontology-Mediated Query Answering) in data-rich settings.

Abstract

In this paper, we explore the issue of inconsistency handling over prioritized knowledge bases (KBs), which consist of an ontology, a set of facts, and a priority relation between conflicting facts. In the database setting, a closely related scenario has been studied and led to the definition of three different notions of optimal repairs (global, Pareto, and completion) of a prioritized inconsistent database. After transferring the notions of globally-, Pareto- and completion-optimal repairs to our setting, we study the data complexity of the core reasoning tasks: query entailment under inconsistency-tolerant semantics based upon optimal repairs, existence of a unique optimal repair, and enumeration of all optimal repairs. Our results provide a nearly complete picture of the data complexity of these tasks for ontologies formulated in common DL-Lite dialects. The second contribution of our work is to clarify the relationship between optimal repairs and different notions of extensions for (set-based) argumentation frameworks. Among our results, we show that Pareto-optimal repairs correspond precisely to stable extensions (and often also to preferred extensions), and we propose a novel semantics for prioritized KBs which is inspired by grounded extensions and enjoys favourable computational properties. Our study also yields some results of independent interest concerning preference-based argumentation frameworks.

Querying and Repairing Inconsistent Prioritized Knowledge Bases: Complexity Analysis and Links with Abstract Argumentation

TL;DR

This work studies querying and repairing inconsistent prioritized knowledge bases (KBs) that integrate an ontology, facts, and a priority relation over conflicting facts. It transfers optimal repair notions from databases to KBs, provides a comprehensive data-complexity analysis for query entailment, uniqueness, and enumeration across DL-Lite dialects, and establishes deep links to abstract argumentation by showing Pareto-optimal repairs correspond to stable extensions and often to preferred extensions in preference-based SETAFs. It further develops a grounded repair semantics inspired by grounded extensions, computable in polynomial time in favorable settings, and demonstrates a practical under-approximation that preserves tractability. By connecting prioritized KBs to PSETAFs, the paper enables cross-fertilization with argumentation theory while offering tractable reasoning primitives for inconsistency-tolerant OMQA (Ontology-Mediated Query Answering) in data-rich settings.

Abstract

In this paper, we explore the issue of inconsistency handling over prioritized knowledge bases (KBs), which consist of an ontology, a set of facts, and a priority relation between conflicting facts. In the database setting, a closely related scenario has been studied and led to the definition of three different notions of optimal repairs (global, Pareto, and completion) of a prioritized inconsistent database. After transferring the notions of globally-, Pareto- and completion-optimal repairs to our setting, we study the data complexity of the core reasoning tasks: query entailment under inconsistency-tolerant semantics based upon optimal repairs, existence of a unique optimal repair, and enumeration of all optimal repairs. Our results provide a nearly complete picture of the data complexity of these tasks for ontologies formulated in common DL-Lite dialects. The second contribution of our work is to clarify the relationship between optimal repairs and different notions of extensions for (set-based) argumentation frameworks. Among our results, we show that Pareto-optimal repairs correspond precisely to stable extensions (and often also to preferred extensions), and we propose a novel semantics for prioritized KBs which is inspired by grounded extensions and enjoys favourable computational properties. Our study also yields some results of independent interest concerning preference-based argumentation frameworks.

Paper Structure

This paper contains 22 sections, 45 theorems, 52 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Querying Inconsistent Prioritized KBs
  4. Complexity Analysis
  5. Overview
  6. Query Entailment
  7. Uniqueness and Enumeration
  8. Case of Transitive Priority Relations
  9. Preference-Based Argumentation
  10. Argumentation Frameworks
  11. Enriching AFs with Preferences
  12. Set-Based Argumentation Frameworks
  13. Adding Preferences to SETAFs
  14. Linking Prioritized KBs and PSETAFs
  15. Optimal Repairs vs. PSETAF Extensions
  16. ...and 7 more sections

Key Result

Theorem 9

For DLs satisfying PolyCons, repair checking is in coNP for globally-optimal repairs, in P for Pareto- or completion-optimal repairs. For DLs satisfying PolyCons and PolyBCQ, G-AR and G-IAR entailment are in $\Pi^{p}_{2}$, G-brave entailment in $\Sigma^{p}_{2}$, P-AR, P-IAR, C-AR and C-IAR entailmen

Figures (1)

  • Figure 1: Prioritized KB example. $\mathcal{T}$ formalizes knowledge about animal groups and $\mathcal{A}$ gives information about individuals $a$ and $b$. An arrow from $\alpha$ to $\beta$ indicates that $\alpha\succ\beta$ while a dotted line indicates a conflict without priority between assertions.

Theorems & Definitions (90)

  • Definition 1: Repair
  • Definition 2: Conflict
  • Definition 3: Priority relation, completion
  • Definition 4: Prioritized KB
  • Definition 5: Optimal repairs
  • Example 6
  • Definition 7: AR, IAR and brave semantics
  • Example 8: Ex. \ref{['ex:prio-repairs']} cont'd
  • Theorem 9
  • Theorem 10
  • ...and 80 more