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Dung's Argumentation Framework: Unveiling the Expressive Power with Inconsistent Databases

Yasir Mahmood, Markus Hecher, Axel-Cyrille Ngonga Ngomo

TL;DR

This work establishes an exact expressivity bridge between Dung's abstract argumentation frameworks and inconsistent databases constrained by functional and inclusion dependencies. By constructing conflict and defense databases, the authors show that AF extensions correspond to subset repairs, and that more nuanced AF semantics (stable, semi-stable, stage) map to attribute-based covering repairs. They introduce maximal-content-preservation repairs and provide polynomial-time translations to AFs, enabling transfer of complexity and reasoning results across the two formalisms. The findings open avenues for applying database repair techniques to argumentation reasoning and suggest future work on complete/grounded semantics and broader constraint classes.

Abstract

The connection between inconsistent databases and Dung's abstract argumentation framework has recently drawn growing interest. Specifically, an inconsistent database, involving certain types of integrity constraints such as functional and inclusion dependencies, can be viewed as an argumentation framework in Dung's setting. Nevertheless, no prior work has explored the exact expressive power of Dung's theory of argumentation when compared to inconsistent databases and integrity constraints. In this paper, we close this gap by arguing that an argumentation framework can also be viewed as an inconsistent database. We first establish a connection between subset-repairs for databases and extensions for AFs, considering conflict-free, naive, admissible, and preferred semantics. Further, we define a new family of attribute-based repairs based on the principle of maximal content preservation. The effectiveness of these repairs is then highlighted by connecting them to stable, semi-stable, and stage semantics. Our main contributions include translating an argumentation framework into a database together with integrity constraints. Moreover, this translation can be achieved in polynomial time, which is essential in transferring complexity results between the two formalisms.

Dung's Argumentation Framework: Unveiling the Expressive Power with Inconsistent Databases

TL;DR

This work establishes an exact expressivity bridge between Dung's abstract argumentation frameworks and inconsistent databases constrained by functional and inclusion dependencies. By constructing conflict and defense databases, the authors show that AF extensions correspond to subset repairs, and that more nuanced AF semantics (stable, semi-stable, stage) map to attribute-based covering repairs. They introduce maximal-content-preservation repairs and provide polynomial-time translations to AFs, enabling transfer of complexity and reasoning results across the two formalisms. The findings open avenues for applying database repair techniques to argumentation reasoning and suggest future work on complete/grounded semantics and broader constraint classes.

Abstract

The connection between inconsistent databases and Dung's abstract argumentation framework has recently drawn growing interest. Specifically, an inconsistent database, involving certain types of integrity constraints such as functional and inclusion dependencies, can be viewed as an argumentation framework in Dung's setting. Nevertheless, no prior work has explored the exact expressive power of Dung's theory of argumentation when compared to inconsistent databases and integrity constraints. In this paper, we close this gap by arguing that an argumentation framework can also be viewed as an inconsistent database. We first establish a connection between subset-repairs for databases and extensions for AFs, considering conflict-free, naive, admissible, and preferred semantics. Further, we define a new family of attribute-based repairs based on the principle of maximal content preservation. The effectiveness of these repairs is then highlighted by connecting them to stable, semi-stable, and stage semantics. Our main contributions include translating an argumentation framework into a database together with integrity constraints. Moreover, this translation can be achieved in polynomial time, which is essential in transferring complexity results between the two formalisms.

Paper Structure

This paper contains 9 sections, 12 theorems, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. A DB View of Abstract Argumentation
  4. Conflict DBs via Functional Dependencies
  5. Defense DBs via Inclusion Dependencies
  6. Inconsistent Databases for AFs
  7. $\space$Attribute-Based Repairs $\space$&$\space$ Other Semantics$\space$
  8. Stable, Semi-stable, and Stage Semantics
  9. Discussion, Conclusion, and Future Work

Key Result

Theorem 5

Let $\mathcal{F}$ be an AF without self-attacking arguments and ${\mathcal{C}}_{\mathcal{F}}$ be its corresponding conflict database. Then, for every $S\subseteq A$, $S$ is conflict-free (resp., naive) in $\mathcal{F}$ iff $S_T \subseteq T$ is a repair (maximal) for ${\mathcal{C}}_{\mathcal{F}}$.

Figures (4)

  • Figure 1: Hierarchy of ICs and syntactic form for most commonly studied constraints arming2016complexity. Formulas $\varphi$ and $\psi_i$ are conjunctions of database atoms and $\beta$ is a formula using only (in)equality symbols.
  • Figure 2: Argumentation framework from Example .
  • Figure 3: The AF $\mathcal{F}$ (left) from Ex. and a conflict database (right) modeling $\mathcal{F}$.
  • Figure 4: The edge-colored AF $\mathcal{F}$ (left) from Example and a conflict database ${\mathcal{C}}_{\mathcal{F}}$ with attributes assignment corresponding to the colors (right) for conflicts in $\mathcal{F}$.

Theorems & Definitions (22)

  • Example 1
  • Example 2
  • Definition 3: Conflict Database
  • Example 4
  • Theorem 5
  • Lemma 6
  • Example 8
  • Theorem 9
  • Definition 10: Defense database
  • Example 11
  • ...and 12 more