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Instantiations and Computational Aspects of Non-Flat Assumption-based Argumentation

Tuomo Lehtonen, Anna Rapberger, Francesca Toni, Markus Ulbricht, Johannes P. Wallner

TL;DR

The paper investigates reasoning in non-flat assumption-based argumentation (ABA) by translating ABA into semantics-preserving bipolar argumentation frameworks (BAFs) and analyzing the resulting computational trade-offs. It proves that, in general, instantiating non-flat ABAFs into BAFs incurs exponential size (via compilability theory), but identifies practical reductions through three redundancy notions and isolates fragments (atomic and additive ABAFs) that admit polynomial-sized instantiations. It then proposes two algorithmic paradigms: (i) an instantiation-based approach that generates a BAF via ASP and reasoned on it with SAT encodings, and (ii) a direct ASP-based approach that operates on the ABAF without full instantiation, with empirical results showing the instantiation-based method often outperforms the direct approach under certain semantics. The findings suggest instantiation-based reasoning can be advantageous for non-flat ABA in many cases, contrasting with flat ABA where direct methods typically dominate, and open avenues for skeptical/prefixed semantics and explanation generation.

Abstract

Most existing computational tools for assumption-based argumentation (ABA) focus on so-called flat frameworks, disregarding the more general case. In this paper, we study an instantiation-based approach for reasoning in possibly non-flat ABA. We make use of a semantics-preserving translation between ABA and bipolar argumentation frameworks (BAFs). By utilizing compilability theory, we establish that the constructed BAFs will in general be of exponential size. In order to keep the number of arguments and computational cost low, we present three ways of identifying redundant arguments. Moreover, we identify fragments of ABA which admit a poly-sized instantiation. We propose two algorithmic approaches for reasoning in possibly non-flat ABA. The first approach utilizes the BAF instantiation while the second works directly without constructing arguments. An empirical evaluation shows that the former outperforms the latter on many instances, reflecting the lower complexity of BAF reasoning. This result is in contrast to flat ABA, where direct approaches dominate instantiation-based approaches.

Instantiations and Computational Aspects of Non-Flat Assumption-based Argumentation

TL;DR

The paper investigates reasoning in non-flat assumption-based argumentation (ABA) by translating ABA into semantics-preserving bipolar argumentation frameworks (BAFs) and analyzing the resulting computational trade-offs. It proves that, in general, instantiating non-flat ABAFs into BAFs incurs exponential size (via compilability theory), but identifies practical reductions through three redundancy notions and isolates fragments (atomic and additive ABAFs) that admit polynomial-sized instantiations. It then proposes two algorithmic paradigms: (i) an instantiation-based approach that generates a BAF via ASP and reasoned on it with SAT encodings, and (ii) a direct ASP-based approach that operates on the ABAF without full instantiation, with empirical results showing the instantiation-based method often outperforms the direct approach under certain semantics. The findings suggest instantiation-based reasoning can be advantageous for non-flat ABA in many cases, contrasting with flat ABA where direct methods typically dominate, and open avenues for skeptical/prefixed semantics and explanation generation.

Abstract

Most existing computational tools for assumption-based argumentation (ABA) focus on so-called flat frameworks, disregarding the more general case. In this paper, we study an instantiation-based approach for reasoning in possibly non-flat ABA. We make use of a semantics-preserving translation between ABA and bipolar argumentation frameworks (BAFs). By utilizing compilability theory, we establish that the constructed BAFs will in general be of exponential size. In order to keep the number of arguments and computational cost low, we present three ways of identifying redundant arguments. Moreover, we identify fragments of ABA which admit a poly-sized instantiation. We propose two algorithmic approaches for reasoning in possibly non-flat ABA. The first approach utilizes the BAF instantiation while the second works directly without constructing arguments. An empirical evaluation shows that the former outperforms the latter on many instances, reflecting the lower complexity of BAF reasoning. This result is in contrast to flat ABA, where direct approaches dominate instantiation-based approaches.
Paper Structure (37 sections, 28 theorems, 20 equations, 1 figure, 5 tables, 2 algorithms)

This paper contains 37 sections, 28 theorems, 20 equations, 1 figure, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Assumption-based Argumentation.
  4. Bipolar Argumentation.
  5. ABA and Bipolar Argumentation.
  6. Computational Complexity.
  7. BAF Generation in Theory
  8. A Lower Bound For Non-Flat Instantiations
  9. Towards Feasible BAF Instantiations
  10. Derivation Redundancy.
  11. Expendable Arguments.
  12. Assumption Redundancy.
  13. Summary.
  14. Fragments
  15. Atomic ABAFs
  16. ...and 22 more sections

Key Result

Theorem 2.9

Let $D$ be an ABAF, $\mathcal{F}_D = (A,\mathrm{Att},\mathrm{Sup})$ the associated BAF, and $\sigma\in\{\mathit{com},\mathit{prf}',\mathit{grd},{\mathit{stb}}\}$. Then

Figures (1)

  • Figure 1: The effect of the number of arguments an ABAF gives rise to on the run time of our approaches w.r.t. complete semantics.

Theorems & Definitions (66)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Example 2.4
  • Definition 2.5
  • Definition 2.6
  • Definition 2.7
  • Example 2.8
  • Theorem 2.9
  • Theorem 3.1
  • ...and 56 more