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Facets in Argumentation: A Formal Approach to Argument Significance

Johannes Fichte, Nicolas Fröhlich, Markus Hecher, Victor Lagerkvist, Yasir Mahmood, Arne Meier, Jonathan Persson

TL;DR

This work introduces facets, a new qualitative tool for gauging argument significance in abstract argumentation by identifying arguments that are credulously but not skeptically accepted under a given semantics. It provides a thorough complexity analysis of decision and counting problems for facets across standard AF semantics, showing that many facet problems are easier than full extension counting while retaining rich explanatory value. The authors also implement a practical framework, Frame, built on Aspartix and clingo, and demonstrate its feasibility on ICCMA'19 instances, illustrating that facet reasoning can efficiently filter and explain large solution spaces. The significance measure S_sigma[F, l] formalizes how approving or disapproving a facet reduces uncertainty, enabling targeted navigation and refinement of argumentative spaces with potential applications in AI systems requiring interpretable argumentation. Overall, facets fill a gap between decision and enumeration, offering a tractable, information-rich lens for analyzing argument significance in complex AFs.

Abstract

Argumentation is a central subarea of Artificial Intelligence (AI) for modeling and reasoning about arguments. The semantics of abstract argumentation frameworks (AFs) is given by sets of arguments (extensions) and conditions on the relationship between them, such as stable or admissible. Today's solvers implement tasks such as finding extensions, deciding credulous or skeptical acceptance, counting, or enumerating extensions. While these tasks are well charted, the area between decision, counting/enumeration and fine-grained reasoning requires expensive reasoning so far. We introduce a novel concept (facets) for reasoning between decision and enumeration. Facets are arguments that belong to some extensions (credulous) but not to all extensions (skeptical). They are most natural when a user aims to navigate, filter, or comprehend the significance of specific arguments, according to their needs. We study the complexity and show that tasks involving facets are much easier than counting extensions. Finally, we provide an implementation, and conduct experiments to demonstrate feasibility.

Facets in Argumentation: A Formal Approach to Argument Significance

TL;DR

This work introduces facets, a new qualitative tool for gauging argument significance in abstract argumentation by identifying arguments that are credulously but not skeptically accepted under a given semantics. It provides a thorough complexity analysis of decision and counting problems for facets across standard AF semantics, showing that many facet problems are easier than full extension counting while retaining rich explanatory value. The authors also implement a practical framework, Frame, built on Aspartix and clingo, and demonstrate its feasibility on ICCMA'19 instances, illustrating that facet reasoning can efficiently filter and explain large solution spaces. The significance measure S_sigma[F, l] formalizes how approving or disapproving a facet reduces uncertainty, enabling targeted navigation and refinement of argumentative spaces with potential applications in AI systems requiring interpretable argumentation. Overall, facets fill a gap between decision and enumeration, offering a tractable, information-rich lens for analyzing argument significance in complex AFs.

Abstract

Argumentation is a central subarea of Artificial Intelligence (AI) for modeling and reasoning about arguments. The semantics of abstract argumentation frameworks (AFs) is given by sets of arguments (extensions) and conditions on the relationship between them, such as stable or admissible. Today's solvers implement tasks such as finding extensions, deciding credulous or skeptical acceptance, counting, or enumerating extensions. While these tasks are well charted, the area between decision, counting/enumeration and fine-grained reasoning requires expensive reasoning so far. We introduce a novel concept (facets) for reasoning between decision and enumeration. Facets are arguments that belong to some extensions (credulous) but not to all extensions (skeptical). They are most natural when a user aims to navigate, filter, or comprehend the significance of specific arguments, according to their needs. We study the complexity and show that tasks involving facets are much easier than counting extensions. Finally, we provide an implementation, and conduct experiments to demonstrate feasibility.
Paper Structure (14 sections, 13 theorems, 3 equations, 1 figure, 3 tables)

This paper contains 14 sections, 13 theorems, 3 equations, 1 figure, 3 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Complexity Classes
  4. Abstract Argumentation
  5. Facet Reasoning
  6. Complexity of Deciding Facets
  7. Atleast/Atmost $k$ Facets Complexity
  8. Exact $k$ Facets
  9. Significance
  10. Implementation and Experiments
  11. Implementation
  12. Design and Expectations
  13. Observations and Summary
  14. Conclusion

Key Result

Lemma 4

Let $\sigma$ be any semantics. Then ${c}_{\sigma} \leq^{{\normalfont\textbf{P}}}_m \textsc{IsFacet}\xspace_{\sigma}$.

Figures (1)

  • Figure 1: An example argumentation framework.

Theorems & Definitions (37)

  • Example 1
  • Example 2
  • Remark 3
  • Lemma 4
  • proof
  • Theorem 5
  • proof
  • Remark 6
  • Theorem 7
  • proof
  • ...and 27 more