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Impact Measures for Gradual Argumentation Semantics

Caren Al Anaissy, Jérôme Delobelle, Srdjan Vesic, Bruno Yun

TL;DR

This work addresses explainability in gradual argumentation by introducing two impact measures, $\\mathtt{ImpDV}$ (a revised version) and $\\mathtt{ImpSI}$ (Shapley-based), and by evaluating them across well-known gradual semantics $\\{\\mathtt{Hbs},\\mathtt{Car},\\mathtt{Max},\\mathtt{CS}\\}$. It provides a nine-principle axiomatic framework to assess how these measures behave with respect to attack structures, directionality, and independence, revealing that $\\mathtt{ImpSI}^{\\sigma}$ generally satisfies all principles for $\\sigma\\in\\{\\mathtt{Hbs},\\mathtt{Car},\\mathtt{Max}\\}$, while $\\mathtt{ImpDV}^{\\sigma}$ often fails Balanced Impact, and both face challenges under $\\mathtt{CS}$. The authors also implement an online prototype enabling computation of acceptability degrees and impact outputs, and propose avenues for explanation-based use of impact measures in gradual semantics. The work advances explainable AI in argumentation by clarifying when and how impact measures reliably explain the influence of argument sets on target arguments, with potential applications in decision support and negotiation. Future directions include formalizing explanations, extending the axiomatics, and evaluating explanations against human-centered criteria.

Abstract

Argumentation is a formalism allowing to reason with contradictory information by modeling arguments and their interactions. There are now an increasing number of gradual semantics and impact measures that have emerged to facilitate the interpretation of their outcomes. An impact measure assesses, for each argument, the impact of other arguments on its score. In this paper, we refine an existing impact measure from Delobelle and Villata and introduce a new impact measure rooted in Shapley values. We introduce several principles to evaluate those two impact measures w.r.t. some well-known gradual semantics. This comprehensive analysis provides deeper insights into their functionality and desirability.

Impact Measures for Gradual Argumentation Semantics

TL;DR

This work addresses explainability in gradual argumentation by introducing two impact measures, (a revised version) and (Shapley-based), and by evaluating them across well-known gradual semantics . It provides a nine-principle axiomatic framework to assess how these measures behave with respect to attack structures, directionality, and independence, revealing that generally satisfies all principles for , while often fails Balanced Impact, and both face challenges under . The authors also implement an online prototype enabling computation of acceptability degrees and impact outputs, and propose avenues for explanation-based use of impact measures in gradual semantics. The work advances explainable AI in argumentation by clarifying when and how impact measures reliably explain the influence of argument sets on target arguments, with potential applications in decision support and negotiation. Future directions include formalizing explanations, extending the axiomatics, and evaluating explanations against human-centered criteria.

Abstract

Argumentation is a formalism allowing to reason with contradictory information by modeling arguments and their interactions. There are now an increasing number of gradual semantics and impact measures that have emerged to facilitate the interpretation of their outcomes. An impact measure assesses, for each argument, the impact of other arguments on its score. In this paper, we refine an existing impact measure from Delobelle and Villata and introduce a new impact measure rooted in Shapley values. We introduce several principles to evaluate those two impact measures w.r.t. some well-known gradual semantics. This comprehensive analysis provides deeper insights into their functionality and desirability.
Paper Structure (12 sections, 11 theorems, 7 equations, 5 figures, 3 tables)

This paper contains 12 sections, 11 theorems, 7 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Background Knowledge
  3. Impact for Gradual Semantics
  4. Revised version of impact measure from Delobelle and Villata
  5. Impact measure based on Shapley value
  6. Observations
  7. Desirable principles for impact measures
  8. List of principles
  9. Links between principles
  10. Axiomatic evaluation and discussion
  11. Related Work
  12. Conclusion and Future Work

Key Result

Proposition 1

The counting semantics does not satisfy the Independence and Directionality properties.

Figures (5)

  • Figure 1: Graphical representation of an argumentation framework.
  • Figure 2: Counter-example for the satisfaction of Property \ref{['prop-attack-removal-monotonicity']} by the counting semantics. Values in blue represent the acceptability degrees for the two AFs for the counting semantics. Values in red represent the Shapley measure for each of the attacks.
  • Figure 3: Representation of an AF with 6 arguments. The red number on an edge $c$ represents $s(c)$.
  • Figure 4: Intensity of attacks with Shapley measure for the h-categoriser semantics. Values in blue are the degrees of the arguments whereas the values in red represent the intensity of the attacks.
  • Figure 5: Illustration of Impact Symmetry

Theorems & Definitions (43)

  • Definition 1: Argumentation Framework
  • Definition 2: Attack Structure
  • Example 1
  • Definition 3: Weighting
  • Definition 4: Gradual semantics
  • Definition 5: h-categoriser
  • Definition 6: Card-based
  • Definition 7: Max-based
  • Definition 8: Counting model
  • Proposition 1
  • ...and 33 more