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Eliciting Rational Initial Weights in Gradual Argumentation

Nir Oren, Bruno Yun

TL;DR

This work tackles the challenge of eliciting initial weights in weighted argumentation by proposing a constrained argumentation framework (CAF) that uses acceptability degree intervals $I(a)\subseteq[0,1]$ to capture both initial weight and final acceptability. It formalizes rationality concepts (rational, fully rational, and $\epsilon$-rational) and develops a pipeline for refining intervals through gradual semantics (e.g., $\sigma^{\mathtt{Hbs}}$, $\sigma^{\mathtt{Car}}$, $\sigma^{\mathtt{Max}}$) to identify feasible initial weights and to sample valid weight assignments. The paper presents algorithms for best $\epsilon$-rational refinements and three strategies to address irrational CAFs, including cost-aware gradient methods and subset-based refinements, with an empirical evaluation showing trade-offs between refinement quality and computational cost across different semantics. These methods offer a practical path to collect more realistic, interval-based input and to align human judgments with formal semantics, with potential applications in data collection, decision support, and climate-impact reasoning. Future work includes sampling the best initial weights, presenting them to users, and extending the framework to probabilistic distributions to better model human reasoning.

Abstract

Many semantics for weighted argumentation frameworks assume that each argument is associated with an initial weight. However, eliciting these initial weights poses challenges: (1) accurately providing a specific numerical value is often difficult, and (2) individuals frequently confuse initial weights with acceptability degrees in the presence of other arguments. To address these issues, we propose an elicitation pipeline that allows one to specify acceptability degree intervals for each argument. By employing gradual semantics, we can refine these intervals when they are rational, restore rationality when they are not, and ultimately identify possible initial weights for each argument.

Eliciting Rational Initial Weights in Gradual Argumentation

TL;DR

This work tackles the challenge of eliciting initial weights in weighted argumentation by proposing a constrained argumentation framework (CAF) that uses acceptability degree intervals to capture both initial weight and final acceptability. It formalizes rationality concepts (rational, fully rational, and -rational) and develops a pipeline for refining intervals through gradual semantics (e.g., , , ) to identify feasible initial weights and to sample valid weight assignments. The paper presents algorithms for best -rational refinements and three strategies to address irrational CAFs, including cost-aware gradient methods and subset-based refinements, with an empirical evaluation showing trade-offs between refinement quality and computational cost across different semantics. These methods offer a practical path to collect more realistic, interval-based input and to align human judgments with formal semantics, with potential applications in data collection, decision support, and climate-impact reasoning. Future work includes sampling the best initial weights, presenting them to users, and extending the framework to probabilistic distributions to better model human reasoning.

Abstract

Many semantics for weighted argumentation frameworks assume that each argument is associated with an initial weight. However, eliciting these initial weights poses challenges: (1) accurately providing a specific numerical value is often difficult, and (2) individuals frequently confuse initial weights with acceptability degrees in the presence of other arguments. To address these issues, we propose an elicitation pipeline that allows one to specify acceptability degree intervals for each argument. By employing gradual semantics, we can refine these intervals when they are rational, restore rationality when they are not, and ultimately identify possible initial weights for each argument.

Paper Structure

This paper contains 12 sections, 10 theorems, 2 equations, 7 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Working with intervals
  4. Determining the rationality of CAFs
  5. Refining intervals
  6. Correcting irrationality
  7. Strategy 1
  8. Strategy 2
  9. Other strategies
  10. Evaluation
  11. Related work
  12. Conclusions and Future Work

Key Result

Proposition 1

If ($\mathbf{cAF}, \sigma$) is $\epsilon$-rational, then ($\mathbf{cAF}, \sigma$) is rational.

Figures (7)

  • Figure 1: Assisted elicitation of argument strength.
  • Figure 2: The area under the green curve represents the acceptability degree space for $a$ (x-axis) and $b$ (y-axis). The vertical lines are $x_1= 0.8$ and $x_2= 1$. The horizontal lines are at $y_1 = 0.5$ and $y_2= 5/9 \approx 0.555$.
  • Figure 3: Representation of a contrained argumentation framework.
  • Figure 4: Representation of Proposition \ref{['prop:rational']}.
  • Figure 5: Representation of an $\varepsilon$-refinement.
  • ...and 2 more figures

Theorems & Definitions (30)

  • Definition 1: Weighted Argumentation Framework
  • Definition 2: Weighted Gradual semantics
  • Definition 3: Weighted h-categorizer
  • Definition 4: Weighted Card-based
  • Definition 5: Weighted Max-based
  • Definition 6: Constrained Argumentation Framework
  • Definition 7
  • Example 1
  • Definition 8
  • Proposition 1
  • ...and 20 more