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CE-QArg: Counterfactual Explanations for Quantitative Bipolar Argumentation Frameworks (Technical Report)

Xiang Yin, Nico Potyka, Francesca Toni

TL;DR

CE-QArg can identify valid and cost-effective counterfactual explanations based on two core modules, polarity and priority, which help determine the updating direction and magnitude for each argument, respectively.

Abstract

There is a growing interest in understanding arguments' strength in Quantitative Bipolar Argumentation Frameworks (QBAFs). Most existing studies focus on attribution-based methods that explain an argument's strength by assigning importance scores to other arguments but fail to explain how to change the current strength to a desired one. To solve this issue, we introduce counterfactual explanations for QBAFs. We discuss problem variants and propose an iterative algorithm named Counterfactual Explanations for Quantitative bipolar Argumentation frameworks (CE-QArg). CE-QArg can identify valid and cost-effective counterfactual explanations based on two core modules, polarity and priority, which help determine the updating direction and magnitude for each argument, respectively. We discuss some formal properties of our counterfactual explanations and empirically evaluate CE-QArg on randomly generated QBAFs.

CE-QArg: Counterfactual Explanations for Quantitative Bipolar Argumentation Frameworks (Technical Report)

TL;DR

CE-QArg can identify valid and cost-effective counterfactual explanations based on two core modules, polarity and priority, which help determine the updating direction and magnitude for each argument, respectively.

Abstract

There is a growing interest in understanding arguments' strength in Quantitative Bipolar Argumentation Frameworks (QBAFs). Most existing studies focus on attribution-based methods that explain an argument's strength by assigning importance scores to other arguments but fail to explain how to change the current strength to a desired one. To solve this issue, we introduce counterfactual explanations for QBAFs. We discuss problem variants and propose an iterative algorithm named Counterfactual Explanations for Quantitative bipolar Argumentation frameworks (CE-QArg). CE-QArg can identify valid and cost-effective counterfactual explanations based on two core modules, polarity and priority, which help determine the updating direction and magnitude for each argument, respectively. We discuss some formal properties of our counterfactual explanations and empirically evaluate CE-QArg on randomly generated QBAFs.
Paper Structure (22 sections, 24 theorems, 9 equations, 11 figures, 3 tables, 3 algorithms)

This paper contains 22 sections, 24 theorems, 9 equations, 11 figures, 3 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Counterfactuals for QBAFs
  5. Strong Counterfactual Problem
  6. $\delta-$Approximate Counterfactual Problem
  7. Weak Counterfactual Problem
  8. Validity and Problem Relationships
  9. Cost-Effective Counterfactuals
  10. Algorithm Design Properties
  11. Algorithms
  12. Formal Properties for Explanations
  13. Evaluations
  14. Settings
  15. Experiment 1: Effectiveness
  16. ...and 7 more sections

Key Result

Proposition 1

If $\sigma$ satisfies s-stability and $\mathcal{Q}$ is acyclic, then the trivial counterfactual is a solution to the strong counterfactual problem.

Figures (11)

  • Figure 1: An example QBAF for loan application. ( Solid and dashed edges indicate attack and support, respectively; the numbers in brackets are the arguments' base scores).
  • Figure 2: Illustration of strong (left), $\delta-$approximate (middle), and weak (right) counterfactual problems. The squares represent all possible base score functions, with $\tau$ the current base score function, and the red (above diagonal) and green (below diagonal) parts as undesirable and desirable alternatives, respectively.
  • Figure 3: An example QBAF (base scores omitted).
  • Figure 4: A QBAF evaluated by the DF-QuAD semantics (inspired by kampik2024contribution).
  • Figure 5: Scalability evaluation for CE-QArg on acyclic (left) and cyclic (right) QBAFs: comparison of average runtime over 100 randomly generated acyclic and cyclic QBAFs.
  • ...and 6 more figures

Theorems & Definitions (56)

  • Definition 1
  • Definition 2
  • Definition 3
  • Example 1
  • Definition 4
  • Definition 5
  • Definition 6
  • Proposition 1: Solution Existence
  • Proposition 2
  • Definition 7
  • ...and 46 more