Strength Change Explanations in Quantitative Argumentation

TL;DR

It is demonstrated that the existing notions of inverse and counterfactual problems can be reduced to strength change explanations, and it is shown that the existing notions of inverse and counterfactual problems can be reduced to strength change explanations.

Abstract

In order to make argumentation-based inference contestable, it is crucial to explain what changes can achieve a desired (instead of the contested) inference result. To this end, we introduce strength change explanations for quantitative (bipolar) argumentation graphs. Strength change explanations describe changes to the initial strengths of a subset of the arguments in a given graph that can achieve a desired ordering based on the final strengths of some (potentially different) subset of arguments. We show that the existing notions of inverse and counterfactual problems can be reduced to strength change explanations. We also prove basic soundness and completeness properties of our strength change explanations, and demonstrate their existence and non-existence in some special cases. By applying a heuristic search, we demonstrate that we can often successfully find strength change explanations for layered graphs that are common in typical application scenarios; still, limitations remain for settings where we do not provide guarantees for the presence (or absence) of explanations.

Figures (2)

• Figure 1: QBAG $\mathcal{G}$ and its updates $\mathcal{G}'$, $\mathcal{G}"$, and $\mathcal{G}^*$. Here and henceforth, a node labelled $\hbox{$\mathsf{x}~(i)\!:\!\mathbf{f}$}$ represents argument $\mathsf{x}$ with initial strength $\tau(\mathsf{x}) = i$ and final strength $\sigma(\mathsf{x}) = \mathbf{f}$. Edges labelled $+$ and $-$ represent support and attack, respectively. Arguments with bold borders are strength change explanation arguments, given the desired ordering $\langle \mathsf{c}, \mathsf{b} \rangle$ and the mutable set$\{\mathsf{a}, \mathsf{e}\}$; arguments with bold dashed borders make up $1$-approximate strength change explanations.
• Figure 2: Inverse and strong counterfactual problems ($\mathcal{G}$, with desired total order $\langle \mathsf{d}, \mathsf{e}, \mathsf{a}, \mathsf{b}, \mathsf{c} \rangle$, and $\mathcal{G}^*$, with topic $\mathsf{c}$ and desired strength $6$, respectively) and their solutions (in $\mathcal{G}'$).

Theorems & Definitions (35)

• Example 1
• Definition 1: Gradual Semantics and Strength Function Potyka:2019Baroni:Rago:Toni:2019
• Proposition 3.1: PB24, Theorem 20
• Proposition 3.2: PB24, Theorem 20
• Definition 2: Final Strength Ordering, $\preceq$-Satisfaction
• Example 2
• Definition 3: Strength Change
• Definition 4: Strength Change Application
• Example 3
• Definition 5: Final Strength Change Explanation (SX)