Counterfactual and Semifactual Explanations in Abstract Argumentation: Formal Foundations, Complexity and Computation

TL;DR

This work introduces counterfactual and semifactual explanations in abstract argumentation frameworks (AF), formalizing CF^σ(g,L) and SF^σ(g,L) as minimal and maximal perturbations of a σ-labelling that affect a goal argument g. It systematically analyzes the computational complexity of CF/SF problems, showing they are generally at least as hard as, and often harder than, classical AF problems, with precise classifications across semantics such as $CO$, $ST$, $PR$, and $SST$. The authors map CF/SF queries to Weak Constrained AF (WAF) and solve them via Answer Set Programming (ASP) with asprin, providing a practical computation strategy and an Explain algorithm that leverages existing AF encodings. They also discuss generalizations (alternative distance measures, multiple goals, and extended AF variants) and outline future work toward probabilistic and structured argumentation frameworks, illustrating the approach’s potential for explainability in argumentation-based decision systems.

Abstract

Explainable Artificial Intelligence and Formal Argumentation have received significant attention in recent years. Argumentation-based systems often lack explainability while supporting decision-making processes. Counterfactual and semifactual explanations are interpretability techniques that provide insights into the outcome of a model by generating alternative hypothetical instances. While there has been important work on counterfactual and semifactual explanations for Machine Learning models, less attention has been devoted to these kinds of problems in argumentation. In this paper, we explore counterfactual and semifactual reasoning in abstract Argumentation Framework. We investigate the computational complexity of counterfactual- and semifactual-based reasoning problems, showing that they are generally harder than classical argumentation problems such as credulous and skeptical acceptance. Finally, we show that counterfactual and semifactual queries can be encoded in weak-constrained Argumentation Framework, and provide a computational strategy through ASP solvers.

Figures (2)

• Figure 1: AF $\Lambda$ of Example \ref{['running-example']}.
• Figure 2: AF of Example \ref{['ex:prel-af']}.

Theorems & Definitions (36)

• Example 1
• Example 2
• Example 3
• Example 4
• Definition 1: Counterfactual (CF)
• Example 5
• Definition 2: CF-Existence Problem
• Example 6
• Theorem 1
• Definition 3: CF-Verification Problem