Beyond But-for Test: Counterfactual Explanation in Abstract Argumentation via Actual Causality (Extended Version)

Technical Summary: Beyond But-for Test: Counterfactual Explanation in Abstract Argumentation via Actual Causality

Problem Statement
In the field of Explainable AI (XAI), abstract argumentation (AA) provides structured explanations for why arguments are accepted under specific semantics. While existing methods answer post-hoc questions by identifying sets of arguments satisfying properties like Relevance, Monotonicity, or Necessity, they often rely on static lists of reasons. Human reasoning, however, frequently employs counterfactual thinking ("what-if" scenarios) to probe causal dependencies.

Current approaches to counterfactual explanation in AA are limited to the but-for test (BFT). This primitive test asks whether the acceptance status of a topic argument would change if a single suspected cause were altered (e.g., by deleting an attack or adding a new attacker). The paper identifies a critical flaw in this approach: it fails to hold other arguments fixed as "witnesses." Consequently, the but-for test produces counter-intuitive results in complex argumentation structures, specifically Preemption (where one cause blocks another) and Overdetermination (where multiple causes are jointly sufficient). In these cases, altering a single cause may not change the outcome because alternative pathways activate, leading the BFT to incorrectly identify or miss actual causes.

Methodology
To overcome the limitations of the but-for test, the authors introduce an intervention-based counterfactual reasoning framework grounded in Structural Equation Models (SEMs) and the Halpern–Pearl (HP) definition of actual causality.

1. Acceptability Model: The framework encodes the acceptance conditions of arguments as a set of equations. For an argument $\alpha$, its label ($in$, $out$, or $und$) is determined by the labels of its attackers. This transforms the argumentation framework (AF) into a model $M_F$ of functions.
2. Intervention Operator: The authors define an intervention operator $[\psi]$ that modifies the model $M_F$ according to a hypothesis $\psi$ (a conjunction of atomic propositions). Unlike simple graph modifications, this operator:
   • Replaces the acceptability equation of the intervened argument(s) with a constant function returning the stipulated label.
   • Allows for compound hypotheses, enabling the simultaneous modification of multiple arguments.
   • Crucially, it supports fixing witness arguments to their actual labels, preventing alternative pathways from distorting the counterfactual evaluation.
3. Refined Counterfactual Condition (AC2m): Moving beyond the BFT, the paper adopts a modified counterfactual condition, AC2m. A hypothesis $\psi$ is an actual cause if:
   • Actuality (AC1): $\psi$ and the effect hold in the original labelling.
   • Modified Counterfactual (AC2m): There exists a modification $\psi'$ of $\psi$ and a set of fixed witnesses $\chi$ (arguments held at their actual labels) such that intervening with $\psi' \land \chi$ changes the status of the topic argument.
   • Minimality (AC3): The cause contains no redundant parts.

Key Contributions

• Formal Framework for Actual Causality in AA: The paper establishes the first formal link between HP actual causality and abstract argumentation, moving beyond the primitive but-for test.
• Handling Preemption and Overdetermination: By fixing witnesses, the method correctly identifies causes in scenarios where the but-for test fails.
  • Preemption: In a scenario where $\alpha$ blocks $\beta$ from defending $\eta$, the but-for test fails to identify $\alpha$ as a cause because removing $\alpha$ reactivates $\beta$. The proposed method fixes $\beta$ (or the path it uses) to its actual state, revealing $\alpha$ as the true cause.
  • Overdetermination: In scenarios where $\alpha$ and $\beta$ are both sufficient to defend $\eta$, the but-for test fails to identify either as a cause (since removing one leaves the other). The proposed method identifies the conjunction $in(\alpha) \land in(\beta)$ as the actual cause.
• Graph Mutilation Visualization: The authors map the logical intervention to graphical operations on AFs (adding attackers, removing attacks, or adding self-loops), providing a visual counterpart to the algebraic intervention.
• Comparative Analysis: The paper compares the new method against existing argument-based explanations (Root Reasons, Sufficient/Necessary sets) and closest-world counterfactuals. It demonstrates that the proposed method is more selective and reliable, particularly in avoiding the "empty explanation" problem found in closest-world approaches when unique labellings exist.

Results and Properties

• Expressiveness: The method supports compound hypotheses, allowing for the explanation of joint causes, which the but-for test (limited to atomic changes) cannot capture.
• Relevance: The method satisfies the Relevance property; all arguments in an explanation are relevant to the topic.
• Non-Monotonicity: Unlike some traditional explanation methods, the counterfactual explanation is not monotonic. Adding arguments to a valid explanation may violate the Minimality condition.
• Superiority in Specific Structures:
  • In Preemption, the method identifies the preempting argument as the cause, whereas Root Reasons may include irrelevant defenders, and Closest-World approaches may yield no explanation.
  • In Overdetermination, the method identifies the joint necessity of multiple arguments, whereas Root Reasons and Sufficient explanations often fail to distinguish between the symmetric defenders or return trivial sets.
  • The method ensures the Existence of an explanation for accepted sink nodes, a property where Closest-World approaches fail when the AF admits only a unique labelling.

Significance and Claims
The paper claims that by integrating the Halpern–Pearl definition of actual causality into abstract argumentation, the proposed framework provides a more refined and human-aligned approach to counterfactual explanation. It argues that the ability to hold witnesses fixed is essential for correctly identifying causes in complex dependency structures, thereby overcoming the "but-for" limitation that plagues current AA explanation methods. The authors position this work as a step toward more robust XAI in argumentation, offering a logical language that is expressive enough to handle cyclic dependencies and complex causal patterns like preemption and overdetermination, while remaining grounded in the structural properties of argumentation frameworks. Future work is noted as necessary to address computational complexity, extend to other semantics (grounded, preferred, stable), and apply the framework to extended argumentation formalisms (PAF, ADF, ASPIC+).