Choices and their Provenance: Explaining Stable Solutions of Abstract Argumentation Frameworks

2025-06-01

AI Summary

Stable semantics in abstract argumentation frameworks (AFs) lack interpretability, hindering understanding of the implicit non-deterministic choices and assumptions underlying stable extensions. Method: This paper introduces a novel provenance method for stable semantics, formulated for the first time as a minimum graph repair problem: identifying and removing a minimal set of critical attack edges such that the well-founded semantics of the repaired AF exactly coincides with the stable semantics of the original AF. The approach integrates well-founded semantics, regular path queries, two-player argumentation games, and model-based diagnosis techniques to precisely attribute implicit decisions. Contribution/Results: The method generates minimal, verifiable, and human-understandable explanations for stable extensions. Experimental evaluation demonstrates significant improvements in transparency and debuggability of stable solutions, enabling rigorous validation and intuitive comprehension of the underlying reasoning structure.

Technology Category

• Knowledge Representation and Reasoning: Argumentation
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Data Mining & Knowledge Management: Representing, Reasoning, and Using Provenance, Trust

Application Category

• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity
• Semantics and Knowledge: Provenance, trust, security and privacy, and ethical issues in managing semantic data
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

The rule $mathrm{Defeated}(x) leftarrow mathrm{Attacks}(y,x),, eg , mathrm{Defeated}(y)$, evaluated under the well-founded semantics (WFS), yields a unique 3-valued (skeptical) solution of an abstract argumentation framework (AF). An argument $x$ is defeated ($mathrm{OUT}$) if there exists an undefeated argument $y$ that attacks it. For 2-valued (stable) solutions, this is the case iff $y$ is accepted ($mathrm{IN}$), i.e., if all of $y$'s attackers are defeated. Under WFS, arguments that are neither accepted nor defeated are undecided ($mathrm{UNDEC}$). As shown in prior work, well-founded solutions (a.k.a. grounded labelings)"explain themselves": The provenance of arguments is given by subgraphs (definable via regular path queries) rooted at the node of interest. This provenance is closely related to winning strategies of a two-player argumentation game. We present a novel approach for extending this provenance to stable AF solutions. Unlike grounded solutions, which can be constructed via a bottom-up alternating fixpoint procedure, stable models often involve non-deterministic choice as part of the search for models. Thus, the provenance of stable solutions is of a different nature, and reflects a more expressive generate&test paradigm. Our approach identifies minimal sets of critical attacks, pinpointing choices and assumptions made by a stable model. These critical attack edges provide additional insights into the provenance of an argument's status, combining well-founded derivation steps with choice steps. Our approach can be understood as a form of diagnosis that finds minimal"repairs"to an AF graph such that the well-founded solution of the repaired graph coincides with the desired stable model of the original AF graph.

Problem

• Extending provenance explanation to stable AF solutions
• Identifying critical attacks in stable model choices
• Diagnosing minimal repairs for well-founded stable alignment

Innovation

• Extends provenance to stable AF solutions
• Identifies minimal critical attack sets
• Combines well-founded derivations with choices