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Subargument Argumentation Frameworks: Separating Direct Conflict from Structural Dependency

Dung's abstract argumentation frameworks model acceptability solely in terms of an attack relation, thereby conflating two conceptually distinct aspects of argumentative reasoning: direct conflict between arguments and the structural dependencies that arise from their internal composition. While this abstraction preserves extension-based semantics, it obscures how justification is grounded in subarguments and how defeats propagate through argument structure. We introduce Subargument Argumentation Frameworks (SAFs), an abstract framework in which direct attack and subargumenthood are represented as independent primitive relations. This separation makes structural dependency explicit at the representational level while leaving its semantic impact to be determined by structure-sensitive notions of defence, admissibility, and complete semantics defined within the framework. We show that projecting SAFs onto attack-only frameworks yields extension-equivalent Dung frameworks under all standard semantics, yet the projection irreversibly loses information about justificatory grounding and structural propagation. SAFs therefore provide strictly greater representational expressiveness while remaining semantically compatible with Dung's theory, thereby offering a principled basis for structure-sensitive accounts of defence, justification, and explanation in abstract argumentation.

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