Argument Decomposition in Abstract Dialectical Frameworks

Johannes E. Bendler, Tjitze Rienstra

Track: Type A (Regular Papers)

Keywords: Argumentation Theory, Knowledge Representation, Non-monotonic reasoning, Explainable AI, Abstract Dialectical Frameworks (ADFs)

Abstract: Abstract Dialectical Frameworks (ADFs) represent a powerful generalization for various argumentation frameworks and non-monotonic reasoning formalisms, wherein propositional acceptance conditions determine the acceptability of statements. This research introduces three decomposition operations addressing logical negation, conjunction, and disjunction, which systematically deconstruct complex acceptance conditions into simpler components while preserving the framework's extensions under standard semantics. For each operation, rigorous proofs are provided, demonstrating that the transformed ADF produces identical extensions under admissible, preferred, complete, and grounded semantics for all statements of the original framework. Through iterative application of these decomposition operations, any ADF can be transformed into a maximal decomposed ADF with minimal acceptance conditions, thereby enhancing explainability and modularity. Furthermore, these maximal decomposed ADFs exhibit the properties of Bipolar ADFs, thus potentially yielding computational advantages and better translatability into other formalisms such as Boolean Networks. This decomposition approach establishes a formal foundation for structural optimization, as well as improved explainability and transparency in argumentative reasoning systems.

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Submission Number: 70