The paper presents a new framework for modeling abstract argumentation graphs that takes into account the order in which arguments are presented. This is achieved by using an Action Description Language (ADL) to formalize the argumentative process and update the acceptability status of arguments.
The key highlights and insights are:
The framework models the actual dialogue in real-time, updating the acceptability of arguments based on a set of defined rules inspired by argumentation labellings. This is in contrast to previous approaches that build a dialogue a posteriori to justify the membership of an argument to a particular semantics.
The framework establishes formal properties such as termination and correctness with respect to the classical Abstract Argumentation Framework (AAF). It also discusses two notions of completeness, where the second form aims to find an order of enunciation for each extension of the complete semantics.
To achieve the second form of completeness, the authors propose a modification to the transformation based on a "last enunciated last updated" strategy. This ensures that the acceptability update of a newly stated argument occurs last, allowing the framework to handle even-length and odd-length cycles.
The paper also provides a preliminary discussion on handling other semantics, such as the grounded, preferred, and stable semantics, and the technical challenges they raise.
Overall, the proposed framework integrates the order of argument enunciation into the modeling of abstract argumentation, enabling the deduction of a unique outcome for each dialogue and laying the groundwork for future work on explanations based on causal reasoning.
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by Yann Munro, ... at arxiv.org 10-01-2024
https://arxiv.org/pdf/2409.19625.pdfDeeper Inquiries