Dung’s abstract argumentation framework is a popular formalism in formal argumentation. The present work develops paraconsistent labeling semantics for abstract argumentation such that the incomplete and inconsistent information can be expressed, and it introduces a Hilbert-style axiomatic system which is proven to be sound and complete. Additionally, we make a comparison between the logic developed in the present work and some relevant theories of abstract argumentation.
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Yuanlei Lin (2024) studied this question.
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