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This paper introduces Deductive ASPIC$^{\ominus}$, a novel structured argumentation framework that combines gen-rebuttals from ASPIC$^{\ominus}$ with the Joint Support Bipolar Argumentation Frameworks (JSBAFs) of Deductive ASPIC$-$, incorporating preferences. The framework is designed to satisfy five key rationality postulates (closure, direct consistency, indirect consistency, non-interference, and crash-resistance) that are crucial for logical soundness. The authors prove that Deductive ASPIC$^{\ominus}$ achieves full satisfaction of these postulates under a version of preferred semantics, a feat not previously accomplished by existing ASPIC-style frameworks under credulous semantics in the presence of undercuts.
Finally, a structured argumentation framework that doesn't break basic logical rules!
ASPIC-style structured argumentation frameworks provide a formal basis for reasoning in artificial intelligence by combining internal argument structure with abstract argumentation semantics. A key challenge in these frameworks is ensuring compliance with five critical rationality postulates: closure, direct consistency, indirect consistency, non-interference, and crash-resistance. Recent approaches, including ASPIC$^{\ominus}$ and Deductive ASPIC$-$, have made significant progress but fall short of meeting all postulates simultaneously under a credulous semantics (e.g. preferred) in the presence of undercuts. This paper introduces Deductive ASPIC$^{\ominus}$, a novel framework that integrates gen-rebuttals from ASPIC$^{\ominus}$ with the Joint Support Bipolar Argumentation Frameworks (JSBAFs) of Deductive ASPIC$-$, incorporating preferences. We show that Deductive ASPIC$^{\ominus}$ satisfies all five rationality postulates under a version of preferred semantics. This work opens new avenues for further research on robust and logically sound structured argumentation systems.
