Abstract
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.
