Satisfying Rationality Postulates of Structured Argumentation Through Deductive Support -- Technical Report

TL;DR

This paper introduces Deductive ASPIC$^{ m heta}$, a new structured argumentation framework that satisfies all five key rationality postulates under preferred semantics, enhancing logical robustness.

Contribution

It combines ASPIC$^{ m heta}$ with JSBAFs and preferences to meet all rationality postulates simultaneously, addressing previous limitations.

Findings

Deductive ASPIC$^{ m heta}$ satisfies all five rationality postulates.

The framework works under a credulous preferred semantics.

It advances the formal foundations of structured argumentation.

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.