Compact Argumentation Frameworks

TL;DR

This paper introduces compact argumentation frameworks (AFs), a minimal and fair subclass where each argument appears in at least one extension, analyzing their properties, transformations, and computational complexity.

Contribution

The paper defines compact AFs, explores their relationships across semantics, and investigates their computational properties and transformation conditions.

Findings

Compact AFs ensure each argument appears in at least one extension.

Verification remains coNP-hard for certain semantics within compact AFs.

Transformations to equivalent compact AFs depend on specific conditions.

Abstract

Abstract argumentation frameworks (AFs) are one of the most studied formalisms in AI. In this work, we introduce a certain subclass of AFs which we call compact. Given an extension-based semantics, the corresponding compact AFs are characterized by the feature that each argument of the AF occurs in at least one extension. This not only guarantees a certain notion of fairness; compact AFs are thus also minimal in the sense that no argument can be removed without changing the outcome. We address the following questions in the paper: (1) How are the classes of compact AFs related for different semantics? (2) Under which circumstances can AFs be transformed into equivalent compact ones? (3) Finally, we show that compact AFs are indeed a non-trivial subclass, since the verification problem remains coNP-hard for certain semantics.