Compact Argumentation Frameworks
This work addresses incremental theoretical improvements in abstract argumentation for AI researchers, focusing on formal properties of fairness and minimality.
The paper tackles the problem of identifying and analyzing compact argumentation frameworks (AFs), a subclass where every argument appears in at least one extension under a given semantics, ensuring fairness and minimality. It shows that compact AFs are non-trivial, with verification remaining coNP-hard for certain semantics.
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.