On Undisputed Sets in Abstract Argumentation

Authors

  • Matthias Thimm University of Hagen

DOI:

https://doi.org/10.1609/aaai.v37i5.25805

Keywords:

KRR: Argumentation, KRR: Computational Complexity of Reasoning, MAS: Agreement, Argumentation & Negotiation

Abstract

We introduce the notion of an undisputed set for abstract argumentation frameworks, which is a conflict-free set of arguments, such that its reduct contains no non-empty admissible set. We show that undisputed sets, and the stronger notion of strongly undisputed sets, provide a meaningful approach to weaken admissibility and deal with the problem of attacks from self-attacking arguments, in a similar manner as the recently introduced notion of weak admissibility. We investigate the properties of our new semantical notions and show certain relationships to classical semantics, in particular that undisputed sets are a generalisation of preferred extensions and strongly undisputed sets are a generalisation of stable extensions. We also investigate the computational complexity of standard reasoning tasks with these new notions and show that they lie on the second and third level of the polynomial hierarchy, respectively.

Downloads

Published

2023-06-26

How to Cite

Thimm, M. (2023). On Undisputed Sets in Abstract Argumentation. Proceedings of the AAAI Conference on Artificial Intelligence, 37(5), 6550-6557. https://doi.org/10.1609/aaai.v37i5.25805

Issue

Section

AAAI Technical Track on Knowledge Representation and Reasoning