---
title: "When Incompleteness Does Not Matter: The Case of Incomplete Abstract Argumentation Framework (Under the Possible Perspective)"
authors:
  - "Bettina Fazzinga"
  - "Sergio Flesca"
  - "Filippo Furfaro"
doi: "10.24963/ijcai.2026/426"
url: "https://ijcai.org/proceedings/2026/426"
pdf: "https://ijcai.org/proceedings/2026/0426.pdf"
venue: "Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence"
year: 2026
pages: "3829-3836"
track: "Main Track"
keywords:
  - "Uncertainty in AI: Uncertainty representations"
  - "Knowledge Representation and Reasoning: Argumentation"
---

# When Incompleteness Does Not Matter: The Case of Incomplete Abstract Argumentation Framework (Under the Possible Perspective)

Bettina Fazzinga, Sergio Flesca, Filippo Furfaro

*Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence*, pages 3829-3836. DOI: [10.24963/ijcai.2026/426](https://doi.org/10.24963/ijcai.2026/426)

## Abstract

Incomplete Abstract Argumentation Frameworks (iAAFs) extend Abstract Argumentation Frameworks (AAFs) by allowing arguments and attacks to be specified as uncertain, enabling a compact representation of alternative argumentation scenarios. 
Despite extensive work on reasoning with iAAFs, their expressive power relative to standard AAFs is still unclear. 
We address this question by studying whether the reasoning based on possible-extensions in iAAFs can be reduced to classical reasoning 
on AAFs. 
Our analysis relates iAAFs and AAFs via two comparison notions:
equivalence, where an AAF yields as extensions exactly the possible extensions of an iAAF, 
and projection-equivalence, where such extensions are obtained by projecting away auxiliary arguments.
We characterize the semantics under which these relationships hold, and, in these cases,  provide constructive transformations from iAAFs to AAFs, thus also enabling classical argumentation tools to be applied to qualitative-uncertainty reasoning.