Some Results about the Expressivity of Preference-Incomplete Structured Argumentation Frameworks

2026-06-22

AI Summary

This study investigates the expressive power of structured argumentation frameworks with incomplete preference information—specifically ASPIC⁺—in representing uncertain defeat relations. Through a systematic comparison with various abstract argumentation formalisms that accommodate uncertainty in defeat, the work uncovers fundamental expressivity limitations inherent to ASPIC⁺ under such settings. The central contribution is the formulation of a non-trivial threshold conjecture concerning the expressibility of uncertain preferences, accompanied by a key preliminary proof. This result establishes a theoretical foundation for understanding the boundaries of modeling preference uncertainty within structured argumentation systems.

Abstract

This paper studies the expressive power of ASPIC$^+$ argumentation frameworks with uncertain preference profiles by comparing them with several abstract formalisms with uncertain defeats. Most of our results are negative (and some of them are theoretically unexpected). We also conjecture a positive, non-trivial threshold for the expressivity of uncertain preferences, and prove some essential preliminary steps toward the confirmation of this conjecture.

Problem

• expressivity
• preference-incomplete
• structured argumentation
• uncertain preferences
• ASPIC⁺

Innovation

• expressivity
• preference-incomplete
• structured argumentation
• ASPIC+
• uncertain defeats