On Looking for Local Expansion Invariants in Argumentation Semantics: a Preliminary Report

TL;DR

This paper investigates local expansion operators in abstract argumentation frameworks that preserve specific semantics, introducing a robustness measure based on the invariance of conflict-free and admissible sets under these operators.

Contribution

It defines and analyzes invariant local expansion operators for AFs and introduces a robustness concept based on their invariance properties.

Findings

Operators are invariant with respect to conflict-free and admissible sets.

A robustness measure quantifies how many times operators can be applied without changing semantics.

The framework provides a basis for understanding stability in argumentation semantics.

Abstract

We study invariant local expansion operators for conflict-free and admissible sets in Abstract Argumentation Frameworks (AFs). Such operators are directly applied on AFs, and are invariant with respect to a chosen "semantics" (that is w.r.t. each of the conflict free/admissible set of arguments). Accordingly, we derive a definition of robustness for AFs in terms of the number of times such operators can be applied without producing any change in the chosen semantics.