Two forms of minimality in ASPIC+

TL;DR

The paper discusses two types of minimality in structured argumentation, focusing on how ASPIC+ inherently ensures a form of minimality and how the other can be integrated.

Contribution

It clarifies the relationship between two minimality notions in argumentation frameworks and shows how to incorporate the first into ASPIC+.

Findings

ASPIC+ arguments are minimal by construction.

Two types of minimality in structured argumentation are identified.

The first minimality can be integrated into ASPIC+ if desired.

Abstract

Many systems of structured argumentation explicitly require that the facts and rules that make up the argument for a conclusion be the minimal set required to derive the conclusion. ASPIC+ does not place such a requirement on arguments, instead requiring that every rule and fact that are part of an argument be used in its construction. Thus ASPIC+ arguments are minimal in the sense that removing any element of the argument would lead to a structure that is not an argument. In this brief note we discuss these two types of minimality and show how the first kind of minimality can, if desired, be recovered in ASPIC+.