Strong Admissibility for Abstract Dialectical Frameworks

TL;DR

This paper introduces the concept of strong admissibility for abstract dialectical frameworks (ADFs), extending the notion from abstract argumentation frameworks, and shows that these interpretations form a lattice structure.

Contribution

It defines strong admissibility for ADFs and proves that strongly admissible interpretations form a lattice with the grounded interpretation as the top element.

Findings

Strong admissibility for ADFs is formally defined.

Strongly admissible interpretations form a lattice structure.

Grounded interpretation is the top element in this lattice.

Abstract

Abstract dialectical frameworks (ADFs) have been introduced as a formalism for modeling and evaluating argumentation allowing general logical satisfaction conditions. Different criteria used to settle the acceptance of arguments are called semantics. Semantics of ADFs have so far mainly been defined based on the concept of admissibility. However, the notion of strongly admissible semantics studied for abstract argumentation frameworks has not yet been introduced for ADFs. In the current work we present the concept of strong admissibility of interpretations for ADFs. Further, we show that strongly admissible interpretations of ADFs form a lattice with the grounded interpretation as top element.