Strong Admissibility for Abstract Dialectical Frameworks
This work addresses a theoretical gap in argumentation theory by extending the notion of strong admissibility, previously studied for abstract argumentation frameworks, to the more general ADFs.
This paper introduces the concept of strong admissibility for Abstract Dialectical Frameworks (ADFs), which are formalisms for modeling and evaluating argumentation. It demonstrates that strongly admissible interpretations of ADFs form a lattice structure, with the grounded interpretation serving as the top element.
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.