Semi-Stable Semantics for Abstract Dialectical Frameworks

Abstract dialectical frameworks (ADFs) have been introduced as a formalism for modeling and evaluating argumentation allowing general logical satisfaction conditions. Different criteria that have been used to settle the acceptance of arguments are called semantics. However, the notion of semi-stable semantics as studied for abstract argumentation frameworks has received little attention for ADFs. In the current work, we present the concepts of semi-two-valued models and semi-stable models for ADFs. We show that these two notions satisfy a set of plausible properties required for semi-stable semantics of ADFs. Moreover, we show that semi-two-valued and semi-stable semantics of ADFs form a proper generalization of the semi-stable semantics of AFs, just like two-valued model and stable semantics for ADFs are generalizations of stable semantics for AFs.