On Three-Valued Acceptance Conditions of Abstract Dialectical Frameworks

Abstract Dialectical Frameworks ( adf s) are generalizations of Dung's abstract argumentation frameworks ( af s) where each argument has an associated acceptance condition expressed by a boolean formula. The resulting extension is robust enough not only to model the attack relation original to af s, but also others types of dependencies and interactions between arguments. A recent development in adf s proposed an alternative formalization involving three-valued acceptance conditions, connecting the original definitions of adf s to the concept of three-valued argument labellings, a core concept in computational argumentation literature. In this paper, we revise some of the main semantics defined under this three-valued approach and prove our definitions hold equivalence to well-known semantics of af s.