Weighted Abstract Dialectical Frameworks through the Lens of Approximation Fixpoint Theory

Weighted abstract dialectical frameworks (wADFs) were recently introduced, extending abstract dialectical frameworks to incorporate degrees of acceptance. In this paper, we propose a different view on wADFs: we develop semantics for wADFs based on approximation fixpoint theory, an abstract algebraic theory designed to capture semantics of various non-monotonic reasoning formalisms. Our formalism deviates from the original definition on some basic assumptions, the most fundamental is that we assume an ordering on acceptance degrees. We discuss the impact of the differences, the relationship between the two versions of the formalism, and the advantages each of the approaches offers. We furthermore study complexity of various semantics