@misc{421, author = {Jesse Heyninck and Matthias Thimm and Gabriele Kern-Isberner and Tjitze Rienstra and Kenneth Skiba}, title = {Arguing about Complex Formulas: Generalizing Abstract Dialectical Frameworks}, abstract = {Abstract dialectical frameworks (in short, ADFs) are a unifying model of formal argumentation, where argumentative relations between arguments are represented by assigning acceptance conditions to atomic arguments. This idea is generalized by letting acceptance conditions being assigned to complex formulas, resulting in conditional abstract dialectical frameworks (in short, cADFs). We define the semantics of cADFs in terms of a non-truth-functional four-valued logic, and study the semantics in-depth, by showing existence results and proving that all semantics are generalizations of the corresponding semantics for ADFs.}, year = {2021}, url = {https://sites.google.com/view/nmr2021/home?authuser=0}, }