Abstract Dialectical Frameworks – An Analysis of Their Properties and Role in Knowledge Representation and Reasoning

Abstract dialectical frameworks (ADFs) are a formalism for representing knowledge about abstract arguments and various logical relationships between them. This work studies ADFs in detail. Firstly, we use the framework of approximation fixpoint theory to define various semantics that are known from related knowledge representation formalisms also for ADFs. We then analyse the computational complexity of a variety of reasoning problems related to ADFs. Afterwards, we also analyse the formal expressiveness in terms of realisable sets of interpretations and show how ADFs fare in comparison to other formalisms. Finally, we show how ADFs can be put to use in instantiated argumentation, where researchers try to assign meaning to sets of defeasible and strict rules. The main outcomes of our work show that in particular the sublanguage of bipolar ADFs are a useful knowledge representation formalism with meaningful representational capabilities and acceptable computational properties