dialectical frameworks have been introduced as a formalism for modeling argumentation allowing general logical satisfaction conditions and the relevant argument evaluation. Different criteria used to settle the acceptance of arguments are called semantics. Semantics of ADFs have so far mainly been defined based on the concept of admissibility. However, the notion of strongly admissible semantics studied for abstract argumentation frameworks has not yet been introduced for ADFs. In the current work we present the concept of strong admissibility of interpretations for (...) ADFs. Further, we show that strongly admissible interpretations of ADFs form a lattice with the grounded interpretation as the maximal element. We also present algorithms to answer the following decision problems: whether a given interpretation is a strongly admissible interpretation of a given ADF, and whether a given argument is strongly acceptable/deniable in a given interpretation of a given ADF. In addition, we show that the strongly admissible semantics of ADFs forms a proper generalization of the strongly admissible semantics of AFs. (shrink)

argumentation, as originally defined by Dung, is a model that allows the description of certain information about arguments and relationships between them: in an abstract argumentation framework, the agent knows for sure whether a given argument or attack exists. It means that the absence of an attack between two arguments can be interpreted as “we know that the first argument does not attack the second one”. But the question of uncertainty in abstract argumentation has received much attention in the last (...) years. In this paper, we survey approaches that allow to express information like “There may be an attack between these arguments”. We describe the main models that incorporate qualitative uncertainty in abstract argumentation, as well as some applications of these models. We also highlight some open questions that deserve some attention in the future. (shrink)

1. The last 25 years have seen an increasing interest in the area of formal argumentation. The ultimate goal of the field is to come up with computational models of how we make decisions, based on...