Constrained Incomplete Argumentation Frameworks

Abstract

Operations like belief change or merging have been adapted to the context of abstract argumentation. However, these operations may require to express some uncertainty or some disjunction in the result, which is not representable in classical AFs. For this reason, some of these works require a set of AFs or a set of extensions as the outcome of the operation, somehow to represent a disjunction of AFs or extensions. In parallel, the notion of Incomplete AFs (IAFs) has been developed recently. It corresponds to AFs where the existence of some arguments or attacks may be uncertain. Each IAF can be associated with a set of classical AFs called completions, that correspond to different ways of “resolving the uncertainty”. While these IAFs could be good candidates for a compact representation of a “disjunction” of AFs, we prove that this model is not expressive enough. Then we introduce Constrained IAFs, that include a propositional formula allowing to select the set of completions used for reasoning. We prove that this model is expressive enough for representing any set of AFs, or any set of extensions. Moreover, we show that the complexity of credulous and skeptical reasoning is the same as in the case of IAFs. Finally, we show that CIAFs can be used to model a new form of extension enforcement.