Verification in argument-incomplete argumentation frameworks

Abstract

Incomplete knowledge in argumentation frameworks may occur during the single steps of an elicitation process, when merging different beliefs about the current state of an argumentation framework, or when it is simply not possible to obtain complete information. The semantics of argumentation frameworks with such incomplete knowledge have previously been modeled in terms of an inco mplete attack relation among the given arguments by Cayrol et al. [12] or when adding an argument that interacts with already present arguments [14]. We propose a more general model of argument-incomplete argumentation frameworks with a variable set of arguments, and we study the related verification problems for various semantics in terms of their computational complexity.