Verification in attack-incomplete argumentation frameworks

Abstract

We tackle the problem of expressing incomplete knowledge about the attack relation in abstract argumentation frameworks. In applications, incomplete argumentation frameworks may arise as intermediate states in an elicitation process, when merging different beliefs about an argumentation framework’s state, or in cases where the complete information cannot be fully obtained. To this end, we employ a model introduced by Cayrol et al. [10] and analyze the question of whether certain justification criteria are possibly (or necessarily) fulfilled, i.e., whether they are fulfilled in some (or in every) completion of the incomplete argumentation framework. We formally extend the definition of existing criteria to these incomplete argumentation frameworks and provide characterization and complexity results for variants of the verification problem.