Identifying Necessary and Sufficient Conditions for the Enforcement Problem of Argumentation Frameworks

Abstract

In the dynamics research of argumentation frameworks (AFs), the enforcement problem deals with changing an AF for the purpose of ensuring that a certain set of desired arguments becomes (part of) an extension. In this paper we focus on expansions of an AF where solely the addition of new arguments and attacks is allowed and the original framework remains unchanged. Existing results about the enforcement problem under strong and normal expansion are all sufficient conditions. We argue that necessary and sufficient conditions are essential concerning the solvability of the enforcement problem. Specifically, two necessary and sufficient conditions are identified for the non-strict enforcement in respectively the odd-length cycle free and the even-length cycle free AFs under strong expansion. This result can be used to determine that when new arguments satisfying the condition are unavailable, enforcing the desired set simply becomes unsolvable.