Possible Controllability of Control Argumentation Frameworks -- Extended Version

The recent Control Argumentation Framework (CAF) is a generalization of Dung's Argumentation Framework which handles argumentation dynamics under uncertainty; especially it can be used to model the behavior of an agent which can anticipate future changes in the environment. Here we provide new insights on this model by defining the notion of possible controllability of a CAF. We study the complexity of this new form of reasoning for the four classical semantics, and we provide a logical encoding for reasoning with this framework.