In their daily use arguments are usually not completely enunciated. That is, we often rely on implicit parts, for example, unstated premises, sometimes referred to as enthymemes. Completions of partially stated arguments can favor knowledge engineering processes, where the workload of an engineer can be reduced by suggesting such completions. In this work, we focus on an integral aspect of completing arguments: valid argument structure of a completion. We phrase our results in the formal model of assumption-based argumentation (ABA). Based on an alternative characterization of tree-based arguments in ABA, we provide a declarative approach to compute completions of partial arguments in answer set programming (ASP), including the possibility of preferential reasoning in completions. We empirically evaluate a resulting prototype.