Reasoning is a crucial part of natural language argumentation. To comprehend an argument, one must analyze its warrant, which explains why its claim follows from its premises. As arguments are highly contextualized, warrants are usually presupposed and left implicit. Thus, the comprehension does not only require language understanding and logic skills, but also depends on common sense. In this paper we develop a methodology for reconstructing warrants systematically. We operationalize it in a scalable crowdsourcing process, resulting in a freely licensed dataset with warrants for 2k authentic arguments from news comments. On this basis, we present a new challenging task, the argument reasoning comprehension task. Given an argument with a claim and a premise, the goal is to choose the correct implicit warrant from two options. Both warrants are plausible and lexically close, but lead to contradicting claims. A solution to this task will define a substantial step towards automatic warrant reconstruction. However, experiments with several neural attention and language models reveal that current approaches do not suffice.