Convincing someone of the truth value of a premise requires understanding and articulating the core logical structure of the argument which proves or disproves the premise. Understanding the logical structure of an argument refers to understanding the underlying "reasons" which make up the proof or disproof of the premise - as a function of the "logical atoms" in the argument. While it has been shown that transformers can "chain" rules to derive simple arguments, the challenge of articulating the "reasons" remains. Not only do current approaches to chaining rules suffer in terms of their interpretability, they are also quite constrained in their ability to accommodate extensions to theoretically equivalent reasoning tasks - a model trained to chain rules cannot support abduction or identify contradictions. In this work we suggest addressing these shortcomings by identifying an intermediate representation (which we call the Representation of the Logical Structure (RLS) of the argument) that possesses an understanding of the logical structure of a natural language argument - the logical atoms in the argument and the rules incorporating them. Given the logical structure, reasoning is deterministic and easy to compute. Therefore, our approach supports all forms of reasoning that depend on the logical structure of the natural language argument, including arbitrary depths of reasoning, on-the-fly mistake rectification and interactive discussion with respect to an argument. We show that we can identify and extract the logical structure of natural language arguments in three popular reasoning datasets with high accuracies, thus supporting explanation generation and extending the reasoning capabilities significantly.