In many argumentative texts a substantial amount of knowledge remains implicit. This implicit knowledge is often crucial for a deep understanding and correct interpretation of arguments. In this work we investigate how to automatically reconstruct implicit knowledge in argumentative texts, and how the reconstruction of implicit knowledge can help in improving computational argument analysis. We point out that knowledge which stays implicit can in most cases be framed as commonsense knowledge, which has been shown to be helpful for solving many Natural Language Processing (NLP) tasks. However, it has not yet been leveraged for an in-depth analysis of arguments. This work closes this research desideratum by integrating commonsense knowledge in computational argument analysis. We explore ways to fill implicit knowledge gaps in arguments automatically by utilizing commonsense knowledge, in order to build bridges between argumentative sentences – with the ultimate goal of improving argument analysis.