We examine the learnability of Commonsense knowledge relations as represented in CONCEPTNET. We develop a neural open world multi-label classification system that focuses on the evaluation of classification accuracy for individual relations. Based on an in-depth study of the specific properties of the CONCEPTNET resource such as relation ambiguity or argument heterogeneity, we investigate the impact of different relation representations and model variations. Our analysis reveals that the complexity of argument types and relation ambiguity are the most important challenges to address. We design a customized evaluation method to address the incompleteness of the resource that can be expanded in future work.