Existing discourse formalisms use different taxonomies of discourse relations, which require expert knowledge to understand, posing a challenge for annotation and automatic classification. We show that discourse relations can be effectively captured by some simple cognitively inspired dimensions proposed by Sanders et al.(2018). Our experiments on cross-framework discourse relation classification (PDTB & RST) demonstrate that it is possible to transfer knowledge of discourse relations for one framework to another framework by means of these dimensions, in spite of differences in discourse segmentation of the two frameworks. This manifests the effectiveness of these dimensions in characterizing discourse relations across frameworks. Ablation studies reveal that different dimensions influence different types of discourse relations. The patterns can be explained by the role of dimensions in characterizing and distinguishing different relations. We also report our experimental results on automatic prediction of these dimensions.