Discourse relation classification has proven to be a hard task, with rather low performance on several corpora that notably differ on the relation set they use. We propose to decompose the task into smaller, mostly binary tasks corresponding to various primitive concepts encoded into the discourse relation definitions. More precisely, we translate the discourse relations into a set of values for attributes based on distinctions used in the map-pings between discourse frameworks proposed by Sanders et al. (2018). This arguably allows for a more robust representation of discourse relations, and enables us to address usually ignored aspects of discourse relation prediction, namely multiple labels and underspecified annotations. We study experimentally which of the conceptual primitives are harder to learn from the Penn Discourse Treebank English corpus, and propose a correspondence to predict the original labels, with preliminary empirical comparisons with a direct model.