Discourse markers (by contrast, happily, etc.) are words or phrases that are used to signal semantic and/or pragmatic relationships between clauses or sentences. Recent work has fruitfully explored the prediction of discourse markers between sentence pairs in order to learn accurate sentence representations, that are useful in various classification tasks. In this work, we take another perspective: using a model trained to predict discourse markers between sentence pairs, we predict plausible markers between sentence pairs with a known semantic relation (provided by existing classification datasets). These predictions allow us to study the link between discourse markers and the semantic relations annotated in classification datasets. Handcrafted mappings have been proposed between markers and discourse relations on a limited set of markers and a limited set of categories, but there exist hundreds of discourse markers expressing a wide variety of relations, and there is no consensus on the taxonomy of relations between competing discourse theories (which are largely built in a top-down fashion). By using an automatic prediction method over existing semantically annotated datasets, we provide a bottom-up characterization of discourse markers in English. The resulting dataset, named DiscSense, is publicly available.