In this paper we present the first, to the best of our knowledge, discourse parser that is able to predict non-tree DAG structures. We use Integer Linear Programming (ILP) to encode both the objective function and the constraints as global decoding over local scores. Our underlying data come from multi-party chat dialogues, which require the prediction of DAGs. We use the dependency parsing paradigm, as has been done in the past (Muller et al., 2012; Li et al., 2014; Afantenos et al., 2015), but we use the underlying formal framework of SDRT and exploit SDRT's notions of left and right distributive relations. We achieve an F-measure of 0.531 for fully labeled structures which beats the previous state of the art.
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