Methods for learning with ambiguous labelings have previously been proposed in the context of multi-class classification (Jin and Ghahramani, 2002), sequence-labeling (Dredze et al., 2009), log-linear LFG parsing (Riezler et al., 2002), as well as for discriminative reranking of generative constituency parsers (Charniak and Johnson, 2005).
to Dredze et al., who allow for weights to be assigned to partial labels, we assume that the ambiguous arcs are weighted uniformly.