The authors are not aware of any specific theoretical linguistic evidence for the planarity or outerplanarity of semantic dependency DAGs.
we consider the three datasets from SemEval 2014 task 8 on Broad Coverage Semantic Dependency Parsing (Oepen et al., 2014), referred to as PAS, DM and PCEDT, following the packing conversion into DAGs described in , without the actual label packing or edge removal heuristic, finding that almost all DAGs are outerplanar (and therefore also planar).