  Semantic parses are directed acyclic graphs (DAGs), so semantic parsing
should be modeled as graph prediction. But predicting graphs presents difficult
technical challenges, so it is simpler and more common to predict the
linearized graphs found in semantic parsing datasets using well-understood
sequence models. The cost of this simplicity is that the predicted strings may
not be well-formed graphs. We present recurrent neural network DAG grammars, a
graph-aware sequence model that ensures only well-formed graphs while
sidestepping many difficulties in graph prediction. We test our model on the
Parallel Meaning Bank---a multilingual semantic graphbank. Our approach yields
competitive results in English and establishes the first results for German,
Italian and Dutch.
