A key problem in processing graph-based meaning representations is graph parsing, i.e. computing all possible derivations of a given graph according to a (competence) grammar. We demonstrate, for the first time, that exact graph parsing can be efficient for large graphs and with large Hyperedge Replacement Grammars (HRGs). The advance is achieved by exploiting locality as terminal edge-adjacency in HRG rules. In particular, we highlight the importance of 1) a terminal edge-first parsing strategy, 2) a categorization of a subclass of HRG, i.e. what we call Weakly Regular Graph Grammar, and 3) distributing argument-structures to both lexical and phrasal rules.

We propose variable-in-situ logico-semantic graphs to bridge the gap between semantic graph and logical form parsing. The new type of graph-based meaning representation allows us to include analysis for scope-related phenomena, such as quantification, negation and modality, in a way that is consistent with the state-of-the-art underspecification approach. Moreover, the well-formedness of such a graph is clear, since model-theoretic interpretation is available. We demonstrate the effectiveness of this new perspective by developing a new state-of-the-art semantic parser for English Resource Semantics. At the core of this parser is a novel neural graph rewriting system which combines the strengths of Hyperedge Replacement Grammar, a knowledge-intensive model, and Graph Neural Networks, a data-intensive model. Our parser achieves an accuracy of 92.39% in terms of elementary dependency match, which is a 2.88 point improvement over the best data-driven model in the literature. The output of our parser is highly coherent: at least 91% graphs are valid, in that they allow at least one sound scope-resolved logical form.

This paper is concerned with semantic parsing for English as a second language (ESL). Motivated by the theoretical emphasis on the learning challenges that occur at the syntax-semantics interface during second language acquisition, we formulate the task based on the divergence between literal and intended meanings. We combine the complementary strengths of English Resource Grammar, a linguistically-precise hand-crafted deep grammar, and TLE, an existing manually annotated ESL UD-TreeBank with a novel reranking model. Experiments demonstrate that in comparison to human annotations, our method can obtain a very promising SemBanking quality. By means of the newly created corpus, we evaluate state-of-the-art semantic parsing as well as grammatical error correction models. The evaluation profiles the performance of neural NLP techniques for handling ESL data and suggests some research directions.