Parsing into Variable-in-situ Logico-Semantic Graphs (2020)

Abstract: 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.

## introduction graphs have recently become popular as a strategy for encoding sentence-level semantics, and related data-driven parsing techniques have been making rapid progress. the primary component of popular semantic graphs, e.g. elementary dependency structure (eds; @xcite and abstract meaning representation (amr; @xcite , is the predicate-argument structure, with the predicate being a concept that takes a number of arguments. though expressive for many applications, this predicative core does not fully match the need for logical forms that used to stand in the central area of semantic parsing. partly due to the lack of model-theoretic semantics, it is rather difficult to add scope information related to quantification, negation and modality to a graph. partly due to the lack of logical deduction engines, it is rather difficult to directly perform automated reasoning over graphs. this paper proposes to express logical forms with variable-in-situ graphs for the ongoing advances in graph-centric formalisms, algorithms and neural architectures. this leads us to a novel neural graph rewriting system that combines the strengths of hyperedge replacement grammar (hrg; @xcite and graph neural networks @xcite ). on the one hand, it can be viewed as an improved graph embedding model that explicitly explores recursive structures that are defined by an hrg. on the other hand, it can be viewed as an enhanced graph grammar with which all nodes involved in derivations of graphs are assigned vector-based distributed encodings. based on our neural graph rewriting system, we develop a new parser for minimal recursion semantics (mrs; @xcite . by means of the deepbank @xcite data, 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. we also consider the structural validity of logico-semantic graphs following the original design of mrs. the output of our parser is highly coherent: at least 91% graphs are coherent, in that they allow at least one sound scope-resolved logical form. ## neural graph rewriting automatically constructing a semantic representation can be achieved by exploring the compositionality principle: the meaning of a complex expression is a function of the meanings of its parts and of the syntactic rules by which they are combined. in this perspective, both meanings of its parts and the function of syntactic rules can be precisely defined by graph fragments. in this paper, we investigate how to manipulate semantic graph fragments with hrg, a context-free rewriting system for generating graphs. we give a formal description of hrg, and then show how to model syntactico-semantic composition through graph rewriting. recursive neural networks are also important for handling linguistic data. in this section, we will further augment an hrg with a hypergraph-state lstm. ## related work it has been a long time since researchers manipulated semantic construction following the principle of compositionality. different formalisms have been developed to express the syntactic-semantic interface in natural language utterances. to manipulate compositional construction, hrg is a popular framework to define a graph-structured syntax-semantics interface @xcite . am algebra @xcite is another formalism to handle graph construction which has been successfully explored to build semantic parsers @xcite . compositional vector representation is also widely studied in recent years. @xcite encodes syntactic dependency trees with a recursive recurrent neural network, which acts as the core of a bottom-up dependency parser. @xcite introduced recurrent neural network grammar, a probabilistic model of sentences with explicit phrase structure. a recursive syntactic composition function is used to compute an embedding of a completed phrasestructure subtree. modeling discrete structures with principled neural networks has received an increasing interest. @xcite proposed graph convolution network to classify nodes in graphs. dag-structured lstm is a natural extension to tree lstm which treats nodes as basic states @xcite . graph-state lstm can be used in both generation task @xcite and relation extraction @xcite . ## conclusion graph-structured meaning representations provide an effective way to encode rich semantic information of natural language sentences and have been extensively studied recently. we enriched the discussion by studying an alternative graph-based representation for underspecified logical forms. in particular, we introduced a novel neural graph rewriting system and developed a new state-ofthe-art semantic parser for variable-in-situ graphs.