Abstract
In this thesis, we study the semantic parsing task that is considered as a structured prediction problem. We also investigate its applications to solving math word problems (including arithmetic word problem solving and equation parsing tasks). First, for semantic parsing, we study the multilingual settings. A simple yet effective method is proposed to learn distributed representations of the logical forms from data annotated with different languages. The learned representations contain shared information across different languages. This novel approach is built on the matrix factorization on the co-occurrence matrix that is constructed from the multilingual sentence-semantic settings. Incorporating such cross-lingual distributed representations as features, two existing monolingual semantic parsers yields better performance. For the task of solving math word problems, we consider two scenarios: additionsubtraction and general problems. As for the first scenario, we propose Quantity Tagger, a latent-variable labeling approach. Such a model converts the task of solving addition-subtraction problems into a sequence labeling problem that can be considered as a degenerated semantic parsing problem. For the general cases, a simplified model, named Text2Math, is designed to semantically parse text into math expressions. We tackle the problem from an end-to-end structured prediction view where our algorithm aims to predict the complete math expression at once as a tree structure. Compared to baselines, both Quantity Tagger and Text2Math achieve better performance on two scenarios, respectively.