Parsing Natural Language into Propositional and First-Order Logic with Dual Reinforcement Learning

Proceedings of the 29th International Conference on Computational Linguistics, pages 5419–5431 October 12–17, 2022. 5419 Parsing Natural Language into Propositional and First-Order Logic with Dual Reinforcement Learning Xuantao Lu♣, Jingping Liu♠∗, Zhouhong Gu♣, Hanwen Tong♣, Chenhao Xie⋆, Junyang Huang♣, Yanghua Xiao♣♡∗, Wenguang Wang♢, ♣Shanghai Key Laboratory of Data Science, School of Computer Science, Fudan University ⋆SenseDeal Intelligent Technology Co., Ltd., Beijing, China ♠School of Information Science and Engineering, East China University of Science and Technology ♡Fudan-Aishu Cognitive Intelligence Joint Research Center ♢DataGrand Inc., Shanghai, China {xtlu20, shawyh}@fudan.edu.cn, jingpingliu@ecust.edu.cn, xiechenhao@sensedeal.ai Abstract Semantic parsing converts natural language utterances into structured logical expressions. We consider two such formal representations: Propositional Logic (PL) and First-order Logic (FOL). The paucity of labeled data is a major challenge in this field. In previous works, dual reinforcement learning has been proposed as an approach to reduce dependence on labeled data. However, this method has the following limitations: 1) The reward needs to be set man- ually and is not applicable to all kinds of logical expressions. 2) The training process easily col- lapses when models are trained with only the re- ward from dual reinforcement learning. In this paper, we propose a scoring model to automati- cally learn a model-based reward, and an effec- tive training strategy based on curriculum learn- ing is further proposed to stabilize the training process. In addition to the technical contribu- tion, a Chinese-PL/FOL dataset is constructed to compensate for the paucity of labeled data in this field. Experimental results show that the proposed method outperforms competitors on several datasets. Furthermore, by introducing PL/FOL generated by our model, the perfor- mance of existing Natural Language Inference (NLI) models is further enhanced. 1 Introduction Semantic parsing is the task of mapping natural lan- guage utterances into logical expressions. As two major logical forms of text representation, Proposi- tional Logic (PL) and First-order Logic (FOL) play an increasingly important role in a wide range of downstream tasks including Inductive Logic Pro- gramming (ILP) (Yang and Song, 2019), Question Answering (QA) (Longo and Santoro, 2020) and Interpretable Reinforcement Learning (Ma et al., 2020; Kimura et al., 2021) because they are capable ∗ Corresponding Author English-FOL Natural Language Utterance Some volunteers include executives and professionals. Logical Expression exists x1.(_volunteer(x1) & exists x2. (_executive(x2) & _professional(x2) & _include(x1, x2))) Table 1: Example of the English-FOL dataset. Text in olive denotes quantifiers, and text in teal denotes predicates. x1 and x2 denote variables, and & denotes logical connectives. of discovering and representing knowledge in an explicit symbolic structure that can be understood and examined by human (Evans and Grefenstette, 2018). It is worth noting that all of these tasks have a prerequisite, i.e., parsing natural language utter- ances into PL/FOL. The results of parsing directly affect the performance of downstream tasks. Thus, it is crucial to have a strong semantic parser for PL/FOL. Some solutions have been proposed to parse nat- ural language into PL/FOL. One of the most typical methods is to model the parsing task as …

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