Automatic Understanding and Formalization of Plane Geometry Proving Problems in Natural Language: A Supervised Approach

Abstract

Automatically understanding natural language problems is a long-standing challenging research problem in automatic solving. This paper models the understanding of geometry problems as a problem of relation extraction, instead of as the problem of semantic understanding of natural language. Then it further proposes a supervised machine learning method to extract geometric relations, targeting to produce a group of relations to represent the given geometry problem. This method identifies the actual geometric relations from the relation candidates using a classifier trained from the labelled examples. The formalized geometric relations can then be transformed into the target system-native representations for manipulation in various tasks. Experiments conducted on the test problem dataset show that the proposed method can extract geometric relations at high F1 scores. The comparisons also demonstrate that the proposed method can achieve good performance against the baseline methods. Integrating the automatic understanding method with different geometry systems will greatly enhance the efficiency and intelligence in geometry tutoring.