Towards Generating Controllable and Solvable Geometry Problem by Leveraging Symbolic Deduction Engine

TL;DR

This paper introduces SDE-GPG, a novel framework that leverages symbolic deduction to generate high-quality, controllable, and solvable geometry problems with diagrams, addressing challenges in multi-modal problem translation and difficulty control.

Contribution

The paper proposes a new pipeline for geometry problem generation using symbolic deduction, ensuring controllability and solvability, and reducing translation biases.

Findings

Effective generation of readable and solvable geometry problems

Control over problem difficulty and knowledge points

Automatic diagram drawing supports problem comprehension

Abstract

Generating high-quality geometry problems is both an important and challenging task in education. Compared to math word problems, geometry problems further emphasize multi-modal formats and the translation between informal and formal languages. In this paper, we introduce a novel task for geometry problem generation and propose a new pipeline method: the Symbolic Deduction Engine-based Geometry Problem Generation framework (SDE-GPG). The framework leverages a symbolic deduction engine and contains four main steps: (1) searching a predefined mapping table from knowledge points to extended definitions, (2) sampling extended definitions and performing symbolic deduction, (3) filtering out unqualified problems, and (4) generating textual problems and diagrams. Specifically, our method supports to avoid inherent biases in translating natural language into formal language by designing the mapping table, and guarantees to control the generated problems in terms of knowledge points and difficulties by an elaborate checking function. With obtained formal problems, they are translated to natural language and the accompanying diagrams are automatically drew by rule-based methods. We conduct experiments using real-world combinations of knowledge points from two public datasets. The results demonstrate that the SDE-GPG can effectively generate readable, solvable and controllable geometry problems.