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

2025-06-03

AI Summary

Generating high-quality, controllable, and guaranteed-solvable geometry problems for educational applications remains challenging. Method: This paper proposes the first generative framework integrating a symbolic deductive engine. It comprises four stages: (1) knowledge-concept mapping—constructing definition-expansion tables to mitigate semantic discrepancies between natural language and formal representations; (2) symbolic derivation; (3) solvability verification via formal checking functions; and (4) joint text-image generation. This pipeline enables precise control over knowledge coverage and problem difficulty. Contribution/Results: The work is the first to deeply embed symbolic reasoning into the generative pipeline; introduces a deterministic formal-to-natural-language translation mechanism; and employs verifiable checking functions to ensure full controllability and 100% solvability. Experiments demonstrate state-of-the-art performance across readability, solvability, knowledge-alignment accuracy, and difficulty calibration. Both human evaluation and automated validation metrics significantly outperform all baselines.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Computer Vision: Visual Reasoning & Symbolic Representations
• Natural Language Processing: Generation

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

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.

Problem

• Generating controllable geometry problems using symbolic deduction
• Ensuring solvable problems via mapping and filtering steps
• Automating diagram creation for multi-modal geometry questions

Innovation

• Symbolic deduction engine for problem generation
• Mapping table ensures formal language translation
• Rule-based diagram and text generation