Autoformalization of Game Descriptions using Large Language Models

TL;DR

This paper presents a framework that uses large language models to automatically translate natural language game descriptions into formal logic, enabling formal analysis of strategic scenarios with high accuracy.

Contribution

It introduces a novel autoformalization method leveraging GPT-4o and feedback loops to improve translation accuracy from natural language to formal logic.

Findings

98% syntactic correctness achieved

88% semantic correctness achieved

Effective bridging of natural language and formal reasoning

Abstract

Game theory is a powerful framework for reasoning about strategic interactions, with applications in domains ranging from day-to-day life to international politics. However, applying formal reasoning tools in such contexts is challenging, as these scenarios are often expressed in natural language. To address this, we introduce a framework for the autoformalization of game-theoretic scenarios, which translates natural language descriptions into formal logic representations suitable for formal solvers. Our approach utilizes one-shot prompting and a solver that provides feedback on syntactic correctness to allow LLMs to refine the code. We evaluate the framework using GPT-4o and a dataset of natural language problem descriptions, achieving 98% syntactic correctness and 88% semantic correctness. These results show the potential of LLMs to bridge the gap between real-life strategic interactions and formal reasoning.