FGeo-DRL: Deductive Reasoning for Geometric Problems through Deep Reinforcement Learning

The human-like automatic deductive reasoning has always been one of the most challenging open problems in the interdiscipline of mathematics and artificial intelligence. This paper is the third in a series of our works. We built a neural-symbolic system, called FGeoDRL, to automatically perform human-like geometric deductive reasoning. The neural part is an AI agent based on reinforcement learning, capable of autonomously learning problem-solving methods from the feedback of a formalized environment, without the need for human supervision. It leverages a pre-trained natural language model to establish a policy network for theorem selection and employ Monte Carlo Tree Search for heuristic exploration. The symbolic part is a reinforcement learning environment based on geometry formalization theory and FormalGeo\cite{FormalGeo}, which models GPS as a Markov Decision Process\cite{MDP}. In this formal symbolic system, the known conditions and objectives of the problem form the state space, while the set of theorems forms the action space. Leveraging FGeoDRL, we have achieved readable and verifiable automated solutions to geometric problems. Experiments conducted on the formalgeo7k dataset have achieved a problem-solving success rate of 86.40\%. The project is available at https://github.com/PersonNoName/FGeoDRL.