  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, which models
GPS as a Markov Decision Process. 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.
