FGeo-HyperGNet: Geometric Problem Solving Integrating Formal Symbolic System and Hypergraph Neural Network
arxiv(2024)
摘要
Geometric problem solving has always been a long-standing challenge in the
fields of automated reasoning and artificial intelligence. We built a
neural-symbolic system to automatically perform human-like geometric deductive
reasoning. The symbolic part is a formal system built on FormalGeo, which can
automatically perform geomertic relational reasoning and algebraic calculations
and organize the solving process into a solution hypertree with conditions as
hypernodes and theorems as hyperedges. The neural part, called HyperGNet, is a
hypergraph neural network based on the attention mechanism, including a encoder
to effectively encode the structural and semantic information of the hypertree,
and a solver to provide problem-solving guidance. The neural part predicts
theorems according to the hypertree, and the symbolic part applies theorems and
updates the hypertree, thus forming a predict-apply cycle to ultimately achieve
readable and traceable automatic solving of geometric problems. Experiments
demonstrate the correctness and effectiveness of this neural-symbolic
architecture. We achieved a step-wised accuracy of 87.65
accuracy of 85.53
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