Hilbert-Geo: Neural-Symbolic Framework for Solid Geometry
Hilbert-Geo has been unveiled by researchers as the inaugural comprehensive formal language framework for solid geometry, filling a significant void in geometric problem-solving that predominantly emphasizes plane geometry. This framework features a broad library of predicates and a specialized repository of theorems. The proposed Parse2Reason approach consists of two phases: parsing and reasoning. During the parsing phase, conditional description language (CDL) is utilized to depict problem statements and solid diagrams. In the reasoning phase, relational inference and algebraic calculations are executed using formal CDL alongside the theorem repository. This research is documented on arXiv with the identifier 2605.16385.
Key facts
- Hilbert-Geo is the first unified formal language framework for solid geometry.
- The framework includes an extensive predicate library and a dedicated theorem bank.
- A Parse2Reason method is proposed with two steps: parsing then reasoning.
- Conditional description language (CDL) is used to represent problem descriptions and solid diagrams.
- Reasoning leverages formal CDL and the theorem bank for relational inference and algebraic computation.
- Most prior works focus on plane geometry and fail in solid geometry due to 3D spatial diagrams.
- The research is published on arXiv with ID 2605.16385.
- The approach targets multimodal reasoning problems in geometric problem solving.
Entities
Institutions
- arXiv