Automated Completion of Statements and Proofs in Synthetic Geometry: an Approach based on Constraint Solving
This work addresses the challenge of automating mathematical reasoning in synthetic geometry, offering a novel approach for mathematicians and AI researchers, though it is incremental in its domain-specific application.
The paper tackles the problem of completing incomplete conjectures and proofs in synthetic geometry by developing a framework that uses coherent logic and constraint solving to transform under-specified conjectures into proper theorems and proof sketches into human-readable, machine-checkable proofs.
Conjecturing and theorem proving are activities at the center of mathematical practice and are difficult to separate. In this paper, we propose a framework for completing incomplete conjectures and incomplete proofs. The framework can turn a conjecture with missing assumptions and with an under-specified goal into a proper theorem. Also, the proposed framework can help in completing a proof sketch into a human-readable and machine-checkable proof. Our approach is focused on synthetic geometry, and uses coherent logic and constraint solving. The proposed approach is uniform for all three kinds of tasks, flexible and, to our knowledge, unique such approach.