Geometric theorem proving by integrated logical and algebraic reasoning

摘要

Algebraic geometric reasoning by the Gröbner basis method and Wu's method has been shown to be powerful enough to prove those complex geometric theorems that could not be proved by ordinary logical reasoning methods. These algebraic reasoning methods, however, have a crucial limitation: they cannot correctly handle any geometric concepts involving order relations such as between and congruent angles. To overcome this limitation, we propose a novel geometric reasoning method, where both logical and algebraic reasoning methods are integrated into a unified reasoning process. In this paper, we prove the soundness of the proposed reasoning method and demonstrate its effectiveness with several illustrative examples.