Geometric Theorem Proving by Integrated Logical and Algebraic Reasoning

Abstract

Algebraic reasoning by Grobner bases method and Wu's method has been shown to be enough powerful to prove those complex geometric problems which could not been proven by logical reasoning. These algebraic methods, however, share a crucial limitation that they cannot handle any geometric concepts involving ordering relations like between and congruent angles. To solve this problem, we propose an integrated reasoning method which combines both logical reasoning based on geometric axioms and theorems and algebraic reasoning by Grobner bases method. In this paper, we prove the soundness of the proposed method and demonstrate its effectiveness with several illustrative examples.