A new method for implementation of geometric theorems

This paper outlines the optimization of the two first parts of the three major components of the  scene descriptions of the geometrical shapes, namely (1) fuzzy logic scheme, (2) an integrated algebraic and logical reasoning, and (3) the machine learning technique. After arguing the need for using fuzzy expressions in spatial reasoning, the integration of approximate references into spatial reasoning using absolute measurements is outlined. The integration here means that the satisfiability of a spatial expression including possibly fuzzy one is conducted by both logical and algebraic reasoning. Then, the implementation of spatial expression evaluation is briefly described. The paper ends by the conclusion and the problems to be studied. The reasoning algorithm of this system not only uses the one-piece system, algebraic method and first-order logical method, but by introducing fuzzy spatial propositions and how to integrate them, as well as classical propositions in this system, it has a high power compared to classical systems.