GRAMY: A Geometry Theorem Prover Capable of Construction

Noboru Matsuda, Kurt VanLehn
2004 Journal of automated reasoning  
This study investigates a procedure for proving arithmetic-free Euclidean geometry theorems that involve construction. "Construction" means drawing additional geometric elements in the problem figure. Some geometry theorems require construction as a part of the proof. The basic idea of our construction procedure is to add only elements required for applying a postulate that has a consequence that unifies with a goal to be proven. In other words, construction is made only if it supports backward
more » ... application of a postulate. Our major finding is that our proof procedure is semi-complete and useful in practice. In particular, an empirical evaluation showed that our theorem prover, GRAMY, solves all arithmetic-free construction problems from a sample of school textbooks and 86% of the arithmetic-free construction problems solved by preceding studies of automated geometry theorem proving.
doi:10.1023/b:jars.0000021960.39761.b7 fatcat:xrlropabqjegndsfrigtujtg24