Abstract
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 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.
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Matsuda, N., VanLehn, K. GRAMY: A Geometry Theorem Prover Capable of Construction. Journal of Automated Reasoning 32, 3–33 (2004). https://doi.org/10.1023/B:JARS.0000021960.39761.b7
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DOI: https://doi.org/10.1023/B:JARS.0000021960.39761.b7