GRAMY: A Geometry Theorem Prover Capable of Construction

  • Authors:

  • Noboru Matsuda;Kurt Vanlehn

  • Affiliations:

  • Intelligent Systems Program, University of Pittsburgh. e-mail: mazda@pitt.edu;Intelligent Systems Program, University of Pittsburgh. e-mail: vanlehn@cs.pitt.edu

  • Venue:
  • Journal of Automated Reasoning
  • Year:
  • 2004

Quantified Score

Hi-index 0.00

Visualization

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.