---
title: "Reasoning of Geometric Concepts based on Algebraic Constraint-directed Method"
authors:
  - "Hitoshi Iba"
  - "Hirochika Inoue"
doi: ""
url: "https://ijcai.org/proceedings/1991/22"
pdf: "https://ijcai.org/proceedings/1991/0022.pdf"
venue: "Proceedings of the Twelfth International Joint Conference on Artificial Intelligence"
year: 1991
pages: "143-150"
track: "Automated Reasoning"
keywords:
---

# Reasoning of Geometric Concepts based on Algebraic Constraint-directed Method

Hitoshi Iba, Hirochika Inoue

*Proceedings of the Twelfth International Joint Conference on Artificial Intelligence*, pages 143-150.

## Abstract

We present an algebraic approach to geometric reasoning and learning. The purpose of this research is to avoid the usual difficulties in symbolic handling of geometric concepts. Our system GREW is grounded on a reasoning scheme that integrate the symbolic reasoning and algebraic reasoning of Wu's method. The basic principle of this scheme is to describe mathematical knowledge in terms of symbolic logic and to execute the subsidiary reasoning for Wu's method. The validity of our approach and GREW is shown by experiments, such as applying to learning-by-example of computer vision heuristics or solving locus problems.