---
title: "A Geometric Approach to Total Envisioning"
authors:
  - "Toyoaki Nishida"
  - "Shuji Doshita"
doi: ""
url: "https://ijcai.org/proceedings/1991/169"
pdf: "https://ijcai.org/proceedings/1991/0169.pdf"
venue: "Proceedings of the Twelfth International Joint Conference on Artificial Intelligence"
year: 1991
pages: "1150-1156"
track: "Qualitative Reasoning"
keywords:
---

# A Geometric Approach to Total Envisioning

Toyoaki Nishida, Shuji Doshita

*Proceedings of the Twelfth International Joint Conference on Artificial Intelligence*, pages 1150-1156.

## Abstract

Conventional envisioners proposed in qualitative physics have two difficulties in common: ambiguities in prediction and inability of reasoning about global behaviors. We take a geometric approach to overcome these difficulties and have implemented a program PSX2NL which can reason about global behaviors by analyzing geometry and topology of solution curves of ordinary differential equations in the phase space. In this paper, we highlight a flow grammar which specifies possible patt erns of solution curves one may see in the phase space. Th e role of a flow grammar in PSX2NL is twofold: firstly, it allows PSX2N L to reason about complex patterns in a uniform mann er ; secondly, it allows PSX2NL to switch to an approximate, top-down algorithm when complete geometric clues are not available due to the difficulty of mathematical problems encountered.