---
title: "The Orders of Magnitude Models as Qualitative Algebras"
authors:
  - "Louise Travé-Massuyès"
  - "Núria Piera"
doi: ""
url: "https://ijcai.org/proceedings/1989/202"
pdf: "https://ijcai.org/proceedings/1989/0202.pdf"
venue: "Proceedings of the Eleventh International Joint Conference on Artificial Intelligence"
year: 1989
pages: "1261-1265"
track: "Knowledge Representation"
keywords:
---

# The Orders of Magnitude Models as Qualitative Algebras

Louise Travé-Massuyès, Núria Piera

*Proceedings of the Eleventh International Joint Conference on Artificial Intelligence*, pages 1261-1265.

## Abstract

This paper provides a unifying mathematical framework for orders of magnitude models used in Qualitative Physics . An axiomatic of the qualitative equality is provided and a general algebraic structure called qualitative algebra is defined . It is shown that the usual model (+,-,0,?} and the extended model recently introduced by Dubois and Prade are particular cases in the class of models that are generated from a partition of the real line . Any of these models can be structured as qualitative algebra. On the other hand, we characterize those qualitative algebras that are isomorphous, in a qualitative sense. Besides, it is shown that all these models can be embedded into one another as qualitative subalgebras.