The Orders of Magnitude Models as Qualitative Algebras
Proceedings of the Eleventh International Joint Conference on Artificial Intelligence. Knowledge Representation. 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.
@inproceedings{ijcai1989p202,
title = {The Orders of Magnitude Models as Qualitative Algebras},
author = {Travé-Massuyès, Louise and Piera, Núria},
booktitle = {Proceedings of the Eleventh International Joint Conference on
Artificial Intelligence, {IJCAI-89}},
publisher = {International Joint Conferences on Artificial Intelligence},
editor = {N. S. Sridharan},
pages = {1261--1265},
year = {1989},
month = {8},
note = {Knowledge Representation},
url = {https://ijcai.org/proceedings/1989/202},
}
TY - CPAPER TI - The Orders of Magnitude Models as Qualitative Algebras AU - Travé-Massuyès, Louise AU - Piera, Núria T2 - Proceedings of the Eleventh International Joint Conference on Artificial Intelligence, IJCAI-89 PB - International Joint Conferences on Artificial Intelligence PY - 1989 SP - 1261 EP - 1265 UR - https://ijcai.org/proceedings/1989/202 ER -Copied
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