The orders of magnitude models as qualitative algebras

Authors:
L. Trave-Massuyes;N. Piera
Affiliations:
Laboratoire d'Automatique et d'Analyse des Systemes du C.N.R.S., Toulouse Cedex, France;Laboratoire d'Automatique et d'Analyse des Systemes du C.N.R.S., Toulouse Cedex, France
Venue:
IJCAI'89 Proceedings of the 11th international joint conference on Artificial intelligence - Volume 2
Year:
1989

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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.