Abstract
This paper reports the state of the art of qualitative calculus. Within a unifying mathematical framework for orders of magnitude models, we propose an axiomatic for the qualitative equality and a general algebraic structure called qualitative algebra. We show that the usual model {+,-,O,?} 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 a qualitative algebra. Now, whereas effective calculation tools exist when working with signs, we show that numerous problems arise with more sophisticated models. Some isolated results are presented though
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