The Orders of Magnitude Models as Qualitative Algebras

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 qualita­ tive 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 mo­ dels that are generated from a part i t ion of the real l ine. Any of these models can be structured as qualitative algebra. On the other hand, we characterize those qual i tat i ­ ve algebras that are isomorphous, in a qua­ l i t a t i ve sense. Besides, it is shown that a l l these models can be embedded into one another as qualitative subalgebras.