Binary relations for qualitative reasoning

The authors attempt to advance qualitative calculus by using absolute orders of magnitude models. To perform qualitative calculus with orders of magnitude algebras based on finer divisions than those provided by the sign, it is very useful to consider some binary relations to represent human reasoning. The orders of magnitude algebras are given a metric space structure, and the binary relation of `negligibility´ and `having the same order of magnitude´ is formalized. The inference rules arising from relating the qualitative sum and product with these two relations are studied and analyzed. They may be useful in solving qualitative equations or systems of equations