Using tolerance calculus for reasoning in relative order of magnitude models

Abstract

Order of magnitude (OM) reasoning is an approach that offers a midway abstraction level between numerical methods and qualitative formalisms. Relative OM models postulate a set of relations and inference rules on orders of magnitude. The main shortcoming of these models is the difficulty to validate the results they produce when applied to reasoning on real world problems. A widely accepted solution to avoid this deficiency is to extend the relative OM reasoning systems by a tolerance calculus. The way this extension is defined is a sensitive problem, affecting the accuracy of the results produced by the system. In this paper we present two ideas which could help to obtain more accurate results. First, we propose a more refined definition of the negligibility relation which is subject to avoid the artificial growth of tolerances. Second, we show that, in the case of many inference rules, one can derive tighter tolerance bounds when additional information is available.