On extending the quantity space in qualitative reasoning

Recently, much interest has been generated in developing less abstract quantity spaces for qualitative reasoners in an attempt to reduce the fundamental, and essential, ambiguities at source. Several researchers have utilised the theory of non-standard analysis (NSA) as a mathematical underpinning to establish techniques for 'order of magnitude reasoning' (OMR). These are significant developments and result in the elimination of many spurious behaviours. However, several problems exist with these approaches, in particular, when the qualitative description is taken to be an abstraction of an underlying real-valued representation. This research note discusses some limitations preventing the consistent use of OMR when compared to the real-valued case. Further, it is argued that the intuition behind the OMR approach implies graded set membership for representing quantities and the relations between them, rather than the crisp sets supporting NSA. Finally, the note indicates how the theory of fuzzy sets can be used to consolidate and extend the advances made by OMR. © 1992.