The partial distance ordering of size information described above can be used to make only a limited number of deductions about the scene described. It can tell us that the thickness of a sheet of paper is smaller than the depth of a file box, and that it will therefore not protrude above the top of the box if it is placed inside. If two sheets of paper are placed on top of one another, however, we can make no conclusions at all about whether or not they fill the box. This is because we may know that one size (the box depth) is larger than another (the paper thickness), but we do not know how much larger it is.
An answer to the question of how many sheets of paper will fit in the box could easily be found by a system that had absolute information about the thickness of the paper and the depth of the box. Absolute information is not required, however; a person can answer this question without measuring the thickness of the paper. The qualitative knowledge that supports this reasoning is the fact that the thickness of a sheet of paper is of a different order of magnitude from the depth of the box.
Order of magnitude information can be included in the partial distance ordering by the use of much-larger, much-smaller and nearly-equal size relationships in addition to those for larger and smaller. Such a provision enables not only comparisons of size after addition operations as in the above example, but a complete qualitative arithmetic as discussed by Raiman, in his paper ``Order of Magnitude Reasoning'' [Rai86].
Order of magnitude information is easy to incorporate into the partial distance ordering, because it can simply be superimposed on the relative size information, leaving the previous ordering intact. Where such information is given, it provides extra useful data, but a scene description could be composed without any order of magnitude information. In this case, the reasoning system could continue to operate, but there would be more questions that it could not answer.
The addition of order of magnitude capabilities does not therefore affect the graceful degradation of the system when given incomplete data, but it does provide it with more power when more information is available.