Incomplete information should preferably be ignored during problem solving unless the missing information is necessary to solve the problem. The PDO/EPB representation provides for unkown information to be ``hidden'' (and thereby ignored) by the use of multiple levels of detail. Areas of a boundary which are irrelevant to a problem can be described extremely coarsely - perhaps just as a ``wiggle''.
In the case where information is incomplete, but the missing quantities are required for the problem solution, the system must be able to hypothesise a constrained range of values for the unknown quantity. This ability was explained in the discussion of determination of fit in the path planning system. An unknown magnitude, whether a calculated ``synthetic'' magnitude or simply one that could not be measured, can be represented in the partial distance ordering as being completely unconstrained. The qualitative reasoning system can then make use of a repertoire of qualitative geometry techniques for constraining the value.
There are few conventional robot reasoning systems which are as readily able to operate with incomplete information. Firstly, numeric values are represented either as having a known value, or not having a value: there is no way of offering varying levels of detail to cover an intermittent lack of fine resolution. Secondly, if a hypothetical value is assigned to an unknown quantity, most systems cannot represent it as a range of plausible values, or even distinguish it from exact (measured) quantities. Some solid modelling systems do include facilities for representing tolerance information [RC86], and at least one robot motion planning system accounts for errors in part measurements or robot motion [Bro82a], but these numerical methods do not apply to as wide a range of problems as the PDO/EPB method.
The ability to operate with incomplete information can be useful in planning and control tasks if information cannot be obtained (for instance, the example given in the introduction: a partly hidden key which must be withdrawn by making use of a hypothetical description of the hidden portion). The ability to operate with hypothetical data is also an important facility in design tasks - the use of a partial distance ordering allows a designer to specify any (or no) constraints on an unknown value, and then continue normal operations as if the value had been specified exactly. A qualitative geometric reasoning system would be able to notify the designer as soon as the constraints became insufficient or over-restrictive.