The importance of explanation in expert systems has been documented fr
om the early days of their development; there is an equally pressing n
eed for explanation in systems that employ a decision-making process b
ased on quantitative reasoning This is particularly necessary for user
s who do nor have a sophisticated understanding of the formal apparatu
s that the system employs to reach its decisions. In order to generate
meaningful answers to questions asked by such unsophisticated users,
an explanation facility must translate the formal structures of the pr
oblem solving system into the concepts with which the user understands
the problem domain. Previous work on the explanation of quantitative
systems is based on the assumption that the user has al least a basic
grasp of the formal approach of the problem solving system. However, i
n realistic application situations, it is more likely the case that in
order for the human user to understand why a mathematically-based adv
ice-giving system makes the suggestions that it does, the problem solv
ing rationale of the system must be explained in the user's own terms,
which are typically different from those of the mathematical system.
To develop an explanation methodology that is capable of justifying th
e results of a system based on quantitative reasoning to an uninitiate
d user we employ a representation that enables our explanation facilit
y to translate the abstract mathematical relationships that make up a
quantitative system into the domain-specific concepts with which a typ
ical user approaches the problem solving task. In our system, the proc
ess of generating explanations, therefore, involves translating one se
t of concepts into another. An added feature of this system is that it
is capable of providing explanations from two perspectives: that of t
he quantitative problem solving system, and that of the human user who
is familiar with the domain problem but not with the mathematical app
roach. We have implemented this approach to explaining quantitative sy
stems by creating an explanation facility for a problem in the manufac
turing domain. This facility responds to user queries about a scheduli
ng system that uses a mathematically-based heuristic to choose jobs fo
r an annealing furnace.