MVILAIN@G.BBN.COM (Marc Vilain) (11/25/87)
BBN Science Development Program
AI Seminar Series Lecture
THEORIES OF COMPARATIVE ANALYSIS
Daniel S. Weld
MIT Artificial Intelligence Lab
(WELD@REAGAN.AI.MIT.EDU)
BBN Labs
10 Moulton Street
2nd floor large conference room
10:30 am, Tuesday December 1
This talk analyzes two approaches to a central subproblem of automated
design, diagnosis, and intelligent tutoring systems: comparative
analysis. Comparative analysis may be considered an analog of
qualitative simulation. Where qualitative simulation takes a structural
model of a system and qualitatively describes its behavior over time,
comparative analysis is the problem of predicting how that behavior will
change if the underlying structure is perturbed and also explaining why
it will change.
For example, given Hooke's law as the model of a horizontal,
frictionless spring/block system, qualitative simulation might generate
a description of oscillation. Comparative analysis, on the other hand,
is the task of answering questions like: ``What would happen to the
period of oscillation if you increase the mass of the block?'' I have
implemented, tested, and proven theoretical results about two different
techniques for solving comparative analysis problems, differential
qualitative (DQ) analysis and exaggeration.
DQ analysis would answer the question above as follows: ``Since force is
inversely proportional to position, the force on the block will remain
the same when the mass is increased. But if the block is heavier, then
it won't accelerate as fast. And if it doesn't accelerate as fast, then
it will always be going slower and so will take longer to complete a
full period (assuming it travels the same distance).''
Exaggeration can also solve this problem, but it generates a completely
different answer: ``If the mass were infinite, then the block would
hardly move at all. So the period would be infinite. Thus if the mass
was increased a bit, the period would increase as well.''
Both of these techniques has advantages and limitations. DQ analysis is
proven sound, but is incomplete. It can't answer every comparative
analysis problem, but all of its answers are correct. Because
exaggeration assumes monotonicity, it is unsound; some answers could be
incorrect. Furthermore, exaggeration's use of nonstandard analysis makes
it technically involved. However, exaggeration can solve several
problems that are too complex for DQ analysis. The trick behind its
power appears to have application to all of qualitative reasoning.
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