From: AAAI Technical Report SS-99-07. Compilation copyright © 1999, AAAI (www.aaai.org). All rights reserved.
ALMOST NOTHING’S
PERFECT
(A
Research
Description)
Leona F. Fass
Muchof our research has been concerned with devising techniques for the representation,
conveyance and
acquisition of knowledge, as we have sought solutions to
problems of"learnability." To develop a general learning
theory we have examined the notion of correct information, or behavior, within a knowledgedomain- as distinguished from that behavior which is incorrect. Wehave
also investigated the means to represent these knowledge
classes perfectly.
In most problems we have considered, a knowledge
domainis (potentially) infinite, so no realistic learning
process would have access to a complete set of behavioral data. The successful solution to a learning problem
thus might depend on the representation and conveyance
of infinite knowledge(possibly correct and incorrect behavior) by finite means. If a successful solution is to
be perfect, selected/observable finite information must
convey the behavior of the entire infinite domain, by
representing it completely.
Whenwe first considered learnability problems we did
seek solutions that were perfect, characterizing infinite
behaviors from finite information examples. Weinitially
sought correct finite results and then, from a universe of
potential behavioral models we sought results that were
"elegant" and the "best." In the specific problem we first
investigated, correctness, perfection and elegant representation of infinite knowledge all were possible, and
were achieved effectively.
In that instance we sought finite models for (contextfree) linguistic knowledge, and we discovered them by exploiting the structures existing within the infinite bodyof
language. Congruenceclasses of linguistic structures corresponded to components of unique finite generative and
recognitive models. Structural representatives of each of
the classes provided a specific finite set of information
samples su~cient for construction of models by effective
inductive inference.
Furthermore, by imposing constraints on the domain
in which the language structures were found, we discovered we could simplify the process of obtaining a recognitive solution. Representatives of "correct" structure
classes were all that needed to be considered in the search
for an accepting recognitive model. The components of
a recognizer that processed "incorrect" behavior could
then be determined simply, by default.
Finally, with the imposition of constraints on the domain containing the "correct" structures, we have shown
that a finite relatively-complementary selection of "incorrect" structures could provide adequate supplementary information for testing of potential models. Given
a potential example of the unique generative or recognitive model just described, we can determine from finite selected information whether or not it behaves as it
should. Producing all of the behavioral sample that was
found to be sufficient for inference, and none of the "incorrect" relative-complement set, the potential model is
adequately tested, and determined to be correct. Unlike
most problem areas where testing against infinite possible incorrect behavior could continue forever, with our
constrained system the process selects domain-specific
information and knows when to stop.
Analyzing our apparent success in obtaining "perfect"
problem solutions from selected information, we determined general conditions under which our techniques
would apply. If a behavior is finitely-realizable,
and if
it can be decided whether a domain element is within
the behavior ("correct") or not ("incorrect") then
can discover characterizing solutions effectively. In such
cases selected data and experiments will lead an inductively inferential search, and a corresponding testing procedure, to identify a finite modelfor an infinite behavior,
effectively and "perfectly."
Seeking to extend our solution methods to searching
for finite behavioral models in other problem areas we
found it necessary to relax our standard for assessing the
quality of a result. Rather than seeking "elegant," best
or "perfect" solutions to more general knowledge representation or learning problems, we have begun to accept
results that are feasible. Such instances include problems
of modelingbehaviors where it is unclear whether a finite
result exists (e.g., modelingthe infinite set of sentences
in a growing natural language); where it is not possible to fully classify correctness vs. incorrectness (e.g.,
seeking to discover from behavioral examples a program
that precisely fulfills its specification); or wherenone of
our conditions and domain constraints can realistically
apply (as in processes of discovery in the real world of
natural science).
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In such cases we are satisfied to obtain approximate
results using selected information that is, by definition,
incomplete and sometimes, uncertain. We may impose
some structure on a behavior to apply our search techniques to modeling a subset of knowledge, dealing with
anomalous situations as they arise. This way we accept
partial success by discovering models for some of a behavior, rather than abandoning a search for a behavioral
representation once we knowit cannot be perfect.
Selected References
Cherniavsky, J.C., "Computer Systems as Scientific
Theories - A Popperian Approach To Testing," Proc. of
the Fifth Pacific Northwest Software Quality Conference,
Portland, October 1987, pp 297-308.
Cherniavsky, J.C., It. Statman and M. Velauthapillai, "Testing and Inductive Inference: Abstract Approaches," Proc. of the First Workshop on Computational Learning Theory, Morgan-Kaufmann, 1988.
Popper, K., The Logic of Scientific Discovery, Harper
Torch Books, NewYork, 1968.
Valiant, L., "A Theory of the Learnable," Communications of the ACM,Vol. 27 (1987), pp. 1134-1142.
Weyuker, E.J., Assessing Test Data Adequacy through
Program Inference,"
ACMTransactions
on Programming Languages and Systems, Vol. 5 (1983), pp.641-655.
ing her Ph.D she held research, administrative and/or
teaching positions at Penn and Temple University. Since
then she has been on the faculties of the University of
California, Georgetown University and the Naval Postgraduate School. Her research primarily has focused on
language structure and processing; knowledge acquisition; and the general interactions of logic, language and
computation. She has had particular interest in inductive inference processes, and applications/adaptations of
inference results to the practical domain. She may be
reached at Mailing Address: P.O. Box 2914, Carmel,
CA 93921
Selected Relevant Papers and Presentations
by
the Author
Fass, L.F., "A Common
Basis for Inductive Inference
and Testing," Proc. of the Seventh Pacific Northwest
Software Quality Conference, Portland, September 1989,
pp 183-200.
Fass, L.F., "Inference, Testing and Verification,"
Ninth International
Congress on Logic, Methodology
and Philosophy of Science and Logic Colloquium 91, Uppsala, Sweden, August 1991. Abstracted in Congress
VolumeI, p. 193, and in J. Symbolic Logic, Vol. 58, No.
2 (June 1993), pp. 763-764.
Fass, L.F., "Modeling Perfect Behavior: A GoalDriven Learning Analysis," in Notes of the AAAISpring
Symposium on Goal-Driven Learning, Stanford, March
1994, pp. 125-127.
Fass, L.F., "Black Box Science," in Notes of the AAAI
Spring Symposiumon Systematic Methods of Scientific
Discovery, Stanford, March 1995, pp. 116-117.
Fass, L.F., "Learning (Language) within a Context,"
Proc. of the Joint Conference on Information Sciences/Third International Conference on Computational
Intelligence and Neuroscience, Research Triangle Park,
N.C., October 1998, Vol. II, pp. 56-59.
Leona F. Fass received a B.S. in Mathematics
and Science Education from Cornell University and an
M.S.E. and Ph.D. in Computer and Information Science
from the University of Pennsylvania. Prior to obtain-
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