BLACK BOX SCIENCE
LeonaF. Fass
From: AAAI Technical Report SS-95-03. Compilation copyright © 1995, AAAI (www.aaai.org). All rights reserved.
Wehave looked at the process of discovery as an
aspect of reasoning about knowledge, particularly in
relation to problemsof knowledgeacquisition or learning.
In those problemswe have found to be of interest, a body
of knowledgeto-be-acquired maybe infinite. Still, it can
be "learned" through discovery of a model that correctly
represents
the knowledge in some finite
way.
Realistically, experiments or observations that determine
the characterizing modelalso must be t’mite. A successful
discovery process concludes, determining a model of
knowledge, effectively. Once the model is acquired the
body of knowledgeis learned, in the sense that it is
precisely characterized.
within a domain of candidates. If the process is
sufficiently constrained, a unique M(e.g., minimal
structure) for S maybe obtained. Instances of this process
include determining the internal structure (and thus, all
future behavior) of a vending machine, from observations
of its operation; determining a grammarG for an entire
language L, given a sentence sample; or finding a
"simplest" programP to implementa particular function f,
when the function is described only by selected
input/output,i.e., ( x, f(x) ), pairs.
A testing process, on the other hand, experiments
with a given candidate M~ claimed to modelS, to see if it
indeed does satisfy that specification.
Unlike the
inference process, the testing process "knows"S and so,
how a model of S should always behave. It is nontrusting or, adversarial process that maysystematically
choose experiments (using positive data from S, and/or
negative data from "not S") to discover whether, or where,
a potential model M1 may be incorrect. The goal of
testing is to detect incorrectness of a given "box" Mt so
that the box maybe "fixed" and a better potential model
of S maybe found (this is the "Popperian"view [2,5]).
Since only finite knowledge can be observed
effectively, we view the entire body of knowledgeas a
black box. The process of discovering a knowledge
model is, from our perspective,
experimentally
determining correct structure of the "black box", given
finite samples or examplesof howit does, or should (or
should not) "behave".
For some time we have investigated systematic
methods of "black box discovery" for learning or
knowledgeacquisition, in the sense we have described.
Wefirst considered a language acquisition problem,
establishing discovery of a linguistic modelfrom explicit
experiments with appropriate data. Our success in this
area led us to examine other problem domains, seeking a
general procedure for modeling knowledge. Webegan
with a "positive" process, using techniques of inductive
inference [1] to discover a model constructively.
Motivated by Cherniavskyet al. [3] and by his "Popperian
approach" [2] (after the late Karl Popper [5]), we then
investigated the default discovery of a correct model
"adversarially", by testing for incorrectness.
But, if no experiment detects incorrectness and /f
experimentationis deemedsufficient, the discovery of the
correct "box" MI is verified. Mt might be a newly built
vending machine on a trial run; a grammarclaimed to
generate a language L; or a programclaimed to compute
f(x) on input x. A "Popperian" would be satisfied if
vending machineshort-circuit were detected; an incorrect
sentence generated; or a program bug found. In each
case, reparation of the discovered defect could yield a
better potential behavioral model. A "verificationist"
could be satisfied if sufficient experiments detected no
such errors. With adequate experimentation a successful
testing process might establish that M~ produces exactly
what is claimed, and nothing else.
Here we briefly describe these two related processes
for discovering correct "black box" models, and thus
acquiring knowledge. Wealso describe some cases where
the processes might, or can, be applied.
At fu’st glance inference and testing might seemto be
complementary processes to discover, for some body of
knowledge, a correct "black box" model. Inference would
systematically construct a correct "box" M1 through t’mite
experiments, or correctness could be discovered through
systematic effective tests. But inference and testing are
not complementary processes for discovering correct
models, for testing is more difficult than inference
[2,3,6,7]. Successful inference depends on finitely
t.
characterizing
correct behavior of the "box" M
Successful testing will discover correct M~ only if its
experiments characterize correctness and incorrectness,
effectively.
Aninductive inference process discovers a correct or
"best" model of knowledge, i.e., having some specified
behavior S, from a finite behavioral sample. In
constructive approaches a characterizing
sample S
(positive data) is observedand generalized to f’md a model
Mfor the entire behavior. This is a trusting process that
depends on selection, provision of, or access to,
appropriate sample data that will lead to correct
generalization. Experiments defined by the sample may
identify componentsof a (black box) modelMfor S, from
116
[5]
Wehave found that when considering behaviors, or
bodies of knowledge,that are finitely-realizable, and for
which membershipqueries are decidable, both inference
and testing will systematically lead to discoveryof correct
models of knowledge. Wehave successfully applied both
techniques in such cases: e.g., discovering finite-state
devices and finite grammatical models. In such cases we
have established existence of precise models, and
systematic experimentation
that terminates upon
discovering them. We have found "approximating"
results, in cases where only some of the conditions
(decidability, realizability, finiteness) apply: e.g.,
discovering correct programs, approximately. (Some of
our results appear in [6-9]). In the fuzzy areas of
cognitive processes [4] we have much to learn about
discovery of models, and so, too, in the noisy, nonconstrained, non-"logical" or non-"algebrized" domainof
"real-life" science. In these cases things don’t fit so neatly
into a "black box".
Popper, K., The Logic of Scientific Discovery,
Harper Torch Books, NewYork, 1968.
Selected Relevant Papers AndPresentations
By The Author
In the area of systematic methods of scientific
discovery, we wouldhope to contribute our experience in
modeling of knowledge, as our research in discovery has
shifted from specific engineering/computer-science
problems into epistemology and philosophy of science.
Wewould hope to gain new insights and perspectives on
discovering
models of knowledge from observed
phenomenaor processes, to propose solutions (or at least
approaches) to the many open problems we have
encountered(e.g. in [4]), and the manywehave yet to see.
[6]
Fass, L. F., "A CommonBasis for Inductive
Inference and Testing," Proc. of the Seventh
Pacific Northwest SoRwareQuality Conference,
Portland, September1989, pp. 183-200.
[7]
Fass, L. F., "Inference, Testing and Verification,"
Ninth Intemational
Congress on Logic,
Methodology and Philosophy of Science and
Logic Colloquium 91, Uppsala, Sweden, August
1991. AbsWactedin Congress VolumeI, p. 193,
and in J. Symbolic Logic, Vol. 58, No. 2, (June
1993), pp. 763-764.
[8]
Fass, L. F., "ModelingPerfect Behavior: A GoalDriven Learning Analysis," in Notes of the AAAI
Spring Symposium on Goal-Driven Learning,
Stanford, March1994, pp. 125-127.
[9]
Fass, L. F., "Modeling Perfect Behavior: A
Machine-Theoretic
Approach", Proc. On
Summary, Joint Conference on Information
Sciences: ComputerTheory and Informatics, Duke
University/Pinehurst N.C., November1994, pp.
141-144.
Selected References
[l]
Angluin, D. and C. H. Smith, "Inductive Inference:
Theory and Methods," ComputingSurveys, Vol.
15 (1983), pp. 237-269.
[2]
Cherniavsky,
[31
Chemiavsky, J. C., R. Statman and M.
Velauthapillai, "Testing and Inductive Inference:
Abstract Approaches," Proc. of the First
Workshop on Computational Learning Theory,
Morgan-Kaufmann,1988.
[41
Lenat, D. B., and R. V. Guha,K. Pittman, D. Pratt,
M. Shepherd, "CYC: Toward Programs With
CommonSense," Communications of the ACM,
Vol. 33 (1990), pp. 30-49.
LeonaF. Fass received a B.S. in Mathematicsand
Science Education from Comell University and an
M.S.E. and Ph.D. in Computer and Information
Science from the University of Pennsylvania.
Prior to obtaining her Ph.D. she held research,
administrative and/or teaching positions at Penn
and TempleUniversity. 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.Dr.
Fass maybe reached at
J.C.,
"Computer Systems as
Scientific Theories -- A Popperian ApproachTo
Testing," Proe. of the Fifth Pacific Northwest
Software Quality Conference, Portland, October
1987, pp. 297-308.
Mailing Address:
117
P.O. Box 2914
Carmel, CA93921