From: AAAI Technical Report SS-95-03. Compilation copyright © 1995, AAAI (www.aaai.org). All rights reserved.
Generic Tasks of Scientific
Discovery
Radl E. Vald~s-P~rez
Computer Science Department and
Center for Light Microscope Imaging and Biotechnology
Carnegie Mellon University
Pittsburgh,
PA 15213- USA
Abstract
Theaim of this paper is conceptualand theoretical: to
proposethe conceptof generic scientific task as an organizing principle for research on scientific discovery,
or morebroadly, scientific inference. Generictasks cut
across various scientific fields, but involverather specific inferences; in any case, their generality is found
only by surveying science as a whole. Computerprograms that carry out these generic tasks maydiffer
somewhatfrom one science to another, but they all
share similar computational mechanisms:hence they
represent generic tasks. Weassemble a broad array
of previous work as evidence to support this concept,
and work out the research plan and methodsthat are
implied by it.
Introduction
Most of the AI work on scientific discovery (including
our own) has been carried out under one of two goals:
to apply AI techniques fruitfully to science, or to show
that computerized human-like search mechanisms can
approximate human performance on scientific
and
mathematical tasks. Wecite just two examples of each:
Firstly, the DENDRAL
project applied AI methods to
the chemical problem of elucidating molecular structure on the basis of mass-spectrometer observations
(Lindsay el al. 1993), and the GRAFFITIproject has
resulted in a program that makes interesting,
plausible conjectures in graph theory (Fajtlowicz 1988;
Chung 1988).
In pursuit.of the second goal, Langley, Simon, Bradshaw, and Zytkow have described several programs
that employ productions systems in a human-like manner to provide simple scenarios for prominent discoveries of the last century (Langley et al. 1987). Earlier, the AMprogram was claimed to make use of
humanoid mechanisms to make conjectures in number theory (Lenat 1982). Manyother programs implemented under either banner could be cited.
Of course, the two goals are not wholly separate: instead, they reflect a special emphasis. For example, an
emphasis on AI performance (or expert) systems serves
nevertheless to confirm the machine-centered half of
23
the theory of heuristic search (Newell &Simon 1976),
whereas research having a cognitive emphasis serves
to open up new scope for expert systems in science.
The above overview leads to an important observation: most AI work on scientific discovery has viewed
discovery either as a domain, i.e., as an outlet for AI
techniques, or as human phenomena to be understood
using humanoid mechanisms, e.g., production systems.
These are worthy goals that merit further work, but
there exist complementaryalternatives.
Here, our goal is to propose such an alternative that
views scientific discovery as abstract phenomenathat
can be studied with the usual methods of empirical
and theoretical science. The term "abstract" signifies
that these phenomena are not the same as the reallife psychological phenomenaof humanscientists making inferences, but are instead the phenomenaof, for
example, the logical and heuristic relations that hold
between a hypothesis and evidence, or the degree of
analogy between two scientific theories. Moreover, we
use the term "phenomena" to emphasize the empirical nature of this alternative viewpoint: these abstract
phenomenaconsist of the abstract inferential problems
that arise within real-life science, regardless of howhuman scientists deal with them.
In science, the presence of rich and interesting phenomenais a cue for developing scientific fields (Norwood Hanson (Hanson 1958) quotes Isaac Newton:
"the task of natural philosophy is to argue from phenomena"). The phenomenaof scientific inference are
rich: the number of records added to the Science Citation Index is upwards of 728,000 per year. Their
interestingness we take as self-evident. It is unlikely
that the inferences that arise within these papers are
all the same, hence there is scope for seeking inferential
patterns that impose order amongvariety.
Any scientific field needs some theory, which can be
as modest as a preliminary conceptual structure; quoting from (Hanson 1958) again: "Theories make phenomenainto systems" (his reference is not to computer
systems, but to systematic knowledge; however, we are
content with both senses). The main purpose of this
paper is theoretical: to propose an organizing concept
Comput~tiona, l
t~iolo~),
Computational
Psycholosy
Computational
Petrolos~
Computation~
Mineralogy
Comput~tlonal
Cherniatr~
Computational
As{ronomy
Computational
Zoology
Computational
Volcanology
Comput~tionM
Fhysics
Computational
G’eology
Computational
Oceanography
Comput gtionM
Physiology
Computational
Materials
Science
Computational
Paleontology
Computatl ~nM
Seismolo ~y
Computational
Meteorology
Figure 1: Usual View of Computation in Science
that can be a fruitful basis for developing a theory of
scientific discovery as abstract phenomena. The concept is that of a 1generic task of scientific discovery.
The rest of this paper explains this concept, argues
why it is promising, and examines related views (due
to the broad scope of this subject, this paper will make
more citations than is customary, but as necessary to
make a convincing case).
Generic Tasks of Scientific
Discovery
Our proposal is that research into the abstract phenomena of scientific
discovery should he organized
around the concept of generic tasks. Rather than slice
up Science and Computation conventionally into computational biology, physics, volcanology, etc. as in Figure 1, we propose slices that are determined by tasks,
which can include disparate sciences such as biology
and physics. The next few sections will develop our
meaning by examining in some detail numerous generic
tasks from science.
Each generic task will involve a single, specific type
of inference that occurs in more than one science. We
selected tasks by identifying programs that automate
specific inferences to a convincing degree, that have a
good link to scientific practice, and that show good
promise of generality within science. For example, we
have excluded simulation, experiment planning, and
theory revision as generic tasks because they are too
broad. Undoubtedly one could identify further generic
tasks within these areas, but that is left for future development of the concept. The more good instances
that can be added to the provisional list below, the
more promising is the concept of generic task of scientific discovery. More generic tasks can certainly be
drawn from applied statistics,
but we emphasize here
those tasks with origins in AI.
Wemake no claim of crisp boundaries between these
tasks; even the possibility that one task wholly contains another is not ruled out. As with any systematic classification (or typology), knowledgeof the best
classes, and of relations amongthem, emerge over time.
Solving differential
equations
A very familiar, generic task in science is solving for
a differential equation. An equation of the same form
1Chandrasekaranhas previously developed the concept
of generic tasks in knowledge-basedexpert systems (Chandrasekaran 1986), and J. McDermotthas expressed similar
views (McDermott1988). Our focus is on science.
24
is solved identically, whether it arises in mechanics,
population biology, or elsewhere. Existing symbolic
computation systems can solve the differential equation y’ -- f(x) over restricted classes of elementary
functions. This is, of course, also knownas indefinite
integration: y-- ff(x)dx.
Solving indefinite integrals is not an isolated case:
there also exist algorithms for solving higher-order differential equations, finding roots of polynomials symbolically, and factoring multivariate polynomials over
various coefficient domains. (Kaltofen 1987) and (Davenport, Siret, & Tournier 1988) provide overviews of
such computational tasks, grouped into the field of
computer algebra.
Optimization
A second example of a generic task in science is optimization. In the case of combinatorial optimization,
there already exists the algorithmic theory and implemented software to solve linear programs, nonlinear programs, mixed-integer linear programs, and even
mixed-integer nonlinear programs. The scope of combinatorial optimization is not limited to engineeringoriented or experiment-planning aspects of science;
theoretical model-building itself can at least sometimes
be formulated as a problem of combinatorial optimization by minimizingthe size of the model (e.g., (ValdesPerez 1994a)), which in some sense corresponds
seeking the simplest theory. Another case is continuous optimization; similarly, such tasks are generic in
the sense that they cut across sciences. A typical application of continuous optimization arises when theories
or models contain free parameters to be optimized on
the basis of experimental data (Box & Hunter 1965).
Inferring
laws from data
Both AI and statistics
have addressed the problem of
finding algebraic laws hidden in data, a task of evident
generality and of both historical and current relevance.
Statistics,
for example, has developed methods of regression that lead to algebraic relations amongmeasured variables (Mandel 1984). The BACON
program
from cognitive science emphasized the creation of new
terms from data using a heuristic search that noticed
correlations between two terms; psychological plausibility was also a motivating factor in the design of the
program. Much work in machine discovery after BACONhas attempted improvements.
These first three cases of generic tasks derive their
generality from the following fact: their starting points
consist of context-free equations, other mathematical
expressions, or numeric data. One may begin to suspect that only such mathematical or numerical problems can be generic. To dispel this suspicion, next we
will consider in some detail a task that involves substantial reasoning specific to a particular science, but
which nevertheless is of a promising degree of generality.
{S,,,} ~
{&,,} -
{&,r}
tutoring system that has been designed to test Anderson’s ACT*(now ACT-R) theory of cognition, which
is based on the formalism of production systems. A
crucial part of the tutor involves model tracing, which
is the task of inferring the production system in the
student’s head from his interaction with the tutor.
Now, a production system is formally an instance of
the schemein Figure 2, and the tutor/student interaction is analogous to the scientist/nature relation in the
laboratory. There is not yet any hard evidence that
these similarities will be exploited at the algorithmic
level, but these and other links among "pathway elucidation" problems in science have been explored elsewhere in some detail (Valdes-Perez, Simon, & Murphy
1992).
The basis for the generic character of pathwayelucidation is that, typically, intermediate products of the
"reaction" are observed experimentally, all of which
must be linked via a pathway. Usually there is a rich hierarchy of constraint on pathways, ranging from what
are plausible participants, plausible "reactants" and
"products" of a step, plausible steps, and plausible
combinations of steps (Valdes-Perez 1994c). Sometimes pathway-like models are called other names:
paths, assemblies, nucleations, channels, mechanisms,
etc.; the main issue is whether they consist of discrete
steps.
There is a formal analogy between the pathways of
Figure 2 and a proof in logic, in which ’---*’ is logical implication. Indeed, there is no restricted meaning
to the symbol ’---’ as used above, which allows for its
adaptation here both to the ’--*’ of cognitive psychology and the ’--+’ of chemistry; a logical proof certainly
fits the pathway schema also. However, proofs are not
typically "elucidated" on the basis of peeks at the intermediate steps. If they were, or if proofs were planned
in advance by stipulating lemmas through which the
proof must pass, then then proof "elucidation" could
be another instance of the generic task.
{&,r}
{&,,} --+ {&,r}
Figure 2: Pathways
Pathway elucidation
There are many problems across science whose solutions take the form of a pathway (or, a set of steps),
as illustrated in Figure 2, in which Si,t and Si,r refer
to a set of items on the left and right (respectively)
of the ith step. Typically, a pathway describes some
physical process that consists of multiple steps, and a
typical means to elucidate the multi-step process is by
collecting experimental evidence on its various manifestations, as allowed by current experimental technique.
For example, an experimental biochemist’s study of
a multi-step reaction may lead to the hypothesis that
the underlying reaction pathwaylooks like this:
ornithine
+ ammonia + carbon dioxide
ammonia "4- citrulline
arainine "1" water
~
~
~
water + citrttlline
arfinine + water
urea + ornithine
Hans Krebs proposed this very pathway in 1932 to describe the formation of urea in vivo (Holmes 1980), and
stages leading to this discovery were modelled in the
KEKADA
program (Kulkarni & Simon 1988). But not
all chemical pathways are this simple. Many common
cases involve a dozen or so steps, and some important
reactions are suspected to consist of more than a hundred steps.
A computer program named MECHEM
automates a significant part of this task: it can propose
highly plausible pathwaysof moderate size on the basis
of experimental evidence (Valdes-Perez 1994b; 1994d;
1995).
Chemistry is not the only source of pathwayelucidation problems. Determining multi-step processes on the basis of experimental data is a problem that arises in nuclear physics (Hodgson 1988),
petrology (James B. Thompson, Laird, & Thompson 1982), and most especially biology. A biological
problem of great current importance is protein folding; the experimentalist’s role is to elucidate the pathways that describe how a protein chain folds into its
natural state from a denatured state (Levinthal 1968;
Richards 1991). We add that numerous problems in
biology involve the attempt to reconstruct some sort
of pathway on the basis of experimental evidence. We
have reported preliminary results on one such problem: endocytic pathways in cell biology (Valdes-Perez,
Simon, & Murphy 1992).
To further support the idea that there is a rich set
of generic tasks that cuts across the sciences, we can
adduce the surprising link of pathway elucidation with
the science of psychology, specifically cognitive psychology. (Anderson el al. 1990) discuss an interactive
Discrete
model building
Recently we identified a generic task of building discrete models in science by analyzing six computer programs that modelled or automated different aspects of
scientific reasoning in biology, chemistry, and physics
(Valdes-Perez,
Zytkow, & Simon 1993). The commonframework extracted from these systems involves
search in spaces of matrices (in which simpler models
correspond to smaller matrices) constrained by domain
laws such as conservation and analogous constraints.
In parallel with the work on matrix-space search, we
developed PAULI(Valdes-Perez 1994a; Valdes-Perez
& Erdmann 1994; Valdes-Perez c) as an improvement
on Kocabas’s BR-3 program (Kocabas 1991), borrowing representational
ideas from MECHEM,
which was
one of the six systems that were initially included in
the matrix-space search concept. Wethen selected the
task addressed by one of the systems (GELL-MANN
25
(Fischer & Zytkow 1990)) and demonstrated a new
tomation (Valdes-Perez a) that has some advantages
over the original program. This body of work constitutes evidence for the generic character of what we are
provisionally calling discrete model building.
Detecting
patterned
behavior
A commontask in experimental science is to look
for patterns within phenomena. For example, (Oliver
1991) advises the reader to "Go for the spatial pattern"
as a powerful heuristic of discovery in the earth sciences, but which is generally applicable to other fields
that study complex phenomena. Of course, spatial patterns do not typically come into being out of whole
cloth, rather they are woven by behavioral patterns:
looms make patterned cloths not by weaving randomly,
but by means of a patterned behavior on the part of
the loom.
A recent paper described a systematic technique
(PENCHANT)for finding complex patterned behavior within typical processes that are studied in sciences
such as cell biology and cognitive psychology (ValdesPerez & Perez 1994). The biological process consisted
of manycells undergoing concurrent divisions, and the
psychological process involved a chess master reconstructing a board position from memory. Since that
paper, we have begun projects to apply PENCHANT
to other scientific processes, such as particles impinging on an astronomical detector, a subject’s eye movements in psychology, and other, more complex processes in biology.
The PENCHANT
method began with "field work"
in developmental biology in which we discovered unsuspected patterned behavior in time-lapse images of
developing fruitfly embryos (Valdes-Perez & Minden).
Wethen proceeded to propose a model that governed
these processes and showed that the model accounted
well for the observations. By introspection, later we
were able to reconstruct our initial inference of patterned behavior as follows:
¯ If cell divisions were truly random(as was believed),
then the manycells would, by chance, lead to some
crowding;.
¯ Time-lapse images show the cells to be well spaced.
¯ Therefore, the cell division process cannot be random.
From this specific inference, we extracted a generic
method by generalizing the underlined terms: cell divisions became the process(es), and crowding became a
(variety of) spatial and geometric features. The PENCHANTmethod can be viewed as a complex permutation test (Edgington 1980), but we have not so far
encountered any similar method in our diverse contact
with scientists.
These applications are convincing evidence that detecting patterned behavior is a generic task of scientific
discovery. While PENCHANT
has not yet stumbled
26
on a convincing discovery, it has made some modest
ones, and we are in hot pursuit of others. Moreover,
PENCHANT
follows closely on the heels of a human
discovery whose key step the program can reproduce.
Elucidating
topological/spatial
structure
A significant number of tasks in natural science consist of proposing discrete, structural modelsof objects.
The earliest significant work that involved computer
scientists
was the DENDRAL
project (Lindsay et al.
1993), which started with the discovery by J. Lederberg at Stanford of an algorithm to generate the possible isomeric structures of a given molecular formula.
That algorithm led to a sustained effort to automate
the elucidation of molecular structure on the basis of
mass-spectrometric and other data. The subsequent
PROTEAN
project (Hayes-Roth et al. 1986) at Stanford attempted to elucidate protein structure, which
was considerably more difficult, since protein molecules
are muchlarger than the molecules typical of organic
chemistry that DENDRAL
was confronted with. DENDRALand PROTEAN
both used constraint-based
exclusion paradigms, so perhaps the elucidation of topological/spatial structure can be counted tentatively as
a generic task.
Related
Views
The previous sections have explicated the concept of
generic tasks at some length. In brief, we are proposing an organizational concept that provides a sustainable principled basis for research into the relations of
computation and scientific inference. Wehave emphasized tasks of discovery, although not exclusively, but
the scope of the concept extends to nowadays more
routine tasks of scientific inference, such as solving a
differential equation. The inspiration for this concept
derives part!y from the book by Langley, Simon, Bradshaw, and Zytkow (Langley et al. 1987), who took
broad view of science and examined to what extent the
programs they described could be applicable elsewhere
in science.
This organizational concept contrasts with the "orthodox" view of the computational sciences depicted
previously in Figure 1. Figure 3 illustrates
our proposal, supplemented with other generic tasks that cannot be elaborated here (Valdes-Perez b).
A Research
Plan
One fruitful research plan follows simply from the concept of generic scientific task. Given the current state
of understanding, any of the following steps will advance the subject:
¯ Identify a new task of scientific inference that seems
susceptible to automation.
¯ Automate it, or at least provide a computer aid.
¯ Seek applications, to show that the automation is
credible.
Biolo~
Chemistry’
- - ¯
to see where in science a process-oriented phenomenon
had been reported as random on the basis of experimental data. (In this case, PENCHANT
found new
patterns, but they turned out to be artifacts of the assumption that certain objects having a nonzero area
could be modelled as point-like objects).
Finally, howdoes one automate the scientific task?
Wesuggest the use of all available tools: the concepts
and techniques of AI, operations research, theoretical
computer science, applied mathematics and statistics,
and so on. Wepropose to study the abstract phenomena of scientific inference, not to apply AI and only
AI. An analogy: (Hanson 1958, p. 72) remarks that
"Physics is not applied mathematics. It is a natural
science in which mathematics can be applied." Similarly, a science of the abstract phenomenaof scientific
inference is not applied AI, it is a science in which AI
can be applied. Nevertheless, it should remain a part
of AI, just as game-playing and natural language processing have remained in AI. The commonphenomena
of all these areas is inference of somesort, so they will
always have a degree of cohesion.
solv.in~ differential equations
opt~m~zatmn
inferrin$ algebraic law~
pat hwa~elucidation
discrete model buildin$
detectin~ patterned behavior
elucidatin[~ topolosical structure
findin~ differential ec~uation models
reconstructin~ evolutionary trees
uncoverin$ causal relations
qualitative analysis of diff eqs
)tual clusterin
lnvartants
Jroblems
Figure 3: SomeGeneric Tasks of Scientific
Discovery
¯ Generalize within science: Look for analogous tasks
from another science, or from another subfield within
the same science.
¯ If there is evidence that the task is generic within
science, add the task to the list of knowngeneric
tasks.
¯ Compare the new task to other generic tasks in
search of further generalizations.
One might generate more research steps by considering
generically what is being proposed: a typology (or even
a beginning taxonomy) of scientific inference founded
on computation. Typologies require the development
of concepts, demonstration of their worth, hierarchical organization in the more structured case of taxonomies, etc. Perhaps even the scientific task (carried
out here in this section by the author) of proposing
research plan on the basis of a typological viewpoint
could be studied systematically and generically.
What tools or heuristics can help to carry out this
research plan? For example, how does one "identify
a new task of scientific inference that seems susceptible to automation"? From our experience, a good
step is to insert oneself personally within scientific contexts, e.g., becoming a memberof an interdisciplinary
center, reading scientist’s (especially experimentalist’s)
papers, attending seminars in other departments, and
so on. One can then ask such fruitful questions as:
Whatis the space of hypotheses that is implicitly being considered by such and such inference?
Given a successful automation or computer aid for
a task X, how does one "look for analogous tasks from
another science"? We have found that one fruitful
method is to browse databases of scientific abstracts
(e.g., INSPEC, PERIODICALS,MEDLINE,etc.) using synonyms for the terms that describe X. For example, we have sought analogues to chemical pathway
elucidation elsewhere, e.g., by first using "elucidat?" to
find what other process-oriented phenomenaare elucidated in science, thus generating synonymsfor "pathway". We have also used this method to seek other
tasks of detecting patterned behavior. For example,
we worked with a biophysicist on crystal growth after
finding a relevant paper in INSPEC(Durbin, Carlson,
& Saros 1993) by searching on the keyword "randomly"
Conclusion
Wehave proposed a new view of scientific discovery
that is based on the concept of generic tasks. Each
generic task in science is general because it is present
in various sciences, but at the same time is specific
because it involves one mode of inference, or a small
number of them.
This view of scientific inference houses disparate
pieces of work from computer algebra, computational
statistics,
operations research, theoretical computer
science, and artificial intelligence under a single roof
whose commonpurpose is the principled development
of systematic methods of scientific inference. Wehave
identified a number of credible generic tasks: almost
every task is represented by at least one computer program, and for each task there is at least some evidence
of genericity. There is no doubt that others that we
have missed could be added to the initial list, but this
would serve to strengthen our proposal, not vitiate it.
Wehave pointed out a research plan that follows naturally from the generic task concept, and have suggested
research heuristics and tools in support of the plan.
Acknowledgments.This work was supported in part by a
Science and TechnologyCenter grant from the National Science Foundation, #MCB-8920118,
and by the Keck Center
for AdvancedTraining in Computational Biology.
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