| |
BACON
and Other Discovery Systems
In his Novum Organon (Book I, Ch. LXI) Francis Bacon had expressed the view
that with a few easily learned rules or a method it
may be possible for anyone undertaking scientific
research to be successful.
And he proposed a method of discovery in the
sciences which will leave little to the sharpness
and strength of men’s wits, but will bring all
wits and intellects nearly to a level.
For as in drawing a straight line or in
inscribing an accurate circle by the unassisted
hand, much depends on its steadiness and practice,
but if a rule or pair of compasses be applied,
little or nothing depends upon them, so exactly is
it with his method.
Today Bacon’s agenda is called
proceduralization for mechanization, and it is
appropriate therefore that a discovery system should
be named BACON.
The BACON discovery system is
actually a set of successive and increasingly
sophisticated discovery systems that make
quantitative empirical laws and theories. Given sets of observation measurements for two or more
variables, BACON
searches for functional relations among the
variables. The
search heuristics in earlier versions of each BACON computer program are carried forward into all later ones, and
later versions contain heuristics that are more
sophisticated than those in earlier versions.
In the literature describing the BACON
systems each successive version is identified by a
numerical suffix, such as BACON.1. The original version, BACON.1,
was designed and implemented by Pat Langley in 1979
as the thesis for his Ph.D. dissertation written in
the Carnegie-Mellon department of psychology under
the direction of Simon, and titled Descriptive
Discovery Processes: Experiments in Baconian Science.
He published descriptions of the system in
"BACON.1:
A General Discovery System" in The
Proceedings of the Second National Conference of the
Canadian Society for Computational Studies in
Intelligence (1978) and as a co-author with
Simon and others in Scientific
Discovery (1987).
BACON
programs are implemented in a list processing
computer language called LISP,
and its discovery heuristics are implemented in a
production-system language called PRISM. The system lists
the observable measurement data monotonically
according to the values of one of the variables, and
then determines whether the values of some other
variables follow the same (or the inverse) ordering.
Picking one of these other variables, it
searches for an invariant by considering the ratio
(or the product) of these variables with the
original one. If
the ratio or product is not constant, it is
introduced as a new variable, and the process
continues the search for invariants.
Examples of some of the simpler search
heuristics expressed in the conditional form of a
production are as follows: (1) If the values of a
variable are constant, then infer that the variable
always has that value.
(2) If the values of two numerical variables
increase together, then examine their ratio.
(3) If the values of one variable increase as
those of another decrease, then examine their
product. The
general strategy used with these heuristics is to
create variables that are ratios or products, and
then to treat them as data from which still other
terms are created, until a constant is identified by
the first heuristic.
BACON.1
has rediscovered several historically significant
empirical laws including Boyle's law of gases,
Kepler's third planetary law, Galileo's law of
motion of objects on inclined planes, and Ohm's law
of electrical current.
A similar system, BACON.3 has rediscovered the ideal gas law and Coulomb's law of
electrical current.
For making these rediscoveries, Simon and his
associates used measurement data actually used by
the original discoverers, and published by W.F.
Magie in A Source Book in Physics (1935).
BACON.4
is a significant improvement over earlier versions.
It was developed and firstly described by
Gary Bradshaw, Pat Langley, and Herbert Simon in
"The Discovery of Intrinsic Properties" in
The
Proceedings of the Third National Conference of the
Canadian Society for Computational Studies in
Intelligence (1980), and it is also described in
their 1987 book.
The improvement is the ability to use nominal
or symbolic variables that take only names or labels
as values. For
example the nominal variable "material"
may take on values such as "lead",
"silver", or "water.”
Values for numerical properties may be
associated with the values of the nominal variables,
such as the density of lead, which is 13.34 grams
per cubic centimeter. BACON.4 has
heuristics for discovering laws involving nominal
variables by postulating associated values called
"intrinsic properties", by inferring a set
of numerical values for the intrinsic properties for
each of the postulated nominal values, and then by
retrieving the numerical values when applying its
numerical heuristics to discover new laws involving
these nominal variables.
The laws rediscovered by BACON.4
include: (1) Ohm's law of electrical circuits, where
the intrinsic properties associated with the
nominal variables are voltage and resistance, (2)
Archimedes law of displacement, where the intrinsic
properties are density and the volume of an
irregular object, (3) Black's law of specific heat,
where specific heat is the intrinsic property, (4)
Newton's law of gravitation, where gravitational
mass is the intrinsic property, and (5) the law of
conservation of momentum, where the inertial mass of
objects is the intrinsic property.
BACON.4
was further enhanced so that it could rediscover the
laws describing chemical reactions formulated by
Dalton, Gay-Lussac, and Comizzaro.
For example it rediscovered Gay-Lussac's
principle that the relative densities of elements in
their gaseous form are proportionate to their
corresponding molecular weights.
Rediscovering these laws in quantitative
chemistry involved more than postulating intrinsic
properties and noting recurring values.
These chemists found that a set of values
could be expressed as small integer multiples of one
another. This
procedure required a new heuristic that finds common
divisors. A
common divisor is a number which, when divided into
a set of values, generates a set of integers.
BACON.4 uses this method of finding common divisors, whenever a new
set of dependent values is about to be assigned to
an intrinsic property.
BACON.5
is the next noteworthy improvement.
It uses analogical reasoning for scientific
discovery. BACON.1 through BACON.4
are driven by data in search for regularities in the
data. Furthermore
the heuristics in these previous BACON systems are almost entirely free from theoretical
presuppositions about domains from which the data
are drawn. BACON.5
incorporates a heuristic for reducing the amount of
search for laws in certain special cases, in which
the system is given very general theoretical
postulates, and then it reasons by analogy by
postulating symmetries between the unknown law and a
theoretical postulate given to the system as an
input. The
general theoretical postulate that Simon gave to BACON.5
is the law of conservation.
The laws rediscovered by BACON.5
using analogy with the conservation law include the
law of conservation of momentum, Black's law of
specific heat, and Joule's law of energy
conservation.
The BACON discovery system was not the first system developed around
Simon's principles of human problem solving with
heuristics. In
1976 Douglas B. Lenat published his Ph.D.
dissertation written at Stanford University and
titled AM: An Artificial Intelligence Approach to Discovery Mathematics as
Heuristic Search.
Allen Newell was one of his dissertation
advisors, and Lenat acknowledges that he got his
ideas from Herbert Simon.
Lenat has since accepted a faculty position
in the computer science department of
Carnegie-Mellon University.
In 1977 he published "The Ubiquity of
Discovery" in The Proceedings of the Fifth International Joint Conference on
Artificial Intelligence, (IJCAI) in which he
relates Simon's theory of heuristic problem solving
in science and describes the specific heuristics in
his AM
discovery system.
While Lenat's article includes discussion of
artificial intelligence in empirical science, his AM system is not for empirical science, but is a computer system
which develops new mathematical concepts and
conjectures with these concepts.
Also in the 1977
IJCAI Proceedings he published "Automated
Theory Formation in Mathematics", which offers
a more detailed description of the system’s
two-hundred fifty heuristics, and which also
discusses his application of the AM
system in elementary mathematics.
He reports that in one hour of processing
time AM rediscovered hundreds of common mathematical concepts including
singleton sets, natural numbers, arithmetic, and
also theorems such as unique factorization.
In 1979 Simon published "Artificial
Intelligence Research Strategies in the Light of AI
Models of Scientific Discovery" in The
Proceedings of the Sixth International Joint
Conference on Artificial Intelligence in which
he considers Lenat's AM system and Langley's BACON
systems as useful for illuminating the history of
the discovery process in the domain of artificial
intelligence itself, and for providing some insight
into the ways to proceed in future research and
development aimed at new discoveries in that field.
He says that AI will proceed as an empirical
inquiry rather than as a theoretically deductive
one, and that principles for the discipline will be
inferred from the computer programs constituting the
discovery systems, although he also notes that in
the scientific profession the community members'
work in parallel, while in the machines the work
proceeds serially.
BACON
created quantitative empirical laws by examination
of measurement data.
Simon and his associates also designed and
implemented discovery systems, that are capable of
creating qualitative laws from empirical data, and
three such systems are described in Scientific
Discovery.
They are named GLAUBER, STAHL and DALTON. The GLAUBER
discovery system is named after the eighteenth
century chemist, Johann Rudolph Glauber, who
contributed to the development of the acid-base
theory. Langley
developed the discovery system in 1983.
For its historical reconstruction of the
acid-base theory GLAUBER
was given facts very similar to those known to
eighteenth century chemists, before they formulated
the theory of acids and bases.
These facts consist of information about
the tastes of various substances and the reactions
in which they take part.
The tastes are "sour",
"bitter", and "salty.”
The substances are acids, alkalis and salts
labeled with common names, which for purposes of
convenience are the contemporary chemical names of
these substances, even though GLAUBER
makes no use of the analytical information in the
modern chemical symbols.
Associated with these common names for
chemical substances are argument names, such as
"input" and "output” that describe
the roles of the chemical substances in the chemical
reactions in which the substances partake. Finally the system is given names for the three abstract
classes: "acid", "alkali", and
"salt.”
When the system is executed with these
inputs, it examines the chemical substances and
their reactions, and then correlates the tastes to
the abstract classes, and also expresses the
reactions in a general law that states that acids
and alkalis react to produce salts.
The second discovery system is STAHL,
which creates a type of qualitative law that Simon
calls "componential", because it describes
the hidden structural components of substances. System STAHL is
named after the German chemist, Georg Ernst Stahl,
who developed the phlogiston theory of combustion.
STAHL
recreates the development of both the phlogiston and
the oxygen theories of combustion. Simon states that discovery systems should be able to arrive
at laws that have been rejected later in favor of
others in the history of science.
And he says that since a discovery system's
historical reconstruction aims at grasping the main
currents of reasoning in a given epoch, then
reproducing the errors that were typical of that
epoch is diagnostic.
Like GLAUBER, STAHL accepts
qualitative facts as inputs, and generates
qualitative statements as outputs.
The input is a list of chemical reactions,
and its initial state consists of a set of chemical
substances and their reactions represented by common
names and argument names, as they are in GLAUBER.
When executed, the system generates a list of
chemical elements and of the compounds in which the
elements are components.
The intermediate states of STAHL's
computation consist of transformed versions of
initial reactions and inferences about the
components of some of the substances.
When the system begins running, it is driven
by data, but after it has made conjectures about the
hidden structures, it is also driven by these
conjectures, which is to say, by theory.
Simon concludes from the rediscovery of the
phlogiston and oxygen theories by STAHL, that the proponents of the two theories reasoned in
essentially the same ways, and that they differed
mainly in their assumptions.
He also applied
STAHL to the rediscovery of Black's analysis of magnesia
alba, and he maintains that the same principles
of inference were used by chemists quite widely in
their search for componential explanations of
chemical substances and their reactions.
The principal significance of this diversity
to Simon is the demonstration that the reasoning
procedures in STAHL
are not ad hoc,
and that STAHL is a general system.
The third discovery system that creates
qualitative laws is DALTON,
which is named after John Dalton.
Like Dalton the chemist, the DALTON
system does not invent the atomic theory of matter;
it employs a representation that embodies the
hypothesis, and that incorporates the distinction
between atoms and molecules invented by Avogado.
DALTON
is a theory-driven system for reaching the
conclusions about atomic weights that BACON.4
derived in a data-driven manner.
And DALTON creates structural laws in contrast to STAHL, which creates componential laws. DALTON is given
information that is similar to what was available to
chemists in 1800.
The input includes a set of reactions and
knowledge of the components of the chemical
substances involved in each reaction.
This is the type of information outputted by STAHL,
and DALTON
uses the same common-name/argument-name scheme of
representation used by STAHL. DALTON is also told which of the substances are elements having no
components other than themselves.
And it knows that the number of molecules in
each chemical substance is important in the simplest
form of a reaction, and that the number of atoms of
each element in a given molecule is also important.
DALTON's
goal is to use this input to develop a structural
model for each reaction and for each of the
substances involved in each reaction, subject to two
constraints. The
first constraint is that the model of a molecule of
a substance must be the same for all reactions in
which it is present.
The second constraint is that the models of
the reactions display the conservation of particles.
Simon applied DALTON to the reaction involving the combination of hydrogen and
oxygen to form water, and the system outputted a
model giving a modern account of the water reaction.
He also considers applying DALTON
to elementary particle physics and to classical
genetics, but he states that the current version is
not adequate to this task.
Since the publication of Scientific
Discovery Simon and his associates have
continued their work on discovery systems and have
pursued their work into new directions.
While BACON
and the other systems described in the 1987 book are
concerned mainly with the ways in which theories can
be generated from empirical data, the question of
where the data come from has largely been left
unanswered. In
"The Process of Scientific Discovery: The
Strategy of Experimentation" (1988) in Models
of Thought Simon and Deepak Kulkarni describe
their new KEKADA discovery system, which examines not only the process of
hypothesis formation, but also the process of
designing experiments and programs of observation.
The KEKADA
discovery system is constructed to simulate the
sequence of experiments carried out by Hans Krebs
and his colleague, Kurt Henseleit, between July 1931
and April 1932, which produced the elucidation of
the chemical pathways for synthesis of urea in the
liver. This
discovery of the ornithine cycle was the first
demonstration of the existence of a cycle in the
metabolic biochemistry.
Simon and Kulkarni's source for this episode
is "Hans Krebs and the Discovery of the
Ornithine Cycle" in Federation
Proceedings (1980) by Frederic L. Holmes of Yale
University. Holmes
also made himself available to Simon and Kulkarni
for consultation in 1986 when their study was in
progress. The
organization of KEKADA is based on a two-space model of learning proposed earlier by
Simon and Lea in "Problem Solving and Rule
Induction: A Unified View" in Knowledge
and Cognition (1974).
The system searches in an "instance
space" and a "rule space", each
having its own set of heuristics.
The instance space is defined by the possible
experiments and experimental outcomes, and it is
searched by performing experiments.
The rule space is defined by the hypotheses
and other higher level descriptions coupled with
associated measures of confidence. The system proceeds through cycles in which it chooses an
experiment from the instance space to carry out on
the basis of the current state of the rule space,
and the outcome of the experiment modifies the
hypotheses and confidences in the rule space.
One of the distinctive characteristics of KEKADA
is its ability to react to surprising experimental
outcomes, and to attempt in response to explain the
puzzling phenomenon.
Prior to carrying out any experiment,
expectations are formed by expectations setters,
which are a type of heuristic for searching the rule
space, and the expectations are associated with the
experiment. The
expectations consist of expected output substances
of a reaction, and expected upper and lower bounds
on the quantities or the rates of the outputs.
If the result of the experiment violates
these bounds, it is noted as a surprise.
Comparison of the course of work of Krebs as
described by Holmes and of the work of KEKADA
in its simulation of the discovery reveals only
minor differences, which Simon and Kulkarni say can
be explained by focus of attention shifts and small
differences in the initial knowledge with which
Krebs and KEKADA
started. The
authors also say that a manual simulation of the
path that Krebs followed in a second discovery, that
of the glutamine synthesis, is wholly consistent
with the theory set forth by KEKADA. They therefore conclude that the structure and heuristics in KEKADA
constitute a model of discovery that is of wider
applicability than the episode used to develop the
system, and that the system is not ad
hoc.
Simon's
Philosophy of Science
Simon's literary corpus is rich enough to
contain a philosophy of science that addresses all
four of the basic questions addressed by academic
professional philosophers.
Aim of Science
What philosophers of science call the aim of
science may be taken as a rationality postulate for
basic scientific research.
Simon explicitly applies his thesis of
bounded rationality developed for economics to
scientific research in his autobiography in an
"Afterword" titled "The Scientist as
Problem Solver", although this explicit statement
would not have been necessary for the attentive
reader of his literary corpus.
Simon describes his theory of discovery as a
special case of his theory of human problem solving,
because both theories are based on his theory of
heuristic search.
And he views his theory of heuristic search
in turn as a special case of his postulate of
bounded rationality.
To this metatheory one need only add that
Simon's application of his postulate of bounded
rationality to scientific discovery amounts to his
thesis of the aim of science.
The function of heuristics is to search
efficiently a problem space of possible solutions,
which is too large to be searched exhaustively. The limited computational ability of the scientist relative
to the size of the problem space is the
"computational constraint", that is the
factor that bounds the scientist's rationality,
constraining the scientist from aiming for anything
like global rationality.
The research scientist is therefore a
satisficer, and the aim of the scientist is
satisficing within both empirical and computational
constraints.
Explanation
Simon's views on the remaining philosophical
topics, explanation and criticism, may also be
considered in relation to the discovery systems.
Consider firstly his statements on
scientific explanation including the topic of
theoretical terms.
The developers of the BACON
systems make a pragmatic distinction between
observation variables and theoretical variables in
their systems.
Simon notes that contemporary philosophers of
science maintain that observation is theory-laden,
and his distinction between observational and
theoretical terms does not deny this semantical
thesis. He
calls his distinction "pragmatic", because
he makes it entirely relative to the discovery
system, and it is also pragmatic in the sense
understood in the contemporary Pragmatist philosophy
of science. Those variables that have their
associated numeric values before input to the system
are considered to be observational variables, while
those that receive their values by the operation of
the discovery system are considered to be
theoretical ones.
He states that in any given inquiry we can
treat as observable any term whose values are
obtained from an instrument that is not itself
problematic in the context of that inquiry.
Thus Langley considers all the values created
by the BACON
programs by multiplication or division for finding
products or ratios to be theoretical terms.
And Simon accordingly calls the values for
nominal variables that are postulated intrinsic
properties theoretical terms.
Unfortunately Simon does not follow through
with this Pragmatist relativizing to problem-solving
discovery systems, but reverts to the Positivist
concept of explanation. In his exposition of DALTON,
which create structural theories, Simon comments
that as an area in science matures its researchers
progress from "descriptions" to
"explanations", and he cites Hempel's Aspects of Scientific Explanation and Other Essays (1965).
Examples of explanations cited by Simon are
the kinetic theory of heat, which provides an
explanation of both Black's law and the ideal gas
law, and Dalton's atomic theory, which provides
explanations for the law of multiple proportions and
Gay-Lussac's law of combining volumes.
He notes that each of these examples involves
a structural model in which macroscopic phenomena
are described in terms of their inferred components. Simon contrasts explanation to the purely phenomenological
and descriptive analyses carried out by BACON.4,
when it rediscovered the concepts of molecular and
atomic weight, and assigned correct weights to many
substances in its wholly data-driven manner.
He affirms that BACON.4's analyses involved no appeal to a particulate model of
chemical elements and compounds, and that what
took the place of the atomic model were the
heuristics that searched for small integer ratios
among corresponding properties of substances. This
concept of explanation is a reversion to the
hypothetical-deductive concept of explanation in
which theories are said to “explain” empirical
laws by deductive connection, and in which theory
and empirical or descriptive generalizations are
distinguished by their semantics.
This is what Hanson referred to as the
almanac view of science.
On the Pragmatist view theory and empirical
description are not distinguished semantically, but
are distinguished pragmatically by their use in the
problem-solving activity that is scientific
research. Theory
is what is proposed for empirical testing, and
description is what is presumed for testing.
Explanation is language that is theory after
it has been empirically tested and not falsified; or
one who speaks of "theoretical
explanation" is merely speaking of a proposed
explanation. This
is the functional view of the language of science
instead of the Positivist almanac view.
Thus given that the discovery systems are
problem-solving systems, defining "theory"
and "explanation" relative to the
discovery system is to define them in a manner
consistent with the contemporary Pragmatist
philosophy. And
on this Pragmatic view the outputted laws generated
by BACON.4
are no less theoretical or explanatory than the
outputs of DALTON.
|
|
