MODELING DISCOVERIES IN PARTICLE PHYSICS
Sakir Kocabas
Pat Langley
(langley @ cs.stanford.edu)
Robotics Laboratory, Computer Science Dept.,
Stanford University, Stanford, CA 94305 USA
Abstract:
This paper describes a discovery system, BR-4, which integrates several research tasks in modeling the discovery of certain quantum properties and conservation laws by physicists in this century. The program is directed by consistency and completeness constraints, and has the capabilities of theory formation and theory revision in its domain, and of explaining its knowledge state by these constraints . BR-4 is capable of formulating new elementary particles and particle reactions, and proposing observations to test their existence. The program revises its domain theory when it detects formal and theoretical contradictions, and when its domain theory conflicts with observational data.
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* Also affiliated with ITU, Faculty of Space Sciences and Technology, Istanbul, Turkey.
** Also affiliated with the Institute for the Study of Learning and Expertise, 2451 High St., Palo Alto, CA 94301 USA.
1. Introduction
Computational modeling of discovery has been the focus of attention by several research groups in the last ten years, and a number of models with different capabilities have been developed. These capabilities include goal selection, experime nt design, data collection, expectation setting, quantitative reasoning, concept formation, hypothesis formation, theory formation, theory revision, explanation, and paradigm shifts by qualitative models. In current models only a few of these discovery tasks have been integrated in one system. The integration of discovery tasks continues to be a difficult problem in this reearch area of artificial intelligence.
The subject of this paper is an integrated discovery model BR-4, with the capabilities of theory formation, event prediction, data acquisition, explanation, and theory revision. Before we describe the system and its behavior, it is appropri ate to present some background information about its task domain, particle physics.
1.1. The Domain of Particle Physics
Particle physics studies the nature of elementary particles - the building blocks of matter - and interactions among these entities. The basic phenomena in this field take the form of reactions, similar in many ways to those found in chemistry. For instance, two such observed reactions* are
p + p --> p + n + pi
pio --> g + g
where the symbols p, n, pi, pio and g represent the proton, neutron, pion, pion-zero and gamma particles, respectively.
As in chemistry, physics require that reactions among elementary particles obey certain conservation laws. For instance, one of the most basic laws states that any such reaction conserve electric charge of the particles involved. Electric charge is an example of a quantum property, and one of the main tasks in particle physics concerns the assignment of values for quantum properties such that observed reactions conserve those properties. Thus, both of the above reactions conserve electric charge provided we assign the commonly accepted charges 1 to p, 0 to n, 1 to pi, 0 to pio, and 0 to g. Other assignments are also possible for this pair of reactions, but they would not be consistent with other observed particles.
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* Typically, physicists infer the occurence of such reactions from tracks in cloud chambers and similar evidence. We will not attempt to model this inference process here, and instead will simply treat reactions as though they are directly observed.
The concern with conservation also explains why some particle reactions are never observed. For example, the process of beta decay,
n --> p + e + /nu,
in which a neutron decays into a proton p, an electron e, and an antineutrino /n , has been widely detected, in contrast, the decay of protons, as in the reactions
p -> pi + pio
p -> /e + g
has never been seen despite its inherent plausibility. All three reactions satisfy conservation of energy and electric charge, yet only the first occurs in nature. However, one can explain the absence of the other reactions by the existence of another quantum property, the baryon number, that must also be conserved and that these two reaction would violate. Thus, another central task in particle physics involves the explanation of unobserved reactions through the postulation of new qantum numbers.
Other activities include the postulation of new particles, either on theoretical or empirical grounds, and the prediction of reactions that satisfy known conservation laws. Testing such predictions leads into the realm of experimental particle phsics, which we will not address here. But the above pursuits cover a wide range of behaviors that occur in this scientific field.
The above analysis of the discovery tasks suggests that six basic operations play a central role in particle physics. First, one must have a representation to receive and evaluate data about domain objects and events, Second, for a given set of particles, quantum numbers and observed reactions, one must be able to determine a set of quantum values that satisfy conservation for those reactions. Third, one must have a mechanism to explain the currently observed and unobservable reactions in terms of the constraints of the model. Fourth, one must be able to posit new quantum properties that account for the absence of unobserved reactions. Fifth, one requires an operator that posits new particles and determine their role in known reactions. Finally, one must have some mechanism for predicting reactions that have not yet been observed, but which follow from the current theoretical model. We have incorporated these operators into BR-4, where they play a central role in the process of theory formation and revision. (We will refer to them as Read-Data, Determine-Values, Explain-Event, Posit-Property, Posit-Particle, and Predict-Reaction, respectively.)
Operators of this sort must alter some internal representation that contains hypotheses about the particles, properties, and reactions that exist. This representation can take many forms, but following Valdes-Perez et al. (1993), one can view it as two matrices. One matrix lists particles against quantum properties, with each matrix entry specifying the value for a specific particle on a specific prorperty. The other matrix lists particles against reactions, with an entry containing the total number of times the particle occurs in the reaction. In this light, the operator for determining quantum values alters entries in the first matrix, whereas each of the other three operators (Posit-Property, Posit-Particle, and Predict-Reaction) extends one or both matrices along one of their dimensions.
In the next section we describe the knowledge representation and the discovery operators of BR-4 together with its control structure in modeling several different discovery taks ith illustrative examples from particle physics. This will be followed by a discussion on the system's methods and proections for future work. The paper ends with a summary of the conclusions drawn from this research.
2. The System's Knowledge Representation and Behavior
In this section we describe the program's knowledge representation methods and its behavior in modeling certain discoveries in particle physics. The program uses a structured knowledge representation similar to qualitative schemas as in AbE (O'Rorke et al, 1990) and the other recent discovery models.
2.1. Knowledge Representation
BR-4's knowledge organization distinguishes descriptive and prescriptive knowledge. The former type of knowledge is represented as frames, and the latter as a series of operators and functions. The program has six operators which are named as follows: Read-Data, Determine-Values, Explain-Event, Posit-Property, Posit-Particle and Predict-Reaction.
The main data items of BR-4 are elementary particles and their reactions. Both are represented as frames in the system's knowledge base. Particle frames include the name of the particle, the quantum properties and their values. The general form of a particle frame is as follows:
frame: P (frame name)
class : particle
q1 : v1
q2 : v2
.......
qn : vn.
where P is the name of the particle, q1,...,qn the quantum properties, and v1,...,vn the corresponding quantum values, which can be -1, 0, or 1.
Particle reactions are represented in a similar way, this time containing information about the reactions, such as the particles involved, the reaction conditions, the physical status of the reaction, and its validity under the current theory. The general form of a particle reaction frame is as follows:
frame: reaction
class : physical event
actual status : A
logical status : L, logical_status(N,L)
reactants : R
products : P
active properties : Q, active_properties(N,Q)
reactants properties : Rp, reactants_properties(Q,Rp)
products properties : Pp, products_properties(Q,Pp)
conditions : (Rp = Pp) or (Rp =/= Pp).
where A indicates whether the reaction has been physically observed or unobserved, and L indicates whether the reaction is valid or invalid under the current theoretical knowledge of the system. R and P are the lists of the particles involved in the reaction as the reactants and the products respectively. Q indicates the vector of quantum properties that play an active role in the reaction, while Rp and Pp are the quantum value vectors of the reactants and the products. Normally, particle reactions are added to the program's knowledge base (e.g. for the reaction (n --> p + e + /nu) as follows:
frame: r1
class = reaction
actual status = observed
reactants = [n]
products = [p,e,/nu].
Such input reaction frames are then transformed into the form below by the Read-Data operator acting on the parent frame:
frame: r1,
class = reaction
actual status = observed
logical status = valid
reactants = [n]
products = [p,e,/nu]
active properties = [q0, q1]
reactants properties = [1, 0]
products properties = [1, 0]
conditions = {[1,0] = [1,0]}.
The amended slots are added after their values are calculated by the Read-Data operator. In this wa, the system's domain theory is built, onwhich BR-4's other operators act as described below in a control structure summarized in Figure 1.
___________
| Read Data | <-- new data
|___________|
| |
__|____|___ ___________
| |--->| Explain |
| | |_Event_____|
| | _____|_____
| |--->| Determine |<------
| Domain |<---|_Value_____| |
| Theory | _____|_____ |
| |--->| Posit |_______|
| |<---|_Property__| |
| | _____|_____ |
| |--->| Posit |_______|
| |<---|_Particle__|
| | _____|_____
| |--->| Predict |
|___________|<---|_Reactions_|
Figure 1. BR-4's general control structure in the
discovery of quantum properties
2.2. Theory Formation and Revision
The program starts with a simple domain theory about several particles and a small number of observable reactions. BR-4's theory formation activites are driven by its Explain-Event operator which acts on particle reaction frames, looking for reactions which cannot be explained with the system's consistency and completeness contraints. The consistency condition states that any observed particle reaction must be valid by the system's domain theory, where validity is defined as compliance with the quantum conservation laws. An inconsistent reaction in this sense, is unexplainable by the Explain-Event operator.
There are two heuristics for eliminating such contradictions. One is to revise the quantum values of particles in a depth-first search with backtracking through the space of values, until a consistent value set is found. The second heuristic is to introduce a hidden particle to balance the reaction, in either the input or the output, positing that it actually takes part in the reaction but for some reason is not directly observable. The system then computes the property values for this particle, identifying it with an already known particle, or creating an entirely new particle. The first heuristic is applied by the Determine-Values operator and the second one by Posit-Particle.
The completeness condition is defined over unobserved reactions. Any unobserved particle reaction must be violating some quantum conservation law. If the domain theory of BR-4 contains an unobservable reaction that does not seem to violate a quantum conservation law, then this is also an unexplainable event for the Explain-Event operator. This means that the system's domain theory is incomplete regarding the unobserved reaction. In such cases, the system's Posit-Property operator takes control, which posits a new quantum property also to be conserved in observed particle reactions, but not by the unobserved reactions. Determining the values of this property requires search, first for the particles in the missing reaction, and an embedded search for the values of particles in other reactions. This search is carried out by the Determine-Values operator, and as before, if the system arrives at a partial combination of values that rules out an observed reaction or fails to eliminate the unobserved one, it backtracks and considers alternative paths until it finds an acceptable set.
We can extend the notion of incompleteness to include theories that do not explicitly specify all reactions that follow from them, as occurs when BR-4's Posit-Particle postulates a ne particle. In this situation, the system's Predict-Reactions operator systematically generates all possible reactions (decays and collisions) of the ne particle involving one, two or three other known particles. For each such tentative reaction R, the program predicts that R will occur if it conserves all known properties.
3. Illustrative Examples From Particle Physics
In this section we describe the behavior of BR-4 on three examples of discovery fom the history of particle physics, involving the neutrino, baryon and lepton numbers, and electron and muon numbers.
Table 1. The quantum values of particles known prior
to the discovery of the neutrino.
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Particle mass charge spin
g 0.0 0 1
e 0.51 -1 1/2
p 938.26 1 1/2
n 939.55 0 1/2
/e 0.51 1 1/2
n 0.0 0 1/2
/n 0.0 0 1/2
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3.1. Discovery of the Neutrino
Until the early 1930's, scientists knew only a few elementary particles, shown in Table 1 along with their mass and their values on the three known quantum properties, energy, charge and spin. The known reactions were also limited to a small number:
p + p --> p + p
e + /e --> g
g --> e + /e
This situation changed after the discovery of the neutron in 1932, when experiments on beta decay revealed the reaction
n --> p + e
in which a neutron decays into a proton and an electron. However, this reaction was problematic in that it violated the conservation of energy and spin, with the total energy and spin counts unbalanced in the reaction. Rather than abandon the conservation law, physicists postulated the presence of a new particle,* also generated during beta decay, that would balance out the missing energy and spin. Although not visible in the reaction, they inferred the property values for this particle from the values for the other particles in the decay process. They concluded that this neutrino has zero rest mass, no electrical charge, and a spin of one half.
Given the reactions above and the quantum numbers in Table 1, BR-4 responds in a similar manner. The system's Explain-Event operator cannot explain the fourth reaction, as it detect passes control to Posit-Property. This operator considers to assign alternative spin values in an attempt to find a consistent set of values that would balance the reaction. But in this case, BR-4 is not allowed to modify the spin values, as these are assumed to be correctly established by observation. This leaves revision of the unbalanced reaction as the
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* In the early 1930's there were serious debates among physicists as to the validity of the conservation laws in the subatomic world.
Table 2. Particle reactions that were (a) observed and (b) not observed
in experiments after the introduction of the particles in Table 1.
-----------------------------------------------------------------------
a) Observed reactions b) Unobserved reactions
p + p --> p + p p --> /e + g
n --> p + e + /nu p --> /e + e + /e
/e + e --> g p --> /e + g + g
g + p --> e + /e + p
/nu + p --> n + /e
nu + n --> p + e
-----------------------------------------------------------------------
only solution as the control passes to the Posit-Particle operator, which adds an extra particle to the output side of the reaction, giving
n --> p + e + nu.
Using the conservation laws, Determine-Values computes the charge and spin of the new particle, nu, as 0 and 1/2 respectively. Another possible revision would have added a new particle with opposite properties to /n, to the input side of the reaction, but physicists favored the former solution as they were thinking in terms of a decay process.
However, the inclusion of the neutrino and its antiparticle leaves the theory incomplete, in that they imply reactions with other known particles. BR-4's Predict-Reactions operator finds no decays for the neutrino, but it does find three collision reactions that are consistent with the theory:
/nu + p --> n + /e
nu + n --> p + e
nu + /nu --> g
which are predicted to be observed in experiments. The first two of these were later detected by physicists. The third reaction has a very low probablity and is rather difficult to detect.
3.2. Proposing Baryon and Lepton Numbers
The discovery of the neutrino left physicists with seven elementary particles,* having the properties and values shown in Table 1. Physicists realized that the existence of these particles, combined with known quantum conservation laws, implied a variety of reactions. Subsequent observations revealed evidence for the predicted reactions in Table 2 (a) but not for those shown in Table 2 (b). For some reason, the three predicted decays of the proton did not occur in nature. To explain this, physicists proposed a new quantum property, known as the baryon number.**
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* The neutrino-antineutrino distinction as experimentally verified in the late 1950's.
** Stuckelberg proposed this new quantum property in 1938 as the protonic charge which was later to be called the baryon number.
Table 3. The quantum values for elementary particles known in 1953
after the discovery of baryon and lepton numbers.
--------------------------------------------------------------------
Particle mass charge spin baryon lepton
g 0.00 0 1 0 0
e 0.51 -1 1/2 0 1
p 938.26 1 1/2 1 0
n 939.55 0 1/2 1 0
/e 0.51 1 1/2 0 -1
nu 0.00 0 1/2 0 1
/nu 0.00 0 1/2 0 -1
mu 105.60 -1 1/2 0 1
/mu 105.60 1 1/2 0 -1
pi 139.60 1 - 0 0
/pi 139.60 -1 - 0 0
pio 135.00 0 - 0 0
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BR-4's Predict-Reactions operator proposes the same reactions, but the Explain-Event operator cannot explain the absence of the reactions in Table 2 (b). The program selects the first reaction, p --> /e + g, and turns it into a set of inequalities, each based on a different combination of values for the particles involved. In this case, it would generate the four ineualities
1 =/= 0 + 0
1 =/= 1 + 1
0 =/= 1 + 0
0 =/= 0 + 1
The Determine-Values operator then selects one of these value sets, say the first, p =1, /e = 0, g = 0, and tests them in the observed reactions, say n --> p + e + /nu, this time treating it as an equality, and obtains
n = 1 + 0 + /nu
which leaves the property values for n and /nu unspecified. Two value sets are possible for this pair, n = 1, /nu = 0 and n = 0, /nu = -1. The first value set is consistent with all the then known reactions, while the second set is inconsistent with the reaction nu + n --> p + e. At any point, detection of an unbalanced reaction that violates conservation of the new property causing backtracking to one of the alternative value sets. If the search exhausts all such sets produced from observed reactions, the system backtracks further and considers alternative value sets generated from the unobserved reactions.
Given the experimental results in Table 2, BR-4 arrives at the value zero for all particles except the proton and neutron, to which it assigns the value one. These settings correspond to those obtained by physicists for the baryon number, which successfully explain the absence of the reactions in Table 2 (b).
Alternatively, by using the value set in the third inequality above, BR-4 would propose another quantum property by assigning the following values to particles: p = 0, n = 0, /e = -1, g = 0, and e = 1. These values correspond to the lepton numbers of elementar particles (see, Table 3).
Table 4. Some particle reactions that were (a) observed and (b) not
observed in experiments after the discovery of baryon and lepton numbers.
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a) Observed reactions b) Unobserved reactions
pi --> /nu + mu mu --> e + g
/pi --> mu + /nu pi --> /mu + g
mu --> e + nu + /nu pi --> /e + g
/mu --> /e + /nu + nu
pio --> g + /e + e
pio --> g + g
pio --> e + e + /e + /e
----------------------------------------------------------------------
In 1935, Yukawa had proposed the existence of additional particles with the mass of about 100 MeV in the nucleus. The reasoning behind Yukawa's proposal, which we have not attempted to model, involved energy calculations on atomic nuclei. Later, in the 1940s, observations on cosmic rays revealed five such particles: the muon (mu) and anti-muon (/mu), the pion (pi) and anti-pion (/pi), and the pion-zero (pio), along with the property values in Table 4. Baryon and lepton numbers could explain the possibility and absence of the reactions of these particles in the 1950s. Some of these reactions are given in Table 5(a) and 5 (b).
3.3. Electron and Muon Numbers
With the discovery of the baryon and lepton numbers, physicists had produced a theory, involving 12 elementary particles and four quantum properties plus the relativistic masses of the particles, that was apparently consistent and complete. Table 3 reflects this state of physical knowledge. Some skepticisms remained, such as for the neutrino, which seemed very difficult to observe for theoretical reasons. However, in 1953, experiments revealed indirect evidence for the reaction
/nu + p --> n + /e.
Unfortunately, this reaction occurred when the anti-neutrino n had been generated through beta decay (n p + e + n ), but not when produced through muon decay (m --> e + nu + /nu).
To resolve this dilemma, scientists postulated that the two reactions actually generated two distinct types of neutrinos, calling the former an electron neutrino (ne) and the latter a muon neutrino (nu_mu). This distinction (and the analogous one for anti-neutrinos) introduced two additional rows in the table of particles. However, it also produced the unobserved reactions shown in Table 5(b), which physicists again sought to explain by introducing yet another property, which they named the electron number.
Our model cannot directly explain the historical distinction into two classes of neutrinos, but we believe it constitutes a variation on the heuristic for postulating new particles that originally led to inference of the neutrino. Once this distinction has been made, BR-4 realizes that its current theory is incomplete, in that it cannot explain the unobserved reactions involving the muon neutrino and its antiparticle. Postulating a new property, it searches the space of values using the same process as it used for the baryon and lepton numbers. The resulting values agree with those proposed by physicists for the electron number, but are not sufficient to rule out the unobserved reaction (pi --> /mu + g). Explanation of this omission requires introduction of yet another quantum property, this one corresponding to the muon number, which physicists postulated in 1962.
Table 5. Some particle reactions that were (a) observed and (b) not
observed in experiments after introducing distinction between electron
neutrinos (nu_e) and muon neutrinos (nu_mu).
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a) Observed reactions b) Unobserved reactions
pi --> /mu _ nu_mu mu --> e + g
/pi --> mu + /nu_mu /nu_mu + p --> n + /e
mu --> e + /nu_e + nu_mu nu_mu + n --> p + e
/mu --> /e + nu_e + /nu_mu pi --> /mu + g
pio --> g + e + /e pi --> /e + g
pio --> g + g
pio --> e + /e + e + /e
----------------------------------------------------------------------
4. Discussion of the Framework
Now that we have seen some examples of BR-4's operation, we can consider the implications of the model for research on scientific creativity, related work on scientific discovery, and some directions for future research on this topic.
4.1 Implications of the Model
Modern scientific research is one of the most complex human activities, requiring the use of different types of general and specific knowledge. It can also involve more than a dozen different search spaces ranging from scientific problem formulation through data collection and evaluation, to hypothesis formation, theory formation and theory revision (see, Kocabas, 1993). Within the research activities, different types of discovery and creativity can be distinguished as logico-mathematical, formal, theoretical and empirical discovery. Current computational models have shortcomings in capturing the details of historical discoveries for reasons described by Tweney (1990). However, this should not diminish their usefulness, as they can provide an overall look into the structure of the developments of theories both in their formation and revision processes. They can also be useful in analyzing the historical progress of scientific ideas and of the possibility of alternative ideas together with their implications.
In this study, our aim has not been to model the historical details of particle physics, but to show that certain computational mechanisms can account for theory formation and revision in this domain. The basic mechanisms in BR-4 -- search guided by heuristic knowledge -- bears close resemblance to those implicated in normal human problem solving, as studied by Newell and Simon (1972), as well as many others.
If correct, this view suggests that some of the creative activities in particle physics has much in common with everyday reasoning. However, modern scientific reasoning is much more reliant on logico-mathematical, theoretical and methodological knowledge than everyday reasoning in addition to empirical and commonsense knowledge. Unlike simple search spaces dealt with in everyday reasoning, it also has to deal with a number of different search spaces at the same time if it has to result in discoveries, or even to make progress at all (see, e.g., Klahr, 1994; Kocabas, 1993). Our model operates only in the spaces of empirical hypothesis and theory formation, event prediction, problem formulation and theory revision.
Previous models of scientific discovery, such as those described by Langley, Simon, Bradshaw, and Zytkow (1987), have taken a similar stance on the creative process. However, most such work has focused on limited aspects of scientific reasoning, such as the discovery of laws or the formation of structural theories.
With BR-4, we have attempted to cover a broader range of the discovery process within a unified framework. We described how the system formulates new problems whenever new data reveals its current theory to be either inconsistent or incomplete. In handling problems of inconsistency, BR-4 relies on depth-first search guided by algebraic and domain heuristics to explore the space of values for quantum properties, resorting to the postulation of new particles only if its search fails.
In dealing with incompleteness, the model predicts new reactions that follow from the introduction of new particles and posits new quantum properties to explain why some of these reactions never occur. The introduction of new particles and new properties constitute important examples of theory formation.
Our system does not provide a detailed account of the historical record, but it does explain several impressive discoveries at a more abstract level, using simple mechanisms of a familiar kind. This limited success provides further evidence that at least some types of scientific creativity does not require any special processes, but can be explained as a straightforward extension of existing theories of human cognition.
4.2 Related Work on Scientific Discovery
Our computational model of discovery draws many of its ideas from earlier work in this area. BR-4 is a direct descendant of Zytkow and Simon's (1986) STAHL, which modeled a variety of qualitative discoveries in the history of chemistry. The detection of inconsistencies in reactions played a central role in this system, with one of its responses being the introduction of new elements like phlogiston, which served much the same role in early chemistry as the neutrino did in particle physics.
Rose and Langley (1986) described STAHLp, a rational reconstruction of the earlier system that showed all of its discoveries could be explained in terms of inconsistencies and their resolution. In addition, they used the system to model a number of other reaction-oriented discoveries from the history of science. Moreover, their approach showed that dependency-directed reasoning simplified the theory revision process, letting their STAHLp handle problems with a search-control scheme that relied on simple hill climbing.
The BR-3 system, presented by Kocabas (1991), extended this framework to include the detection of incomplete theories, and the postulation of new properties to explain the absence of reactions. Kocabas applied this idea to the history of particle physics, using it to explain both the origin of several quantum numbers and the particular values assigned to them by scientists. In related work (Kocabas, 1994), he described another system TREV which formulates new particles and new reactions, but this system does not integrate these functions in its discovery process. BR-3 was the immediate precursor of BR-4, differing mainly in that the former lacked the ability to postulate new particles and to predict new reactions.
Valdes-Perez (in press) has described an alternative approach to discovery in particle physics, which he has implemented in the PAULI system. This scheme use a variation on linear programming to search the space of property values, subject to constraints that reflect observed and unobserved reactions. Also, Fischer and Zytkow (1992) have reported on GELL-MANN, a system designed to explain the formation of the quark theory, which also carries out a search through a space of parameter values subject to constraints.
A more general framework, proposed by Valdes-Perez, Simon, and Zytkow (1993), views the process of formulating structural models in terms of matrix operations. They show how many existing systems, including those described above, can be viewed in this light, with the basic operations involving the extension of a matrix along one or more dimensions and the revision of entries in the cells of the matrix. Our own BR-4 system also fits well into this framework, as suggested by our use of Valdes-Perez et al.'s terminology in Section 2.
Other research on theory revision seems less closely related. Rajamoney's (1990) COAST system designs experiments to distinguish between alternative structural models in physics, and Karp's (1990) HypGene uses a similar idea for biological theories. Kulkarni and Simon (1990) describe KEKADA, a computational model that integrates theory revision, experiment design, and problem formulation to model Krebs' discovery of the urea cycle. Shrager and Langley (1990) consider the relations among these systems in more detail.
4.3. Directions for Future Work
Although BR-4 provides an abstract account for some important developments in the history of particle physics, there remains considerable room for extensions to the model. One direction for improvement involves the notion of explanation. In some sense, the current system formulates explanations when it finds that a newly observed reaction is consistent with the existing theory or when it proposes a new property that rules out an unobserved reaction. However, BR-4 does not generate an explicit proof or other structure that connects assumptions and observations. In future work, we plan to model the explanatory process in more detail, with the system deducing the presence or absence of specific reactions from declara tive statements of quantum properties and conservation laws. In turn, this may let us recast BR-4's operators in terms of an abduction process (Ng & Mooney, 1990; O'Rorke et al., 1990) that modifies assumptions to explain known phenomena.
We also hope to extend the system to handle the introduction of componential models, which describe particles at one level as combinations of more primitive particles. Langley et al.'s (1987) DALTON took some initial steps along these lines to explain the relations between chemical molecules and elements, but we believe that we can adapt BR-4 to explain the origins of the quark theory and its alternatives. The basic task here involves explaining why elementary particles with some quantum properties exist and others do not. The constraints of consistency and completeness, which play such a central role in BR-4, seem well suited for this problem, which involves postulating new component particles (quarks), then searching the space of quantum values and their compositions that satisfy certain constraints (e.g., symmetry) for known particles and violate these constraints for nonexistent ones.
Finally, like most other models of scientific discovery, BR-4 ignores the interactions that occur among different researchers. Scientists cooperate along some dimensions, with theorists passing on predictions to experimentalists, who in turn report their observations to theorists. They also compete in developing theories to explain new findings, in discovering evidence for predicted events, and by noting errors in others' reasoning. The history of particle physics is rich in examples of such interactions, and we believe that some revisions to BR-4 will let us model some of them. In particular, we plan to assign different facets of the system's domain knowledge to different agents, which would communicate through a common representation; we will also let different agents explore different branches when search suggests alternative solutions.
5. Concluding Remarks
In this paper we presented BR-4, an abstract computational model of scientific discovery. We examined the system's behavior on three problems from particle physics, showing that it can replicate, though in a schematic way, important steps in the historical development of this field, some of which were considered major discoveries when first introduced. In particular, BR-4 proposes the existence of the neutrino to avoid violating conservation of spin, it invents baryon and lepton numbers to explain the absence of reactions involving proton decay, and it postulates electron and muon numbers to rule out unobserved neutrino reactions. In addition, the system can determine appropriate quantum values for each particle, and it can predict the reactions implied by a set of particles and quantum properties.
The BR-4 model accomplishes these feats using simple processes that play a central role in many aspects of human cognition. The system employs four basic operators for determining property values, creating new properties, positing new particles, and predicting reactions. Moreover, it uses consistency and completeness constraints to selectively apply these operators, and it incorporates depth-first control scheme to carry out search when necessary. The simplicity of these mechanisms, and their similarity to other processes observed in human behavior, suggest that one can explain some aspects of scientific creativity in similar terms.
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