A Study with CER in High-Temperature Superconductivity
Sakir Kocabas
Dept. of Space Engineering, Istanbul Technical University,
Maslak 80626, Istanbul, Turkey.
Abstract
In this paper we describe a program, CER, which models some of the research activities carried out in the process of the discovery of high-temperature superconductors in 1986 and 1987. These activities include goal and strategy choosing, literature searches, proposing experiments, expectation setting, designing and conducting experiments, data collection, generating and testing hypotheses, modifying hypotheses, and generating explanations.
CER’s design includes many of the elements of scientific research and discovery and provides a step toward a complete computational model. The system has 17 discovery operators which use over 150 methodological rules many of which are general and applicable to other domains of physics and chemistry.
Keywords: Scientific discovery, autonomous operators, methodological rules, consistency, completeness, hypothesis generation, scientific explanation.
1 Introduction
Among the computational models of scientific discovery developed until recently, the KEKADA system (Kulkarni & Simon, 1988; 1990) is interesting in the way it simulates several different research tasks. The CER system described in this paper introduces many improvements on KEKADA by providing a more detailed representation of scientific research and thus constitutes a more comprehensive computational model. CER is designed to model the discovery of high-temperature oxide superconductors in an interrelated series of tasks such as proposing research goals, choosing research strategies, proposing experiments, designing and conducting experiments, data collection, generating and testing hypotheses, verifying, modifying or deleting hypotheses, the supervision of goal satisfaction, and generating explanations.
Our reasons for choosing high-temperature superconductivity as the domain for modeling scientific research are as follows: 1) Research in high-temperature superconductivity is well documented in short articles and research reports published in several leading science journals, 2) it is relatively easy to trace and reconstruct the historical progress of the discoveries, the introduction of new hypotheses, the development and transformation of the theoretical ideas, and their influence on subsequent research in this field, 3) a study into the discoveries in this field should enable us to build more realistic models of scientific research and discovery, and 4) we would be able to test our results in an active field of research.
CER's domain knowledge is largely based on about 1200 research reports and short articles on high-temperature superconductivity, published in science journals such as Physics Today, Nature, Japanese Journal of Applied Physics and Physical Review-B between September 1986 (when Bednorz and Müller's paper first appeared in Zeitschrift für Physik) and November 1988. Some of the information was obtained through interviews with researchers in high-temperature superconductivity. Most of CER's methodological knowledge was elicited from the research reports. The system's general theoretical knowledge, which includes detailed information about all the chemical elements in the Periodic Table as well as information about various oxide compounds, was drawn from physics and chemistry handbooks.
The reports mentioned, contain numerous details of the elements of scientific research such as research goals, strategies, experiments, expectations, experiment results, hypotheses, verification (or falsification) of the expectations and earlier hypotheses, explanations, and also suggestions for further research. Based on these articles and research reports, we have constructed a chronological order of the theoretical and empirical developments in this field.
This paper is organised as follows: Section 2 presents a summary of the developments which led to the discovery of high-temperature superconductors in a chronological order. Section 3 describes the CER system in terms of its knowledge representation, interactions, its operators and its initial knowledge. Section 4 provides an example of how CER simulates the discovery of high-temperature superconductors. In section 5, generality of CER's knowledge representation, system operators, and search methods are discussed. Finally, Section 6 sums up the conclusions drawn from the CER experiment with suggestions for future work.
2 High-Temperature Superconductivity
Superconductivity is a phenomenon occuring at low temperatures in some electrical conductors, in which conduction electrons undergo a collective transition to an ordered state with many unique and remarkable properties. These include the disappearence of electrical resistivity, appearence of large diamagnetism and other unusual magnetic effects, substantial alteration of many thermal properties and the occurence of quantum effects otherwise observable only at the atomic and subatomic level (see e.g. Langenberg, 1987).
2.1 The Discovery of Superconductivity and the Early Developments
The story of superconductivity begins in Leiden in 1911 when H. Kammerlingh Onnes, after succeeding to liquify helium, decided to conduct physical tests on various materials. While measuring the electrical resistivity of mercury, he noticed that the resistivity fell sharply toward zero at 4.2K. Subsequently other superconducting elements, alloys and compounds were found. The temperature at which the transition to superconducting state occurs is called the critical temperature (or Tc). In 1933 W. Meissner and R. Ochsenfeld discovered that a metal cooled into the superconducting state in a magnetic field expels the field from its interior ("Meissner effect").
Superconductivity remained to be a much studied but puzzling phenomenon for nearly half a century after its discovery. A great deal of experimental information was accumulated on its occurence and properties, and several useful phenomenological th
eories were developed. Then in 1957, J. Bardeen, L.N. Cooper and J.R. Schreiffer proposed the first successful micro-physical theory of superconductivity (the BCS theory). This theory can explain how and why the electrons in a conductor may form an ordered superconducting state and makes predictions about many properties of superconductors, which are in good agreement with experimental data. Many of the current theories on superconductivity are variations of the BCS theory.
Onnes' discovery of superconductivity can be characterised by a general research goal such as: "Investigate the physical system in extreme conditions," rather than a specific goal. The extreme conditions are physical conditions such as extremely high/low temperatures, pressures, magnetic fields, electrical fields and gravitational fields. In fact many earlier discoveries in the physical sciences are the products of the activities to accomplish goals suchas these. Modern high-energy physics and astrophysics still have much to study within the framework of this general goal.
2.2 The Discovery of High-Tc Superconductors by G. Bednorz and A. Müller
When Bednorz and Müller started their research, a number of superconducting oxides such as Ba(Pb,Bi)O3 and Li Ti2O4 were known. Also, the superconductivity of oxide coated aluminium films and granules was known. A complete explanation of the origins of the superconductivity in Ba(Pb,Bi)O3 was not available, but was of great intrerest to pysicists in the early 1980s (see Beasley & Geballe, 1984). A summary of the reconstruction of the events that led to the discovery of the La-Ba-Cu-O superconductor, based on the interviews of Khurana (1987a; 1987b) with Bednorz and Müller, is as follows:
1- A. Müller noted that the critical temperature (Tc) of the films composed of small, oxide coated grains of aluminium, was about twice that of pure aluminium which has a Tc of 1.1K.
2- He found this very interesting and wondered whether a similar enhancement in Tc could be made in metallic oxide superconductors whose critical temperatures were already in the 10-15K range.
3- But the theorists told him that because of its low Tc, aluminium was described by the weak-coupling BCS theory, but that the ehancement was not possible in superconductors with Tcs 10-15K, which were better described by the so-called strong-coupling th
eory.
4- Müller decided not to listen to the theorists (see, Khurana, 1987b). Bednorz and Müller thought that they could raise the Tc oxide superconductors.
5- They were motivated by the unusual properties of the superconducting phase of BaPb(1-x)Bi(x)O3 and LiTi2O4 . Despite their low electron density these oxides have relatively high Tcs. They argued that the lower electron density in oxide superconductors was probably compensated for by the enhanced electron-phonon interaction. Bednorz and Müller saw in BaPb(1-x)Bi(x)O3 a possibility of finding superconductors with higher Tcs.
6- They reasoned that increasing the electron density in oxides to values comparable to those in real metals, might allow to increase the Tc.
7- They regarded the metallic behavior in electrical conductivity as an important indicator in selecting compounds for superconductivity tests. They carried out a detailed and determined search for superconductors with high Tcs among oxides with metallic properites.
8- Bednorz and Müller were aware that the resistivity of thin films of BaPb(1-x)Bi(x)O3 increases before the onset of superconductivity, especially if the films do not have the right amount of oxygen.
9- Based on their knowledge about the electrical properties of oxides, they focused on oxides containing copper or nickel in mixed valency states, that is oxides in which a fraction of the transition metal ions are in one valence state and another fraction in a different valence state. They made systematic and careful study measurements on the resistivies.
10- Bednorz also searched the literature for known oxides of copper and nickel and studied carefully whatever was known about their high temperature properties.
11- Their experimental study started with LaNiO3, an oxide in which nickel is in valence +3. They tried to change the electronic bandwidth of the material internally, by substituting aluminium for nickel. (Al and Ni have very low electrical resistivities, high electron densities and have similar valency states.)
12- The substitution was not successful: La-Ni-Al-O became an insulator on cooling.
13- Then they tried substitutions on the lanthanum sites. They tried yttrium substitutions, but ended up with insulating materials. At the time they missed discovering the 90K superconductor. They had the wrong combination - yttrium with nickel instead of copper.
14- The focus of research shifted to copper, because partial substitutions of copper for nickel in LaNiO3 improved the metallic properties.
15- In the course of a literature search, Bednorz learned about the work of C. Michel, L. Er-Rakho and B. Raveau of Universite de Caen on La-Ba-Cu-O, soon after it was published in 1985. Having worked already with a few copper substitutions, Bednorz realized that they could do something with copper alone and with the partial replacement of lanthanum by two-valent barium.
16- They totally replaced Ni with Cu in LaNiO3 and turned their attention to the lanthanum sites for substitutions in the La-Cu-O structure. They tried the partial substitutions of Ba for La in this compound.
17- During these partial substitutions, they discovered the superconductor La(5-x)Ba(x)Cu5O5(3-y) for x=1, x=0.75 and y >>0 which showed onset of superconductivity above 30K.
18- Their first paper received little attention. But S. Tanaka's group at the University of Tokyo and P. Chu's group at the University of Houston independently confirmed superconductivity in La-Ba-Cu-O after they saw the paper by Bednorz and Müller in Zeitschrift für Physik.
19- The Tokyo group by this time (December 1986) independently determined La(2-x)Ba(x) CuO(4-y) to be the superconducting phase, as had Bednorz, Müller and their collaborator Takashige and both groups had obtained further evidence of superconductivity by measuring the Meissner effect.
2.3 Discussion
In contrast to Onnes' discovery of superconductivity, Bednorz and Müller's discovery of high-Tc superconductivity was directed by specific goals. From the account given above, their research goals can be formulated as follows: 1) Explain the unusual increase in Tc of oxide coated films and granules of superconducting metals (e.g. of aluminium), 2) explain why Ba(Pb,Bi)O3 has a high Tc despite its low electron density, 3) study the possibility of the existence of oxide superconductors with higher Tcs.
Bednorz and Muller were motivated by the relatively high Tc of the oxide coated films of aluminium, and by the properties of the oxide superconductors Ba(Pb,Bi)O3 and LiTi2O4. The former had unusual properties: In addition to the low electron densities, it had a small and in some cases non-detectable heat capacity increase at the transition temperature. The origins of the superconductivity in Ba(Pb,Bi)O3 was not known, but was of great intrerest to the scientific community in the early 1980s.
In their experiments, Bednorz and Müller did not try to substitute Y for La in La-Ba-Cu-O, probably because that they had tried the Y substitution earlier on LaNiO3 with unsuccessful results and generalized their reasults. On the other hand, their experimental strategy worked well, so that it would later lead Paul Chu and his group to the discovery of a new class of oxide superconductors, Y-Ba-Cu-O, with much higher Tcs (around 90K) than that of La-Ba-Cu-O.However, the hypothesis "Substitution of Y for La does not improve Tc," did not prove to be useful. A similar situation was observed later, in the substitution of elements with magnetic moments for Y in Y-Ba-Cu-O compounds, with results to disprove the earlier hypothesis that the presence of atoms with magnetic moments markedly suppress superconductivity.
2.4 Later Developments
We will not list the subsequent developments here, for this would far exceed the limits of this paper. Instead, we will present a brief discussion as follows: After the results of Bednorz and Müller were confirmed by Tanaka's group at the university of Tokyo and Chu's group at the University of Houston, research on the La-Ba-Cu-O based compounds accelerated. The proliferation of research groups involved in high-Tc superconductivity introduced parellelism into research in this field with each group having its own set of priorities, specific goals and strategies.
While many groups continued to search for materials with higher Tcs, some focused their efforts on the physical and chemical structure of the new materials, some groups were conducting experiments to test the validity of the current theoretical explanations of the phenomenon, and still others on how to improve the methods of manufacturing these materials. Yet, the research strategies adopted by Bednorz and Müller were followed by most of those research groups that were directly invol ved in finding materials with higher Tcs. For a long time (over 12 months), experiments were conducted to find compounds with higher Tcs in the La-Ba-Cu-O based materials.
It appears that a combination of "hill-climbing" and "depth-first search" research strategy was adopted in research during this period, determined by the early discovery of Y-Ba-Cu-O superconductor which has about three times the Tc of the original La-Ba-Cu-O compound. The strategy shift took place only after almost all the possible substitutions on the Y-Ba-Cu-O were exhausted. In fact the successful substitution of non rare-earth elements was coincided with the strategy switch to the Ba(Pb,Bi)O3 oxide, which led to the discoveries of Tl-Ba-Cu-O and Bi-Ba-Sr-Cu-O superconductors, one after the other, both with Tcs above 100K.
Because of the involvement of many research groups and the variations in their goals and research strategies, many hypotheses were generated on the possible causes of the increase and decrease of the Tc of these materials, some of which were in contradiction with one another. As a result, many of the earlier hypotheses were abandoned (e.g. the hypotheses on the effects of the existence of magnetic elements, crystal structure, the importance of Cu-O chains and Cu-O planes), but some others are still in effect e.g. the hypotheses on the effects of the substitutions of Al, Ag.While some predictions of the BCS theory were refuted e.g. in La-Ba-Cu-O compounds, the energy gap was not related to Tc in the way the BCS theory predicts and the phonon mechanism, and the isotope effect in La-Ba-Cu-O was too small (about 1/10 of the BCS prediction), others remained in effect e.g. the existence of electron pairs.
3 An Overview of CER
CER consists of a knowledge base, an explanation based generalization program (Mitchell, Keller, & Kedar-Cabelli, 1986), a set of system operators each consisting of a series of condition-action rules, a classifier (Nilsson, 1965), and a small set of primitive Prolog function definitions to assist input, output and list processing. In this section the system's organisation and representation of descriptive and definitive knowledge is explained first. This is followed by a desription of the system's control architecture and prescriptive knowledge. The system's prescriptive knowledge is represented by a series of operators, which carry out its research activities. Each operator is described in terms of its inputs, activities and outputs.
Some of these operators use a linear classifier in choosing goals, strategies, methods and processes from among the alternatives. The classifier itself is described in terms of its inputs and outputs.
3.1 The System's Organisation and Representation of Descriptive and Definitive Knowledge
CER's descriptive and definitive knowledge is represented as categorized predicate statements in Prolog, organised in the following categories: 1) logical knowledge, 2) formal knowledge, 3) epistemic knowledge, 4) theoretical, hypothetical, empirical knowledge, 5) factual knowledge, 6) historical knowledge. This categorization is based on the criteria developed by Kocabas (1989), and was implemented in (Kocabas, 1991). Examples of the system's descriptive and definitive knowledge presented in relation with their categories below, also indicate the dimensions of its initial knowledge.
Logical knowledge of CER contains the definitions of logic functions and some logical relationships between types of expressions, e.g.,
"larger" is a transitive relation.
"same_group" is a reflexive relation.
Formal knowledge contains domain definitions, class memberships and class-superclass relationships. Some examples of CER's knowledge in this category are:
Ni is an element in LaNiO3.
"Na" is the symbol of sodium.
Its initial formal knowledge includes statements such as.
Superconductivity is a physical property.
Theoretical analysis is a strategy for explanation.
Gathering knowledge is a strategy for explanation.
Experimentation is a strategy for studying a phenomenon.
Element substitution is a process.
CER's factual knowledge includes factual statements about its domain objects. An example of its factual knowledge is:
The price of Scandium is over US$ 50,000 per kilogram.
CER's theoretical knowledge contains theoretical, hypothetical and empirical statements acquired or generated by the system. Examples of theoretical knowledge are:
The Tc of Y-Ba-Cu-O compound is 91 K.
Specific heat and high-Tc superconductivity are related.
Presence of magnetic ions reduce superconductivity.
Superconductivity and electron density are positively related.
Aluminium, copper, gold and silver have high electrical conductivity.
Substitution of elements with high electrical conductivity improves electron density.
Some of the arguments in theoretical statements refer to processes. CER's knowledge of processes and events are represented by qualitative schemas (Forbus, 1984).Reference to a process in a high level theoretical expression appears as follows:
the(reduces,process(substitution/of,tve,y,ybco),tc).
which means that a tetravalent element substitution forY in Y-Ba-Cu-O superconductor reduces Tc. The process is represented by a schema as follows:
process([substitution/of,[tve,y,ybco]],
substances([E,ybco,...]),
preconditions([formal(tve,E), formal(same_group,E,y),...]),
process_conditions([...]),
products([...])).
where "substances" indicate the substances involved in the reaction, "preconditions" indicate the conditions for the event to take place (e.g., E is a tetravalent element, E is in the same grup as yttrium), "process conditions" describe the physical conditions (such as temperature, pressure, etc.), and "products" indicate the products obtained.
CER's epistemic (or meta) knowledge contains statements about its domain predicates, hypotheses, etc. It is important to know in record, if certain acquired or generated hypotheses can explain a phenomenon under consideration. Some examples of such statements are:
Superconductivity is an important property.
The superconductivity of Ba(Pb,Bi)O3 is not explained.
The isotope effect holds for metal superconductivity.
Electron-phonon interaction mechanism explains superconductivity.
In these statements "isotope effect" and "electron-phonon interaction" refer to an experimental process that can be tested indirectly.
Historical knowledge contains the records of the historical development of research in superconductivity starting from Onnes' discovery of the phenomenon in 1911. It also includes the records of the conducted experiments to avoid repetititons and the records of the refuted hypotheses. Some examples of CER's "historical" knowledge are:
"Superconductivity was discovered by H.K. Onnes in 1911."
"Al was substituted for Ni in formula LaNiO3 to yield compound LaAlO3."
CER's initial knowledge is the logical, formal, epistemic, theoretical, factual and historical knowledge in its knowledge base, as exemplified above. The system's initial knowledge also includes detailed formal, theoretical and factual knowledge about all the chemical elements in the periodic table, covering more than forty properties for each element. Since CER's descriptive knowledge is maintained as separate from its prescriptive knowledge, new descriptive domain knowledge can be added to it. The system also accepts, by interaction, the results of the experiments it has proposed. Some other interactions occur during its activity (e.g. assigning time limits to strategies, methods and experiments). These are indicated in the section that describes the system's behaviour below.
During its run, some information such as the time limits to its goals, strategies, methods and processes are provided to CER by interaction. Also, simulation is carried out externally to represent the activities of the operators that have not yet been implemented, and the outcomes are given to the system.
3.2 CER's Control Knowledge
The design of a comprehensive computational model of discovery must ultimately include all the essential elements of scientific research. Accordingly, it must include the following research tasks: Proposing research goals, choosing a goal among alternatives, formulating a framework for the selected goal, proposing strategies to achieve the goal, choosing a strategy among alternatives, gathering and organising knowledge, identifying and resolving conflicts. It must also include the tasks of proposing, designing and conducting experiments, setting expectations for designed experiments, testing and data collection, generating hypotheses, verifying and modifying hypotheses, supervision of goal satisfaction, generating explanations, and constructing theories by finding higher level relationships in hypothetical and empirical knowledge.
CER's design includes seventeen system operators for its research tasks, and a control opeator with an explanation based learning subsystem. Its operators are organised in two levels, the former are level-1 operators and the latter is its only level-2 operator. Each operator consists of a set of condition-action rules. Currently, as explained below, only five of these operators have been implemented.
In order to accomplish its research objectives, the program has to carry out its research tasks in a certain order. For this reason, it must know which operator to activate first, and what other(s) after the completion of a certain task. The system has a hierarchic homuncular control architecture (Kocabas, 1991b), and learns its control knowledge by explanation based generalization (Mitchell, et al., 1986). The control operator activates the task operators according to the state of a message list that functions like a blackboard.
3.3 CER's Methodological Knowledge and Research Operators
CER's level-1 operators are named as follows: Goal Setters, Goal Choosers, Framework Setters, Strategy Proposers, Knowledge Gatherers, Knowledge Organisers, Conflict Identifiers and Resolvers, Experiment Proposers, Experiment Designers, Expectation Setters, Experimenters, Experiment Data Collectors, Hypothesis Generators, Hypothesis Verifiers, Goal Satisfaction Supervisers, Explanation Generators, and Theory Builders.
Among these, only the Goal Setters, Goal Choosers, Framework Setters, Strategy Proposers and Experiment Proposers have been implemented, while Knowledge Gatherers, Conflict Identifiers and Resolvers, Experiment Designers, Hypothesis Generators and Goal Satisfaction Supervisers are partially developed. The rest have yet to be developed from design to computational implementation. CER is a major project still under development, and the reason for including the latter in the system description at all, is to indicate the scope for its future development.
As will be explained below, some of CER's operators (namely, Goal Choosers, Strategy Proposers, Knowledge Gatherers and Experiment Proposers) employ a simple trainable linear classifier (Nilsson, 1965) in choosing goals, strategies, methods and experiment materials among alternatives. The use of such classifiers is essential in decision making that involves conflicting constraints. We can now describe the system's operators in terms of their inputs, activities and outputs. In their descriptions, occasionally their acronyms are used for conciseness.
3.3.1 Goal Setters
Most intelligent activities can be considered as oriented towards achieving a set of goals, though some of these can be ambiguous or general. CER's goal proposing rules (GS) are confined to scientific interest. CER proposes research goals such as explaining an unusual phenomenon, studying an unexplained phenomenon, and more specifically, studying the possibilities of improving the desired properties of a compound.
Well-defined goals usually have a time limit for their satisfaction. More general and more important research goals are normally given longer time limits. One of the GS rules of CER assigns time limits to the proposed goals, and another one checks if the goals are correctly formulated, and asks them to be reformulated as necessary. The system currently has thirteen such rules. High level description of some of CER's GS rules are as follows:
If a phenomenon shows unexpected or unusual characteristics, then make it your goal to explain it.
If a phenomenon has not been explained, then make it your goal to explain it.
If a phenomenon is not explainable, then make it your goal to study it.
If a physical property is an important property, then try to enhance that property on some substance.
If a goal is entered to the agenda, then assign a time limit to it.
Inputs to Goal Setters are descriptive and definitive knowledge in the knowledge base, by means of which the system can generate its research goals. Inputs to this operator can be epistemic statements such as
The superconductivity of Ba(Pb,Bi)O3 is not explained.
The superconductivity of oxide coated films of aluminium is not explained.
Superconductivity is an important property.
and formal statements like
Superconductivity is a physical property.
Oxide superconductivity is a kind of superconductivity.
and theoretical statements such as
LiTi2 O4 has superconductivity.
Ba(Pb,Bi)O3 has superconductivity.
The outputs of Goal Setters are expressions labeled as messages with the internal label "goal" and an assigned time limit. A goal can be like
Explain the superconductivity of Ba(Pb,Bi)O3.
Improve superconductivity in an oxide compound.
The time limits to goals are given by interaction, which indicate the length of time that the goal can be on the agenda. Any goal whose time limit has expired is dropped from the agenda by Goal Satisfaction Supervisers (described below).
3.3.2 Goal Choosers
Choosing between goals, strategies and experiments can be an important task in scientific research, and in many cases may require, in addition to methodological knowledge, a large amount of commonsense and theoretical knowledge. CER currently has two Goal Choosers (GC), which have both been implemented. One of these rules uses the system's classifier to choose between proposed goals. The classifier uses several criteria: cost, reward, time limit, achievability (by existing knowledge and by existing technology), and likeliness to be achieved by other researchers before. The values of these parameters are qualitative and some of them are given to the classifier externally, while others (such as cost, availability) are drawn from the system's knowledge base. The rules of this operator are as follows:
If there are more than one goals, then use the classifier to choose a goal, and label it as the current goal. If there is only one goal, then label it as the current goal.
If the classification fails, then select a goal randomly.
So, the input to this operator is a set of goals with assigned time limits, and the qualitative values given to the parameters of the classifier for each goal, while the output is a single goal, with the internal label "current goal".
3.3.3 Framework Setters
When a scientist pursues a specific research goal, s/he does not have to recall the unrelated knowledge, but considers knowledge relevant to the research project. S/he would recall the less related knowlege for analogy only when the current research strategies, methods and techniques do not produce the expected results (see, e.g. Lenat & Feigenbaum, 1987).
CER's Framework Setters (FS) copy all knowledge related with the current goal from the static memory into the system's dynamic memory. The program currently has four FS rules. These have not yet been fully implemented, and therefore the task is simulated externally. Some examples of the FS rules are as follows:
If the current goal is to explain a hypothesis, then retrieve from the static memory all the relevant information about the current goal.
If the current goal is to improve a property, then retrieve all the relevant information about that property.
The "relevant information" is retreived syntactically, through the predicate names and the other arguments of the statement that expresses the current goal. The inputs of Framework Setters are the messages, which indicate the focus of the framework (e.g., a set of properties and/or objects).
3.3.4 Strategy Proposers
When a research goal is chosen, there may be alternative strategies for it. Moreover, a research strategy may use different methods. Some research goals are simply achieved by literature search, some others by theoretical analysis, and yet others by experimentation. Scientists choose the most appropriate research strategies and sometimes change them during the course of research to achieve their goal in an economic way. CER's Strategy Proposers (SP) perform their task in accordance with the
system's current research goal. One of the SP rules assigns time limits to the strategies. The system currently has fully implemented fifteen SP rules, one of which use the classifier to choose between alternative strategies, on the basis of cost, time required, and likeliness to succeed. The parameter values to the classifier are given externally. The following are some of CER's SP rules:
If the current goal is to explain a phenomenon, then make a list of all the strategies for finding and explanation.
If the current goal is to improve a property P1 and another property P2 is positively related with P1 and a process S1 improves P2, then propose experiments to apply S1.
If the current goal is to improve a property P1 and a process S1 improves P1, then propose experiments with S1.
If the current goal is to improve a property P1 and a process S1 improves P1 and a process S2 causes S1, then propose experiments with S2.
Inputs to this operator can be formal statements such as
Gathering knowledge is a strategy for finding an explanation.
Theoretical analysis is a strategy for finding an explanation.
Experimentation is a strategy for studying a phenomenon.
and theoretical statements such as
Element substitution improves metallic conductivity.
Electron density and metallic conductivity are positively related.
Metallic electrical conductivity and oxide superconductivity are positively related.
Applying pressure improves superconductivity.
Presence of magnetic ions reduces superconductivity.
Half filled electron bands cause superconductivity.
The inputs also include the message that states the current goal. The outputs of this operator are messages that indicate the considered strategies and current strategy with the assigned time limits.
3.3.5 Experiment Proposers
In scientific research, when experimentation is selected as the research strategy, experiments are proposed in accordance with the type of experimental study. For example, experiments in physics and chemistry can be divided into several major groups that can indicate the type. In addition to the general rules about experiment proposals and designs, rules specific to particular types of processes and techniques can also be defined.
The tasks of this operator include the following: Making a list of relevant processes and techniques for the research, determining the relevant test properties for an experiment, determining the experiment materials having these properties, and choosing the best material from a list of candidates. The last task is carried out by classification over a set of parameters such as availability, likeliness to yield success, cost and relative hazards (i.e. radioactivity, explosiveness, toxicity, flammability and corrosiveness). CER currently has eleven Experiment Proposers (EP), three of which use the classifier to choose experiment materials, substitution elements and substituting elements among alternatives. Some of the rules of this operator are as follows:
If the current goal is to study whether the derivatives of a compound with a specific property have the same property, and the current strategy is experimentation, then choose a process for experimentation.
If the current strategy is experimentation applying a particular process, then record that process as the current process.
If a process has been chosen, then assign a time limit for it.
If the current strategy is to study a phenomenon by experimentation, and a process has been chosen, then determine the relevant properties for the experiments.
If the current goal is to improve a desirable property, the current strategy is experimentation, and a process has been chosen, then select the experiment materials with the relevant properties.
If there are alternative experiment materials for the same process, then choose the best material by classification.
Inputs to Experiment Proposers can be formal statements such as
Polimerization is a process.
Element substitution is a process.
Condensation is a process.
Oxidation is a process.
Ni is an element of LaNiO3.
Y and La belong to the same group.
Sr and Ba belong to the same group.
"Related" is a reflexive relation.
Two properties P and Q are related, if they are positively or negatively related.
Al and Ni have similar electrical conductivity.
and theoretical statements like
Superconductivity and Meissner effect are related phenomena.
Metallic electrical conductivity and thermal conductivity are positively related.
LaNiO3 has metallic electrical conductivity.
LiTi2O4 has metallic electrical conductivity.
Ba(Pb,Bi)O3 has metallic electrical conductivity.
Al has high electrical conductivity.
Ni has high electrical conductivity.
Cu has high electrical conductivity.
Inputs to Experiment Proposers also include the messages that indicate the current goal and current strategy. The outputs are messages indicating the relevant processes, relevant properties, the current process, experiment materials, current experiment materials, substitution elements and substituting elements.
3.3.6 CER's Other Operators
Apart from those described above, the system has twelve other designed operators which have not been implemented. These are: Experiment Designers, Knowledge Gatherers, Goal Satisfaction Supervisers, Conflict Identifiers and Resolvers, Hypothesis Generators, Knowledge Organisers, Expectation Setters, Experimenters, Experiment Data Collectors, Hypothesis Verifiers, Explanation Generators, and Theory Builders. The tasks of each operator are described below.
Experiment Designers (ED). The tasks of this operator include determining the test properties, providing the required process description and providing experiment forms, and assigning a time limit to the current experiment. CER currently has five ED rules. The inputs to this operator are the messages output by the EP rules and some formal knowledge (e.g. process descriptions) from the knowledge base. The outputs are messages indicating test properties, process conditions and experiment forms.
Knowledge Gatherers (KG). An intelligent system gathers knowledge, and filters and translates this knowledge into its own representation language in an intelligible and memorizable form. In order to avoid memory overflow with irrelevant informatio
n, it must have a set of relevance criteria for the kind of knowledge it needs for its current goal set. CER's Knowledge Gatherers has been designed in view of these problems. The system currently has five rules. The inputs to KG's are messages issued by Goal Choosers and Strategy Proposers, and formal statements from the knowledge base. Its outputs are the messages that indicate the current method, and the relevant properties for knowledge gathering.
Goal Satisfaction Supervisers (GSS). An intelligent system that can generate its own goals must also be able to determine when these goals are satisfied during the course of its activities. At present, Karp's (1990) GENSIM/HYPGENE is probably the only system with some capability to supervise the fulfilment of its goals. CER currently has six such rules which monitor goal satisfaction by comparing the research results with the current research goal.
Conflict Identifiers and Resolvers (CIR). Conflicts in knowledge systems can appear in the forms of a) inconsistency, b) incompleteness, and c) incoherence. Identification and resolution of conflicts is an important task in maintaining a dependable knowledge system. In order to be resolved, conflicts must first of all be correctly identified in an efficient way. Conflict identification is much dependent on the knowledge organisation and representation of a system. CER's categorised predicate logic representation Kocabas, 1989) facilitates the identification and resolution of conflicts. As a result, the system can identify several types of inconsistency and incompleteness. Incoherences mainly arise from category and type confusions in language. However, the current version cannot handle incoherence problems.
CER can identify contradictions between i) factual statements, ii) theoretical statements and factual statements, iii) theoretical statements, iv) formal statements, v) historical and theoretical statements, vi) theoretical and formal statements, vii) historical and factual statements. The system has seven rules for identifying contradictions, which record them according to their types. (We did not include all the possible combinations of intercategorical contradictions, but the above seven combinations already provide a detailed classification for identifying contradictions.)
CER identifies a state of incompleteness in its knowledge base in the following forms: i) A factual statement (of an experiment) that is not explainable by a theoretical, hypothetical or empirical statement. ii) a theoretical statement which is not explainable by a more general theoretical statement, iii) absence of an effect, property or object (which can be explained by generating exclusion hypotheses). CER has three rules for identifying these types of incompleteness. One of its conflict identification and resolution rules assigns time limits to the activity of this operator, to maintain functionality against lengthy searches.
CER's resolution of conflicts is facilitated by its systematic identification of them in different types. Each type of conflict is resolved in a separate way. For example, a contradiction between two factual statements is resolved by referring to the corresponding facts (by experimentation and/or observation). On the other hand, if the contradiction is between a theoretical and a factual statement, then the validity of the factual statement is checked and as a result, either the generality of the hypothesis is reduced or the factual statement is discarded. An incomplete state can be resolved by generating a goal to find an explanation or to study the phenomenon involved. Such goals are then considered for research.
Hypothesis Generators (HG). Hypothesis formation is one of the most important activities in scientific research, and has been studied extensively. Various methods of hypothesis formation are described in summary by Lenat and Feigenbaum (1987), and by Darden (1987), who classifies hypothesis formation methods as i) induction, ii) retroduction (or abduction), iii) abstraction, and iv) analogy.
The tasks of CER's Hypothesis Generators include: generating hypotheses on the variations in the physical, chemical, etc., properties of the system under study, using induction, abstraction and abduction and further generalization of the new hypotheses. CER currently has forty HG rules most of which were extracted from the research reports on high-Tc superconductivity. The rules have not yet been implemented. Some of the HG rules are as follows:
If a physical effect P1 cancels another effect P2, then hypothesize that there is another effect related with P1 and P2.
If the value of a property P1 changes in parallel with the changes of the value of another property P2 in a physical system, then hypothesise that P1 and P2 are related.
An example of how CER's HG rules generalize experiment results is as follows:
If P is the result of a set of experiments and E is the corresponding expectation, then generate hypotheses from the result in the following way:
Process: S
Property: P
Expectation: E = The process S has the effect R on P.
Expected Qualitative Variation of P : Ve
Experimental Variation of P: V
If V = Ve, then formulate the hypothesis: The process has the effect R on P.
If V = - Ve, then formulate the hypothesis: The process has the opposite effect of R on P.
If V = 0, then formulate the hypothesis: The process has no effect of R on P.
The results of experiments are generalized into hypotheses in stages. (For example, if the experiment result is stated as a factual statement: "Substitution of Al for Ni in LaNiO3 did not improve conductivity," this is generalized in an increasing degree of abstraction in stages as follows:
a) Substitution of Al for Ni in LaNiO3 does not improve conductivity.
b) Substitution of Al
c) Substitution of Al does not improve conductivity.
If in a later experiment, say, the result is
d) Substitution of Al for Bi in Ba-Pb-Bi-O improves conductivity,
then the hypothesis (c) is deleted. Note that (d) does not contradict (b). This example contains multiple levels of abstraction (Darden, 1987).
Knowledge Organisers (KO). The activities of this operator include the organisation of acquired and generated knowledge, translation of gathered knowledge into the system's representation, and classification of predicate expressions into their categories in accordance with CER's categorization scheme.
Expectation Setters (ES). The activities of this operator include: determining which test properties (e.g. crystal structure, conductivity, specific heat) are expected to change values qualitatively in an experiment and whether the experiment should improve, reduce or should not effect these properties.
Experimenters (E). Experimenters must have the necessary technical knowledge and skills on experiment materials, apparatus, procedures, processes and measurements, and safety measures to conduct the experiments under controlled conditions.
Data Collectors (DC). Data collection is an important stage of research in experimental research. CER currently has only one DC rule which dictates the measurement of qualitative and quantitative test properties.
Hypothesis Verifiers (HV). The activities of this operator include checking if a newly generated hypothesis contradicts knowledge in the dynamic memory and proposing to repeat the experiments to test the results when there is a contradiction.
Explanation Generators (EG). The task of this operator is to search for an explanation to a factual statement or a hypothesis in the system's existing knowledge. An explanation to a proposition (e.g. the results of an experiment) is a set of hypotheses in the knowledge base, from which the former is derivable. For example, consider the hypothesis: "Copper substitution improves conductivity." This is explainable by (or deducible from) the following hypotheses:
An increase in electron density improves conductivity.
Copper substitution causes an increase in electron density.
So, to find an explanation to a factual statement or a hypothesis, CER searches for a set of more general, related hypotheses such that the former is deducible from this set.
Theory Builders (TB). This operator is designed to discover higher level relationships between domain concepts. CER's knowledge organisation allows the integration of quantitative discovery systems such as BACON. Therefore, quantitative discovery can be incoporated into this subsystem.
3.4 CER's Classifier
CER uses only one classifier (Nilsson, 1965; Hunt, 1975) for several different classification tasks.1 In experimental scientific research, preference is normally given to materials that are less costly, more easily available, more likely to yield success, and less hazardous. It is easy to see that these criteria can be in conflict with one another. For example, a particular material can be cheap, but highly toxic; another material can be easily available, but less likely to yield successful results in the proposed experiments. In such cases, the problem is to find the best material against a set of conflicting parameters. Purely rule based methods cannot resolve such problems efficiently, unless some supplementary methods are used to eliminate a large number of such rules, for, as the number of classification parameters increase, the number of rules required for classification can increase exponentially. Whereas a classifier can pack n! sets of rules in a vector of n parameter ranges. Additionally, classifiers can provide approximate solutions with incomplete data. For reasons of space, we will not give a detailed description of CER's classifier here, but will merely provide an outline of its features instead.
CER's classifier is invoked by some of the system's rules, and uses different evaluation matrices for different classification tasks such as choosing goals, strategies, methods, processes and experiment materials from among alternatives. These matrices can be created, developed and modified on the run without impairing the system's activities, and can be saved for future use. The classifier can be trained in two different ways: 1) by directly providing qualitative values to each parameter (e.g. cost, availability, relative hazards, etc.), 2) by learning from failure, in which case, the parameter values given to the correct object are used as increments in modifying the matrix. CER's classifier can build its evaluation matrices entirely by this second type of learning. In other words, learning by failure is applicable to it even when the evaluation matrix is blank. However, in this method learning is incremental and therefore slow.
--------
1 The classifier is a short program (about 4K), also implemented in Prolog.
3.6 The System's General Behaviour
Having described CER's control and research operators, we can now examine its behavior in the framework of its scientific research activities. The system's behavior depends on the control knowledge that it has acquired through training. Therefore, w
e can only present a description of its behavior in reference to a set of control rules that it has acquired after a training session. What follows is the general description of the system's behavior after such a training session.
In its first run, the program generates a set of research goals from the records about unexplained phenomena, important physical properties and contradicting hypotheses in its knowledge base. As illustrated in Figure 2, CER generates basically two kinds of research goals: 1) finding an explanation to a phenomenon, 2) studying a phenomenon. Once it has formulated its research goals, it assigns time limits to them. Its next task is to choose a research goal to focus on. When the research goal is selected, a research framework has to be drawn, so that the system can focus on the relevant aspects of the research problem, by recalling the relevant information about the objects, properties and relations from its static knowledge base. Next, the system proposes research strategies, and then selects a strategy from the general strategies that it knows.
CER knows two general strategies for explaining a phenomenon: Gathering knowledge from external sources, and theoretical analysis. If the current goal is to explain a phenomenon, the system can try to find the explanation by several different methods: Gathering knowledge from books, journals and software, and from experts. The program chooses its strategies and methods by classification. If the explanation is still not found, then the next strategy, theoretical analysis over the new knowledge state may provide the answer.
The system has two strategies for studying a phenomenon: Theoretical analysis and experimentation and/or observation, for which there may be a number of alternative processes and techniques. For example, in studying a physical phenomenon, new materials with certain properties may need to be synthesized, which may require the application of certain processes.
In order to study a phenomenon, CER proposes strategies, and chooses a strategy. If the strategy is experimentation, then it proposes processes for experimentation, and chooses a process. Then it finds the appropriate materials for the experiments, from which the system chooses the best experiment materials. After the experiment materials are determined, experiments are designed, expectations are stated, and then experiments are conducted. The experiment results are compared with the current goal, and if the goal has not been satisfied, alternative materials, processes, and strategies are tried. The research continues until all goals are achieved, or their time limits expire.
CER's search in pursuing its goals can be viewed as a combination of heuristic search and best-first search. Heuristic search is employed by the activities of the system's methodological rules. The program's search in choosing goals, strategies, methods, etc., can be viewed as best-first search, for its behavior in these cases is dependent on the weights given to the alternative choices. CER's control message list functions like a constantly changing agenda, by means of which the system's control operator directs its activities.
4 Simulation of the Discoveries of High-Tc Superconductors
In this section we will describe the steps of CER's behavior when placed in the problem situations faced by the physicists before the discovery of the high-Tc superconductors. CER models a complex series of tasks leading to a discovery, and differences in CER's background knowledge leads it to choose different goals, strategies, methods and experiments, and hence, to different research routes and results. Since some of its operators have not been fully developed computationally, certain activities of the system were simulated externally. In such cases we will discuss the reasons for the interactions, what kind of background knowledge was necessary for CER to make the choices independently, and what might have led Bednorz and Müller to make the choices they did. These are provided in separate paragraphs enclosed in square brackets, following the description of the system's activities.
For reasons of space, we will only provide a summary of CER's behavior in pursuing only one of the goals it proposes in some detail. For simplicity, the descriptions, do not contain any reference to the training of CER's control operator for the control rules. Also, for the same reasons, the classification activities of the system's classifier are described only in terms of the inputs and outputs. The section ends with an overview of the simulation.
4.1 The Simulation
When CER is run, its Goal Setters is activated, which proposes three research goals, on the basis of the system's descriptive and definitive knowledge. These are as follows:
G1: Explain the superconductivity of the oxide coated films of aluminium.
G2: Explain the superconductivity of Ba(Pb,Bi)O3.
G3: Study the possibility of improving superconductivity in an oxide compound.
The Goal Setters assigns time limits to the proposed goals. The time limits are provided by interaction. (In the particular run we describe here, we assigned G2 the shortest and G3 the longest time limits.)
[CER uses its grammatical and theoretical knowledge about the objects and events for formulating these goals. It's Goal Setters operator produces them from statements like: "The superconductivity of oxide coated aluminium films is not explained," "The superconductivity of Ba(Pb,Bi)O3 is not explained," and "Oxide superconductivity is an important property," in the system's knowledge base. The program does not derive such high level knowledge from its theoretical domain knowledge, but is provided with it in its grammatical knowledge. The acquisition of such knowledge requires theoretical, technical, and commonsense knowledge.]
When the goals are proposed in this way, the control operator passes the control to CER's Goal Choosers operator, which uses the system's classifier to choose the goal which must be focused on first. This operator chooses second goal (G2) as the current goal against four criteria: reward, achievability, likeliness to be achieved by others before, and time limits. Each metric has three ranges: high, medium and low.
Once the current goal is chosen, control passes to the Framework Setters operator, which retrieves the other relevant knowledge about Ba(Pb,Bi)O3, and its components Ba, Pb, Bi and O, from static memory to dynamic memory.
[The "relevant knowledge" includes information about the various physical and chemical properties of the compound and its components. CER's Framework Setters operator has not been fully implemented, and its activities are simulated externally.]
Then the Strategy Proposers operator is activated, which considers the strategy of explanation by gathering knowledge and theoretical analysis. Time limits to the strategies in view of the current goal are determined by interaction. The operator u
ses the classifier to choose between the two strategies, and gathering knowledge is selected as the current strategy on the basis of cost, required time, and likeliness to succeed.
[Since the current goal is to explain a phenomenon, only the strategy rules that are related with explaining a phenomenon are activated. CER has only two strategies for explaining a phenomenon, which are knowledge gathering and theoretical analysis. The values to the parameters of the classifier are provided by interaction. To decide about the costs and the likeliness of success requires commonsense and theoretical knowledge. Currently, CER's knowledge base does not contain such knowledge.]
Then control passes to CER's Knowledge Gatherers operator, which uses the classifier to choose between several methods of knowledge gathering such as consulting books, journals, domain experts and software. The classifier chooses to consult domain experts on the basis of the values provided to the parameters of cost, required time, and likeliness to succeed. When the activities of Knowledge Gatherers come to an end, control passes to the Goal Satisfaction Supervisers operator, which decides whether the current goal has been satisfied.
[The outcomes of the supervision of goal satisfaction is provided externally, as this operator has not been implemented. At this stage, if the Goal Satisfaction Supervisers operator decides that the goal has not been satisfied, and the time limits assigned to the current method and strategy has not expired, the control operator transfers control to the Knowledge Gatherers and Strategy Proposers, to try the alternative methods and strategies. This is facilitated by the deletion of the current method and strategy after they have been tried, so that the system can focus on the remaining methods and strategies only.]
After failing to find an explanation for the unusual properties of Ba(Pb,Bi)O3 within the assigned time limit, CER focuses on the first goal (G1) and thus tries to find an explanation for the unusual behaviour of oxide coated films of aluminium. It considers the strategies of explanation and tries knowledge gathering first and then theoretical analysis. These strategies fail to produce an explanation.
When CER ends its research on these two goals, the remaining one (G3) becomes the current goal. Control passes to the Strategy Proposers operator, which proposes the strategy, "Improve metallic conductivity by experimentation," together with two a
lternatives, "Apply P1," and "Apply P2" where P1 and P2 are alternative processes in CER's knowledge base.
[The SP operator proposes these strategies on the basis of CER's theoretical knowledge about superconductivity such as "Metallic electrical conductivity and oxide superconductivity are positively related", "The process P1 improves oxide superconductivity," and "The process P2 improves oxide superconductivity." We do not know what alternative strategies Bednorz and Müller considered, but CER's alternative strategies "Apply P1" and "Apply P2" refer to dummy proceses, and were added to monitor the behavior of the system. In formulating strategies at this stage, various other physical properties (or variables) related with the electronic properties of substances could be considered. Such properties include specific heat, thermal conductivity, average electronegativity and ionic states, from which alternative strategies such as "Improve thermal conductivity," "Reduce average electronegativity," etc could be formulated. However, CER's current knowledge base lacks information about whether there is a relationship between these properties and superconductivity.]
Next, time limits are assigned to the strategies. CER employs its classifier to choose between strategies against cost, time limits and likeliness to succeed. The values to the parameters are provided by interaction for each strategy. The classifier chooses to "improve metallic electrical conductivity by experimentation" as the current strategy.
[Time limits are provided by interaction. Normally, it would require technical, theoretical and commonsense knowledge to estimate how long a strategy should be in the agenda.]
Once the current strategy is decided, the activity of Strategy Proposers come to an end, and control passes to the Experiment Proposers. This operator lists the known processes related with the strategy, and "element substitution" is selected by interaction as the current process from among several other chemical processes. A time limit is given to the current process. This operator also determines the relevant properties for the experiment materials by referring to the knowledge base to find out which physical properties are positively related to metallic electrical conductivity. Metallic thermal conductivity is found to be positively related to metallic electrical conductivity. The operator now determines the experiment materials on which the element substitution is to be applied, by using the relevant properties (in this case metallic electrical and thermal conductivity) as the basis.
The Experiment Proposers operator searches for oxides with these properties in the knowledge base, and finds several such oxides, which include LaNiO3, LiTi2O4, and Ba(Pb,Bi)O3. It uses the classifier to choose the best experiment material among these on the basis of availability, cost and hazards in use. LaNiO3 is chosen as the current experiment material. The substitution elements in LaNiO3 are determined as [La,Ni,O]. The Experiment Proposers operator uses the classifier to choose the best substitution element, which selects Ni as the current substitution element on the basis of likeliness to succeed.
[We do not know what other oxides with metallic properties Bednorz and Müller have considered for the experiments. Again, the values given to the classifier by interaction reflect the theoretical and technical knowledge required for choosing the best experiment material. After LaNiO3 is selected for the experiments, the choice of the substitution element in this compound also requires some theoretical knowledge about the elements and the possible products involved. For the substitutions, La, or even O could be selected depending on the values given to the classification criteria. As we shall see below, CER proposes substitutions on La, as Bednorz and Müller have subsequently tried. We do not know if they ever considered the substitution of oxygen, a substitution that was to be tried much later by physicists, who used sulphur as a substitute, for this element is in the same group with oxygen.]
Once the substitution element is determined, the Experiment Proposers operator has to determine the likely elements to substitute for La in LaNiO3.The operator proposes Au, Ag, Cu, and Al for their high electrical conductivity as the substituting elements. Once again, the classifier is used to determine the best element among these. The values given to the parameters (availability, cost, likeliness to succeed, and relative hazards in this case), cause the classifier to choose Al as the current substituting element.
[Among the proposed substituting elements, gold (Au) is expensive besides being a rather less reactive element. Similar arguments apply to silver (Ag), though to a lesser extent. Copper (Cu) and aluminium (Al) are widely available and much cheaper elements, in addition to being more reactive than the former.]
Once the substituting element is selected as Al from among [Au,Ag,Cu,Al], experiments are proposed. The proposed experiments are: Substitutions of Al for Ni in LaNiO3.A time limit is set for the experiments. Now control passes to the Experiment Designers operator, which determines the test properties, and issues an experiment form that describes the process conditions. Control passes to Experimenters, Data Collectors and Hypothesis Generators.
The results of the experiments are generalized by the Hypothesis Generators, and are added to CER's knowledge base. Control passes to CER's Goal Satisfaction Supervisers operator. The results fail to satisfy the current goal. The time limit on the
experiments expires. The message that refers to the current substituting element (Al) is deleted from the message list.
[The activities of Experiment Designers, Experimenters, Data Collectors and Hypothesis Generators are simulated externally, as these operators have not been implemented. Accordingly, the experiment results and their generalizations are provided by interaction.]
By this time, CER's message list includes messages about the current goal, current strategy, current process, current experiment materials (which include LaNiO3, LiTi2O4, and Ba(Pb,Bi)O3), current substitution elements [La,Ni,O] and the current substituting elements [Au,Ag,Cu].
Because the current strategy is still active, control passes to CER's Experiment Proposers operator. By forceful interaction, this operator is given La as the current substitution element. Otherwise the operator would normally choose Ni again. This is because the current Experiment Proposers of CER tries all the substituting elements for Ni before passing to another substitution element (e.g. La).
[Forceful interaction is carried out to trace Bednorz and Müller's research course during their experiments on LaNiO3.Bednorz and Müller seem to have made an interesting "breadth-first search" choice there in choosing La instead of continuing with the Ni substitutions with the other substituting elements.]
In the absence of any other criteria, the Experiment Proposers operator finds the substituting elements as Sc, Y and Ac by their being in the same group as La in the Periodic Table.
[At this stage of their experiments, Bednorz and Müller could not have chosenY for La on the basis of electrical conductivity, for La and Y have the same electrical resistivity (57.10-8 ohm.m.).]
The Experiment Proposers operator uses the classifier to choose the substitution element from among Sc,Y and Ac, which chooses Y as the substituting element, against the criteria of availability, likeliness to succeed, cost, and relative hazards. Similarly, the Y substitutions fail and the related hypotheses are added to CER's knowledge base as the time limit on the current experiments expire.
[Here, Y is a clear choice among its alternatives in the same group, for Sc (scandium) is a very expensive element (about $ 50,000/kg), while Ac (actinium) is both radioactive and expensive. CER's knowledge base contains fact ual information about the prices, and theoretical information about the radioactivities of the elements.]
As the current strategy and process are still valid, the Task Direction operator activates the Experiment Proposers once again. This time Ni is chosen as the substitution element by forceful interaction. The substituting elements that remain valid from the previous experiments are Au, Ag and Cu.The classifier is used to choose the current substituting element, which it chooses as Cu.The proposed experiments are: Substitutions of Cu for Ni in LaNiO3. A time limit is given for the experiments.
Control now passes to the Experiment Designers operator, which determines the test properties, and issues an experiment form that describes the process conditions. Experiments are conducted ans the results of the experiments are generalized by the Hypothesis Generators, and are added to CER's knowledge base. Control passes to CER's Goal Satisfaction Supervisers operator. This time the experiments succeed: Substitutions of Cu for Ni in LaNiO3 improves electrical conductivity. However, the time limit on the current experiment material (LaNiO3) expires.
[At this stage of their research, Bednorz and Müller conduct a literature search on the oxides of copper and lanthanum. This is when they learn about Michel et al's work on Ba-La-Cu-O (see, Khurana, 1987b). But the latter's work does not include electrical conductivity measurements of these compounds at low temperatures.]
CER's Task Direction operator activates Experiment Proposers operator, which finds the experiment materials as [La-Cu-O, LiTi2O4, Ba(Pb,Bi)O3,...]. The classifier chooses La-Cu-O as the current experiment material. The operator determines the substitution elements as La,Cu, and O.The classifier chooses La as the substitution element. One substituting element, Ba, is found by the use of external knowledge.
[This list of substituting elements could also include Be, Mg, Ca, and Sr, which are in the same group as Ba, but Bednorz and Müller rely on the new information from their literature search.]
Control passes to the Experiment Designers operator again, which determines the test properties, and issues an experiment form that describes the process conditions. The results of the experiments are generalized by the Hypothesis Generators, and are added to CER's knowledge base. Then, control passes to CER's Goal Satisfaction Supervisers operator, which reports the satisfaction of the current goal. The Ba substitutions in La-Cu-O are successful, as they lead to the discovery of the La-Ba-Cu-O superconductor with a Tc of 30K. Figures 6.3 and 6.4 summarize CER's simulation of the experiments leading to the discovery.
4.2 Overview of the Simulation
CER assigns time limits to all goals for their place in the agenda. In scientific research, assigning time limits to goals, strategies, methods and experiments is necessary, although they do not have to be accurate or even explicitly stated. Every researcher has a rough idea, at the beginning of his/her research as to how long a particular problem should be on his/her agenda. Lenat's (1979) AM system also allocates time and space constraints to its search activities.
CER's behavior considerably depends on the outcomes of these classification activities. Different parameter values given to the classifier may change the course of research from one goal, strategy, method, process, and experiment materials to another. Therefore, due to the time limits assigned to each of these, some of the activities implied by the alternative research paths may never be carried out.
Whether the time limits assigned to goals, strategies, methods, etc. has expired, is monitored externally in the current implementation of CER. Real times can be assigned by time related functions of the host programming language. CER also gives emphasis to expressing goals, strategies and methods as clear as possible.
In pursuing the third goal (G3), the integrated uses of CER's classifier plays a more important part than in pursuing the earlier goals, as it is used, not only in choosing between strategies and methods, but also in choosing the experiment materials, substitution elements and the substituting elements. The parameters of the system's classifier cover a practical but realistic range of properties or features such as availability, cost, hazards in use and likeliness to yield success. Some of these parameter values are drawn from knowledge represented in CER's knowledge base (e.g. from statements about the costs and relative hazards of the materials), while some others (e.g. availability, likeliness to succeed) require more background knowledge and experience.
5 Evaluation of CER
It must have become clear from the description of the system's simulation of the discovery of the high temperature superconductors that, in itself, CER's simulation does not constitute an outstanding achievement, as it extensively relies on knowledge provided to it by interaction for its critical decisions. However, this should not overshadow an important feature of the program: CER sets an example to how a complex empirical discovery program can be developed and trained in carrying out itsresearch tasks.
Scientific research and discovery is a complex process, and any computational model may turn out to be incomplete. Nevertheless, a comprehensive design for such a model serves as a good starting point. In this section, we will first take a critical look at the system's organisation of descriptive and definitive knowledge and its research and discovery operators which control the system's methodological rules. Then we will discuss the generality of the system's research strategies and methods, and conclude the section with a discussion on CER's methods of learning and discovery, together with some suggestions for future research.
5.1 Knowledge Organisation
Current discovery systems employ either a frame representation, a rule based or predicate logic representation, or some combination of these. CER's representation of descriptive and definitive knowledge in categorized predicate statements is based on the knowledge organisation methods that we developed earlier (see, Kocabas, 1989), and is different from the methods employed by other researchers.
CER also uses qualitative schemas (Forbus, 1984) for representing processes, but its schemas are somewhat simpler than those of IDS (Nordhausen & Langley, 1987), AbE (Karp, 1990), and COAST (Rajamoney, 1990). On the other hand, the program integrates schemas with its categorized predicate logic representation. This integration enables the system to reason about processes in an efficient way. To illustrate, consider the theoretical statement taken from CER's knowledge base,
the(reduces,process(substitution/of,tve,y,ybco),tc).
which states that the substitution of a tetravalent element forY in the Y-Ba-Cu-O superconductor reduces Tc. As is seen, in this statement, the process identification appears as an argument to a theoretical statement. This means that, new hypotheses from such theoretical statements can be generated by perturbations over the arguments before any direct reference to the process descriptions themselves. The categorization also facilitates the integration of methodological and control knowledge with the system's descriptive and definitive knowledge.
5.2 System Operators
CER's design aims at modeling various tasks carried out in scientific research. Its research operators cover a wide range of research activities, in which they can serve as a starting point for the design of such models. CER's task-based homuncularorganisation suggests that the computational modeling of scientific research and discovery can focus on different aspects of research. Accordingly, one can look at the discovery systems from a number of different angles. This indicates that a whole series of computational models can be developed for studying a number of different aspects of scientific research and discovery. In this way, the relationships between the elements of scientific research can be studied in a systematic way and in finer detail. CER's design enables us to make comparisons between the existing models of discovery, by their system operators, research tasks and activities. By looking at the research operators of these systems and comparing them with a comprehensive model of discovery, we can map their scope in the general framework of scientific research.
CER's operators contain some of the methodological rules of problem generators, problem choosers, strategy proposers and decision makers of Kulkarni and Simon's (1988) KEKADA with minor modifications or improvements.2 This supports their claim that these rules are general. However, an important difference between CER and KEKADA is the former's use of a classifier, while the latter relies on a series of rules for choosing processes and experiment materials.
Classifiers provide three main advantages over the rule based methods in such classification activities: 1) They are more flexible, for it is much easier to dynamically modify or change the evaluation matrix of a classifier than modifying or changing methodological rules, 2) They can pack more information per unit of computational space, and 3) They can be trained, while rules cannot.
In addition to the rules adapted from KEKADA, the system has many other rules that are general and applicable in research in other domains of physics and chemistry. For example, consider one of the rules of CER's Goal Setters:
If a physical property is an important property, then enhance that property in some substance.
-----------
2 For example, the PG1 and EP1 rules of KEKADA are also employed by CER.
This rule is not only applicable to superconductivity, but also to a series of other physical properties such as heat resistance, electrical resistivity, magnetism, radioactivity, semiconductivity and various forms of chemical reactivity.
Also, the majority of CER's hypothesis generating rules were abstracted from the research reports on high-Tc superconductivity, and are general. Only a small percentage of the system's rules are domain specific. This is important, considering th
e number of methodological rules the program uses.
CER does not generate new methodological rules. Currently, there are only a few systems with this capability in a nontrivial sense, such as Lenat's (1983) EURISKO. However, the addition of such rules to CER's operators, and their adaptation to the system's control structure is easy. This is due to the clarity of program's knowledge representation and its trainable homuncular organisation.
5.3 Research Strategies and Methods
CER's main strategies, methods and techniques are the strategies of explanation and theoretical and empirical study, methods of knowledge gathering, and the techniques of experimentation (i.e., various chemical processes). The system's strategies are quite general and applicable to research in different fields of science (see, Figure 6.2). For example, the system's behavior in trying to find explanations to the superconductivity of oxide coated films of aluminium and Ba(Pb,Bi)O3 can be considered as a general model in searching for explanation in scientific research. Similarly, the system's strategies for studying a phenomenon (by theoretical analysis and experimentation) are applicable to research in any experimental science.
Many scientists try to explain a scientific problem by their immediate knowledge before they refer to external sources (e.g. libraries, experts), and and carry out theoretical analysis of the concepts involved. There may be variations in the order of these activities, but the system's design allows these variations by its hierarchic control architecture, and even introduces some new ideas on modeling parallelism in scientific research.
The design idea of the system emphasizes that clarity in goals, strategies, methods and techniques in research activities is important. Lack of clarity in these can bring the activity of an intelligent system to a halt. CER addresses this problem both by the clarity of its knowledge representation, and by its mechanisms for reformulating its goals and strategies as necessary. (However, in the current version, the latter are conducted in a rather simplistic way, as they consist of rewriting the goal or strategy.)
A significant improvement of the system over the earlier systems is its assignment of time limits to the activity of its goals, strategies, methods and experiments. Lenat's AM (Lenat, 1979) and EURISKO (1983), also have this capability, but the latter are formal discovery systems. Assignment of time limits is very important in intelligent activities (such as scientific research which requires a high degree of planning), for such activities are constrained by the principles of economics and resource management.
CER's design includes two main types of theory revision: by experimentation, and by conflict resolution. The system can identify several different types of contradictions between different categories of knowledge. Although the conflict identification and resolution rules have not been fully implemented, they can easily be developed. This is one of the directions for the future development of the system.
In addition to its theory revision capabilities, CER has one important feature: It can revise its research strategies, methods and processes. This is a feature that very few other discovery systems (e.g. KEKADA) currently possess, but not to the extent that CER does.
5.4 Methods of Learning and Discovery
CER conducts search at three different levels: 1) search in directing tasks through the control rules of its level-2 control operator, 2) knowledge level search by the action rules of its level-1 operators, and 3) symbol level search by its classifier. In this, the system integrates the methods of learning at three different levels, and also provides an example to knowledge level control of symbol level systems at the same time, in the way its action rules control the system's classifier.
The system's methods of learning includes learning by experimentation, by generalizations (of its hypotheses), explanation based learning (of its control rules), and learning by classification. The program's generalizations of its experiment results and hypotheses consist of replacing individual objects names (e.g., of an element) with class names that appear as arguments in the expressions.
5.5 Control Knowledge and its Organisation
CER's control architecture has some similarities with blackboard control architecture (Hayes-Roth, 1985), particularly in that its message list can be seen as functioning like a blackboard. However, there are some basic differences. First, the former's knowledge organisation is entirely different from those implemented in the blackboard systems. Second, the latter systems use a global blackboard, while CER uses its message list only as a medium of communication between its operators, and can also use a multiplicity of such message lists in a hierarchic homuncular organisation (Kocabas, 1991b). Third, the system's operators only represent methodological knowledge as opposed to the "knowledge sources" of the blackboard systems, which may also represent descriptive and definitive knowledge. Finally, blackboard systems use sophisticated schedulers to determine which configuration of the blackboard should cause the activation of which knowledge sources, whereas CER can learn its control knowledge.
Several other systems such as LEX (Mithchell, Keller, & Kedar-Cabelli, 1986), PET (Porter & Kibler, 1986), and PRODIGY (Minton & Carbonell, 1987) also have the capability of learning control knowledge by explanation based methods. Among these, PET has the additional capability of learning control in sequences of activities or "episodes". However, these systems operate in relatively narrow domains. They do not employ message lists as CER does, but use the states of their dynamic memory as the problem states. Consequently, they are "flat" systems as opposed to CER's essentially hierarchic control architecture.
A significant point about the organisation and control of CER's methodological knowledge is that it provides a prototypical model of how scientific research and discovery can be taught. According to this model, methodological knowledge (in the form of action rules) can be taught by instruction, while the control and coordination knowledge, by explanation based methods.
What makes CER interesting in this respect is that it illustrates how an intelligent system can be "trained" at least in certain aspects of scientific research such as proposing and choosing research goals, strategies and methods. Its "open" control architecture provides the system flexibility, in which its descriptive and definitive knowledge and its methodological rules can be freely amended or changed. So, if the system performs poorly after the changes, it can be retrained. When new methodological rules are added, the system's control structure can adapt to these changes more easily than the control procedures applied in many other discovery systems. CER's control operator can also be trained by other methods such as classification besides explanation based generalization. However, for this task, the classification requires a large number of training examples, and therefore, is cumbersome.
5.6 CER's behavior on further research in high-Tc superconductivity
We have described how CER models the discovery of the La-Ba-Cu-O superconductor. With its increased knowledge after the discovery, the system can also reproduce the subsequent discoveries of the Y-Ba-Cu-O, Tl-Ba-Ca-Cu-O and Bi-Ca-Sr-Cu-O superconductors. In modeling the discovery of the Sr-La-Cu-O superconductor with a Tc of 40K, CER creates the goal to study the derivatives of La-Ba-Cu-O.
Superconductivity is an electron-related phenomenon and CER can use the other electron-related physical properties in directing its future research. It would therefore propose to use Bi and Pb substitutions for Cu in La-Ba-Cu-O and Y-Ba-Cu-O superconductors on the basis of electronegativity. (Bi, Pb, Tc, Re, Hg, Ag and Cu have the same electronegativities, but among these Tc is very expensive besides being radioactive.) Similarly, the system would propose the substitutions of Ta and Al for Ti in LiTi2O4 on the same basis. We know that in the later experiments, Cu has been successfully replaced by Bi yielding Cu-free superconductors with even higher Tcs. Since its field of application is still active both in theoretical and experimental sense, CER's methods can be put to further test against future developments and more lessons can be learned about the issues of computational modeling of scientific research in an active research area.
Our observations over the research activities in high temperature superconductivity suggest that modern scientific research is not totally a serial activity as it was in the past centuries. It can branch off into smaller research projects each of which can be carried out independently and in parallel. This creates a number of coordination problems which were not faced by the scientists of the earlier centuries. How must the parallel projects be carried out for maximum efficiency in terms of time and resources? How can they effect the overall course of the main research programme? These are some of the questions that face modern scientific research programmes.
As an illustrative example from CER's own field of application to the problem of coordination in research, it is interesting to see that the Tl-Ba-Cu-O and Bi-Ca-Sr-Cu-O superconductors with transition temperatures over 100K were not discovered until after all the rare-earth element substitutions on the Y-Ba-Cu-O superconductor were completed by research groups around the world. Was this because all these research groups were following an established set of heuristics on strategy choice and continued to follow it? Or was it because the decisions about the next strategy were dependent on the complete results of experiments on the La-Ba-Cu-O based superconductors? Is there a more effective set of heuristics on strategy choice? How do the adopted strategies effect the course of research? We hope that this study will open the way to find answers to some of these questions.
6 Conclusions
In this paper we have described CER, a system that models the discovery of high temperature oxide superconductors. The program constitutes a more comprehensive computational model of scientific research and discovery than its predecessors. Our observations into research and discoveries in high temperature superconductivity indicate that scientific research is directed by methodological rules distinct from the rules used in other intelligent human activities in everyday problem solving (e.g. rules derived from commonsense and technical knowledge.)
The system's design clearly reflects our observation that scientific discovery is not a process in itself, but the end result of a series of processes which is called scientific research. Planning is no doubt an important and indivisible component of scientific research, and is guided by some methodological rules like those of CER, as well as by commonsense and technical knowledge. Although planning can take place in various stages of scientific research, such as strategy choosing, experiment design, experimentation, and data collection, there is more to scientific research than planning. This is because there are a series of research activities which cannot be characterized as planning (e.g., conflict identification and resolution, hypothesis formation, hypothesis verification, and generating explanations).
The CER system improves on its predecessors by providing a more detailed treatment of the elements of scientific research. Consequently, the system has a more varied and detailed search space than any previously developed discovery system. Another important improvement introduced by the system is the assignment of time limits to its tasks and activities in pursuing its goals, strategies, methods and experiments. CER's design also emphasizes the need to reformulate its research goals, strategies and methods where necessary, to maintain uninterrupted activity in research.
The program conducts search at three levels: symbol level, knowledge level and control level. The symbol level search is carried out by by the program's classifier, while knowledge level search is conducted by its rules of action, and control level search by the system's control operator. CER's knowledge organisation facilitates the integration of search at different levels, and the use of such different methods of learning as classification, abstraction, and explanation based learning.
Modern scientific research is a complex enterprise usually requiring a large number of small but necessary inventions and discoveries of tools, techniques and subsidiary hypotheses before its main goals and strategies are accomplished. Even the design of an experiment requires a great deal of background knowledge about the methods, materials, processes, experimental tools and their proper arrangement, and about the conditions of measurement. Therefore, a few hundred rules in a computational system can only provide a sketchy model for scientific research and discovery.
Nevertheless, what is interesting and stimulating about the computational modeling of discovery is that it provides us the insights on the reasoning behind the critical decisions taken by the scientists during the course of their research. Moreover, human mind too has its own limitations, and a successful computational model surfaces the unproductive decisions taken by the scientists as well as the good ones during their research. It also provides a panaromic view of the process of research and may even help to develop a methodology (or methodologies) for better strategies for research in different fields. Usually a large number of rules that are used in any research leading to a discovery are informal rules acquired in years of experience and are not recorded or taught in a systematic way.
CER provides a detailed reference for evaluating the research methods, and the methods of representation and control of various models of scientific discovery, as different models may represent different aspects of discovery. The system also provides guidelines for finding how (or how much of) a particular discovery can be effectively represented by a computational model with the methods of machine learning.
The system's pool of methodological knowledge can be used as a starting point for exploring more methodological rules in different domains of research. Currently, there is little known about the methods used by scientists in generating original methodological knowledge, and the role of generalization, abstraction and analogy in generating such knowledge.
The system's homuncular control architecture introduces a new perspective into the design of computational models of research and discovery. An advantage of this hierarchy is that, a system can learn its control knowledge for distributing its tasks over its subsystems by explanation based learning. We have described how explanation based generalization has been applied to train CER's control operator. This control architecture can be extended downwards to the system's action rules, adding more flexibility into the representation of the system's methodological and control knowledge.
Another advantage of the hierarchic organisation of such operators is to enable the system to make maximum possible use of parallelism. However, as Lenat and Feigenbaum (1987) argued in a similar context, there is a limit to what parallelism can offer in modeling scientific research. This is because, scientific research uses a good deal of planning which requires much sequential reasoning. In any case, we hope that the hierarchic homuncular architecture of CER will provide a computational testbed for the uses and the limits of parallelism in such systems.
References
...
Kocabas, S. (1989). Functional Categorization of Knowledge: Applications in computational modeling of scientific research and discovery. PhD Thesis. Dept. of Electronic and Electrical Engineering, King’s College London, University of London.
...
Reference on Superconductivity
Beasley, M.R. and Gaballe, T.H. (1984). Superconducting Materials. Physics Today. October 1984, 60-68.
Edelsack, E.A. (1973). Fundamentals of Superconductivity. In The Science and Technology of Superconductivity. W.D. Gregory, W.N. Matthews Jr, E.A. Edelsack (eds.) Vol. 1, 5-24. New York: Plenum Press.
Khurana, A. (1987a). Search and Discovery: Superconductivity seen above the boiling point of Nitrogen. Physics Today. April, 1987, 17-23.
Khurana, A. (1987b). Search and Discovery: Bednorz and Müller win Nobel Prize for new superconducting materials. Physics Today, December, 1987, 17-19.
Langenberg, D.N. (1987). McGraw Hill Encyclopedia of Science and Technology. 609-617.
