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I STANFORD ARTIFICIAL INTELLIGENCE PROJECT MEMO A IM-141 COMPUTER SCIENCE DEPARTMENT REPORT NO. CS-203 THE HEURISTIC DENDRAL PROGRAM FOR EXPLAINING EMPIRICAL DATA BY BRUCE G. BUCHANAN JOSHUA LEDERBERG CO-PRINCIPAL INVESTIGATORS: E. FEIGENBAUM & J. LEDERBERG I FEBRUARY 1971 COMPUTER SCIENCE DEPARTMENT STANFORD UNIVERSITY
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Page 1: COMPUTER SCIENCE DEPARTMENT STANFORD UNIVERSITYmp063pc2673/mp063pc2673.pdf · stanford artificialintelligenceproject memoaim-141 computer sciencedepartment report no. cs-203 the heuristicdendralprogram

ISTANFORD ARTIFICIAL INTELLIGENCE PROJECTMEMO A IM-141COMPUTER SCIENCE DEPARTMENTREPORT NO. CS-203

THE HEURISTIC DENDRAL PROGRAMFOR EXPLAINING EMPIRICAL DATA

BY

BRUCE G. BUCHANANJOSHUA LEDERBERG

CO-PRINCIPAL INVESTIGATORS: E. FEIGENBAUM & J. LEDERBERG

I FEBRUARY 1971

COMPUTER SCIENCE DEPARTMENTSTANFORD UNIVERSITY

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Il

FEBRUARY 1971STANFORD ARTIFICIAL INTELLIGENCE PROJECTMEMO AIM- Ik1

COMPUTER SCIENCE DEPARTMENT REPORTNO. CS2O3

THE HEURISTIC DENDRAL PROGRAMFOR EXPLAINING EMPIRICAL DATA*l

by

Bruce G. BuchananJoshua Lederberg

Co-Principal investigators: E. Feigenbaum & J. Lederberg

ABSTRACT: The Heuristic DENDRAL program uses an information processingmodel of scientific reasoning to explain experimental data inorganic chemistry. This report summarizes the organizationand results of the program for computer scientists. The pro-gram is divided into three main parts : planning, structuregeneration, and evaluation.

The planning phase infers constraints on the search spacefrom the empirical data input to the system. The structuregeneration phase searches a tree whose termini are models ofchemical molecules using pruning heuristics of various kinds.The evaluation phase tests the candidate structures againstthe original data. Results of the program's analyses of sometest data are discussed.

#This research was supported by the Advanced Research Projects Agency(SD-I83). Much of the work reported here was performed by Mrs. GeorgiaSutherland and Mr. Allan Delfino. The assistance of Dr. Alan Duffieldand Professor Carl Djerassi is also gratefully acknowledged.

Reproduced in the USA. Available from the Clearinghouse for FederalScientific and Technical Information, Springfield, Virginia 22151.Price: Full size copy $3.00; microfiche copy $ .65.

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I

IThe Heuristic DENDRAL Program

for Explaining Empirical Data

IThe Heuristic DENDRAL program applies an information processing model of

scientific reasoning to a specific problem in organic chemistry. It reasons

its way from experimental chemical data to explanatory hypotheses about the

molecular structure of compounds. For now, the program ignores other kinds

of scientific reasoning such as theory formation: its task is to explain

data within an established theory. This report describes the Heuristic DENDRAL

program for IFIP members who might have hoped for a succinct description in

our artificial intelligence reports (for example, [7], [B], [9]) and who would

like to avoid the chemical details found in our publications for chemists [2] ,[33, [k], [53, [63.

i

This paper is divided into three main parts: (i) a brief description of

the task area, mass spectroscopy; (il) a discussion of the artificial intelli-

gence aspects of the program; and (ill) a summary of results.

iI

I. THE TASK AREA

Organic chemists are primarily concerned with either the analysis or

synthesis of compounds, that is, with either identifying or manufacturing

chemical molecules. Mass spectrometry is a branch of analytic chemistry in

which the substance to be identified is vaporized and bombarded with electrons

in a mass spectrometer in order to obtain data on the resulting fragmentations.

lI

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III The data are arranged in a mass spectrum, which shows the masses of fragments

produced in the instrument plotted against their relative abundance. Thus the

task of the chemist is to use his knowledge of the behavior of molecules in a

mass spectrometer to identify the structure of compounds.IThe information processing nature of the problem is one important reason

for selecting the analysis of mass spectra as the task area. Chemists them-

selves use non-mathematical models of organic molecules and of the mass spec-

trometer to analyze mass spectra. They also use many complex judgmental rules.

Another reason for selecting a branch of organic chemistry as the program's

task area is that a notational algorithm for representing and generating chemical

molecules invented by Lederberg [I] is particularly well-suited for computer use.

This algorithm, named DENDRAL, is described in section 11-B of this paper.

IIII

11. PROGRAM ORGANIZATION

Heuristic DENDRAL is organized as a heuristic search program which searches

the space of organic molecular structures for the molecule which best explains

the experimental data. The input to the program is the mass spectrum, empirically

determined by inserting a sample of a compound into the mass spectrometer. Out

of the implicit space of all possible molecular structures the program selects

the structures which best explain the data -- often a single structure. Because

of the size of the space, it is necessary to reduce the search through the

judicious use of heuristics. And, because several structures may be plausible

explanations, it is necessary to provide a means for evaluating alternatives.

iIIIi In test cases, where we know the structure of the sample compound, the

program usually produces the correct structure in its answer set. Its pruning

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and evaluation heuristics are good enough that this is a small set, as can be

seen in the accompanying tables. The working chemist, of course, does not

ordinarilyknow the structure of his sample.IThe heart of Heuristic DENDRAL, as of any heuristic search program, is the

generator of the search tree. The tree, in this case, is the tree of successive

attachments of chemical atoms into larger and larger graph structures . The

generator is the DENDRAL algorithm. At the first node of the tree is the

initial set of unstructured atoms; deeper levels of the tree correspond to

partial structures with more atoms in the structure and fewer unattached atoms.

At the ends of all the branches are complete molecular structures with every

atom in the initial set allocated to some place in the structure. The DENDRAL

algorithm makes all possible attachments of atoms irredundantly at every level,

and it provides the capabilities for heuristic pruning of the tree. Constraints

on the generator take two forms: search reduction based on plans inferred from

the mass spectral data and search reduction based on considerations of chemical

stability.

I A. Planning : Search Reduction Based on the Mass Spectral Data

Among the large numbers of molecular structures at the termini of the

search tree, planning can describe constraints on the space which are severe

enough to limit the number of termini to a few dozen or even just one or two

structures. The search reduction power of the plan depends upon the amount

of chemical theory embodied in the underlying planning heuristics .Ili

1. Constructing Plans from the Data

A plan is a set of constraints for the generator which limits the output

structures to those which are most relevant to the data. The data may be the

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mass spectrum or other experimental data on the sample, for example, a nuclear

magnetic resonance (NMR) spectrum.

From mass spectral data it is often possible to infer that particular

partial structures, or "superatoms" must be contained in each of the candidate

structures. And it is often possible to determine the positions of the super-

atoms within the context of the remaining unstructured atoms. Currently, the

program infers the presence of only one superatom at a time, so the form of

this part of a plan is

HiR2 | Rn

R3 —— y X :

The F in the center of this scheme is the superatom, which has been

identified,

(it is called a "functional group" by chemists, thus the "F".) The R's are

the weights of the appendant radicals, which surround F . Having this information

constrains the search to molecules which conform to the particulars of this

scheme.

Plans are constructed by the planning program by means of a complex set

of judgmental rules like those used by chemists. Sets of peaks in the mass

spectral data often characterize the functional group in the molecule, and thus

identify F in the plan. The context of those peaks in the data, then, place

the functional group in the molecule relative to the other atoms, and thus

identify the R's in the plan. For example, the functional group "ketone"

(C=o) can be identified by the existence of a pair of peaks in the spectrum at

mass points R]_+2B and R2+2B whose sum is the molecular weight plus 28 mass

units . (A few additional constraints insure that accidental peaks in the data

k

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Iwill not indicate the ketone group. For example, at least one of the peaks

must be a prominent peak in the spectrum.) The existence of such a pair of

peaks identifies F as a carbon atom doubly bonded to an oxygen atom.. The

specific values of R-j_ and R2 , say k3 and 71, can then identify the masses

of the two radicals appendant from the ketone group. Thus the final plan

becomes :

I

iii

0

(10) - c - (71)

Other types of data may be employed by the planning program if they are

available. For the analysis of amines, for example, data from nuclear magnetic

resonance experiments greatly augment the power of the planning program. The

tables of results for amines, ethers, alcohols, thioethers and thiols show

the dramatic reduction possible when NMR data are used. In these cases the

NMR data were used to infer the numbers of methyl (CH^) radicals present in

the test samples and were used to help infer the structures of the superatoms.

It will be possible to incorporate judgmental rules to be used with still other

kinds of experimental data, as the need arises.

iThe planning program works best with data from unringed molecules containing

a single functional group. The reason for this is that the mass spectrometry

theory for these molecules is simpler and less ambiguous than for more complex

molecules. The next section digresses somewhat from the present discussion to

explain how we have been able to automate the generation of the planning

heuristics on the basis of the known theory.

i

I

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2. Generating Planning Heuristics from the Theory

Some of the most powerful planning heuristics used by chemists (and by

the program) were noticed to be relatively straightforward consequences of the

theory of mass spectrometry. For the set of molecules containing a single

functional group, the planning heuristics can be generated from a few well-

known rules of mass spectrometry. We have written a program, external to the

Heuristic DENDRAL system, for generating these planning rules.

This external program is in two conceptually distinct parts: a superatom

generator and a planning rule generator. The superatom generator is a specialized

version of the DENDRAL structure generator mentioned previously. Its task is

to construct candidate superatoms for inclusion in the plan. The planning rule

generator uses the theory of mass spectrometry to construct a set of heuristics

for inferring the presence of each superatom in the mass spectral data. The

whole process of constructing plans, then, can be thought of as a problem solving

activity where the input is the mass spectrum together with a set of non-carbon

atoms that may be in functional groups, and the output is a plan or set of

alternative plans for generating candidate structures which explain the data.

I3 . Summary

Regardless of the source of the candidate superatoms and their planning

heuristics, whether from a chemist or from a program, the Heuristic DENDRAL

system uses them to construct plans. It tests each candidate functional group

(superatom) against the original data by applying the planning heuristics. If

the functional group satisfies the criteria, it is put into a plan together

with other inferred constraints. The search reduction effect of planning is

shown in Tables 2-5.

I

I

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I

A severe limitation on this problem solver is that it depends upon knowing

that only one superatom containing non-carbon atoms is present in the structure

of the sample (ignoring hydrogens) and consequently that only one functional

group is present. The theory which the rule generator can use does not always

apply when several functional groups are present, nor has much theory been

developed to tell the program what does happen. Although chemists consider

more complex cases and the generator of superatoms can easily be extended to

handle them, the mass spectrometry theory, and consequently the planning rule

generator, cannot be so easily extended.I

B. Structure Generation

The DENDRAL algorithm provides a representation of objects in the search

space — chemical molecules — and describes the procedure for generating them.

Both the representation and the procedure have proved amenable to computer use,

with very few changes. The algorithm uses no other chemical knowledge than the

valence, or number of allowable links, for each type of chemical atom. Carbon,

for example, has a valence of four, oxygen two, and so forth. Within these mild

constraints the algorithm is capable of generating all topologically possible

non-ringed graph structures from a given collection of chemical atoms. The

actual canons of procedure will not be discussed here. The important point to

note is that the algorithm's output of topologically possible molecular struc-

tures can contain a very great number of structures which are implausible from

the standpoint of chemical stability. Search reduction heuristics on the list

known as BADLIST prune the tree as unstable chemical structures begin to emerge.

This reduction can be seen from Table 1. In the other cases BADLIST has no

effect unless a chemist wishes to change it so as to prune some structuresI

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which are now allowed.

1. The Search Space

The search space itself is organized as an AND/ OR tree which is searched

depth-first. The first level of the tree, after the specification of the

initial collection of atoms, is the set of all possible molecule centers, or

centroids. 'Because any one of these centroids may lead to the solution of the

program, this level is a set of OR nodes. Also, for this reason, the OR nodes

are ordered by the program so that the most likely centroid appears first in

the set. The. next level of the tree, just beyond the node specifying a possible

centroid, specifies the possible ways the remaining atoms in the composition

can be partitioned to the unfilled links of the centroid. A central carbon

atom with three unfilled links, for example, must be completed by having three

radicals, made from the remaining composition, attached to the links. Thus,

beyond that node the program will grow several sets of AND nodes, each set

defining a possible partition of the remaining atoms into three clusters. The

scheme of the tree generation for these two levels is shown in the diagram below.

collection of atoms

d o . . ,^oo centroids with k. links

. . . o^o^ ... 6^ xo-l -o2 "" ; ~-ok . . . partitions of remainingatoms into k clustersof atoms

For each AND set of subproblems, all of which must be successfully completed

if the program is to grow the tree beyond any of the nodes, the program attempts

the most difficult subproblem first. That is, it orders the clusters of atoms

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in the AND nodes so that the cluster of atoms which is least likely to produce

stable radicals is chosen first. If, in fact, no radicals can be built from

the node then all subproblems in the AND set are discarded.

After the first two levels of tree generation, the program is recursive.

Each cluster of unstructured atoms is taken up as a fresh problem: the program

lists all possible centroids and then partitions the remaining atoms into the

appropriate numbers of clusters. And again, at every level until there are no

more unstructured atoms. At this point, the program has completed its generation

of the space.

2. Heuristics Used to Guide Search

Besides selecting likely branches at OR nodes and unlikely branches at AND

nodes, the program reduces its total effort by saving the results of previously-

solved subproblems in a "dictionary". A subproblem of constructing radicals

from a cluster of six carbon atoms, for example, may appear several times over

the whole search space. By saving the result of the first solution of this sub-

problem the program is able to save much work. All that it needs to do is fetch

from the dictionary the list of radicals which have been built from six carbons

and attach them, one at a time, to the partially built molecular structure.

Planning information is passed from the Planner to the Structure Generator

on a list known as GOODLIST. As the name implies, GOODLIST is a list of super-

atoms (and associated partitioning information) which should be included in the

output of the generator. The generator uses this information in two ways.

First, the starting set of atoms is reduced by the composition of the superatoms

on GOODLIST and the superatom names are added to the set. Second, planning infor

mation is used in constructing partitions of the initial composition. Starting

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from the superatom as centroid, the program explores only that part of the tree

in which the primary partitions of the remaining atoms are compatible with the

radical weights specified in the plan. Consider again the planning example

considered in part (A) , where the plan was

cOtf ) - C - (7.1)

This means that generation proceeds by first removing a carbon and an oxygen

atom from the initial set of atoms and then constructing only the partitions

of the remaining atoms which are compatible with weights k-3 and 71? that is,

partitions of C^H-? and CgE^Although rarely used, the ability to accept a chemist's intuitions or

biases is a powerful search reduction tool. BADLIST itself reflects one

scientist's intuitions about the subgraphs responsible for unstable structures.

But beyond that, it is easy for an individual to guide the search by adding

(or deleting) constraints to BADLIST and GOODLIST. A chemist can supress all

occurrences of a superatom from the generator's output by adding that superatom

to BADLIST. Conversely, he can force the occurrence of a superatom in every

output structure by adding that superatom to GOODLIST.

The Structure Generator is the central part of the total Heuristic DENDRAL

program. It was mentioned earlier that the planning program can often specify

such a detailed plan that only a single structure fits the plan. In spite of

this power it is necessary to retain the capabilities of a general heuristic

search program to deal with cases outside the scope of the Planner's power.

The output of the Structure Generator is a list of molecular structures. They

are all plausible candidates for explaining the given mass spectrum because

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they are all chemically stable and they all fit the constraints of the plan

inferred from the experimental data.

C. Evaluation

The purpose of the last phase of the Heuristic DENDRAL program is to cull

the least promising of the plausible candidate structures and rank the remaining

ones. For both of these jobs the program obtains a predicted mass spectrum from

its internal model of the mass spectrometer. The significant peaks in the pre-

dicted mass spectrum are then matched against the original spectrum. A candidatestructure is rejected if its predicted spectrum is inconsistent with the original

data, and the remaining candidates are ranked by how well they explain the

original data

The prediction program, known as the Predictor, consists of two main parts:

a theory of mass spectrometry plus a large number of routines for describing

mass spectrometric processes and manipulating molecular structures in accordance

with those processes. It is not necessary to describe the details of either of

these parts, but the separation of theory from the rest of the program is of

some interest .By separating the theory of mass spectrometry in the Predictor from the

routines which reference it, the theory is much easier to change -- either by

hand or by a program. The theory is a set of data which the program sortsthrough to determine the actions to perform and the parameter settings associated

with those actions. The theory embodied in this data structure is organized as

situation-action rules (or productions). The program checks for the truth of

each situation in the current context and, if true, executes the associated

set of actions. For example, the Predictor checks for the occurrence of the

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ketone functional group by looking for the subgraph C=o in the graph structure

of the molecular structure. If the subgraph is present the program executes

routines for performing cleavages and rearrangement processes characteristic

of ketones.IThe input to this last phase of the program is a set of molecular structures;

the intermediate result is a set of predicted mass spectra, and the final output

is a ranked list of structures which are consistent with the original data.

Consistency, in this case, means that every significant feature of the predicted

spectrum for the candidate structure actually appears in the original data. Thus

the predictive test can only disconfirm candidates. Scoring the candidates on

the basis of how many peaks in the original data they can explain is meant to

estimate degrees of confirmation. The score for a candidate is the sum of the

significance weightings assigned to its predicted mass spectrum by the program.

Thus a candidate which explains peaks thought to be very significant will rank

higher than one which explains as many (or possibly more) peaks of less

significance.

111. RESULTS

Although results of the program's analyses of selected mass spectra have

been published, in chemistry journals (see [2] - [6]) they have not been ade-

quately summarized for computer scientists. The accompanying tables show the

sizes of the problem spaces for different classes of problems and the search

reduction achieved by the program.

i

The ammo acids shown in Table 1 were analyzed without planning, but with

references to the data during structure generation by a simple theory called

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Ithe "zero-order" theory. Ammo acids are characterized by the presence of both

a nitrogen and a carboxylic acid group (-C=o) in the molecule. They happenXOH

to lend themselves to this simple kind of analysis because they tend to fragment

in almost every possible way in a mass spectrometer, just as the zero-order

theory predicts. This is not true of other classes of compounds. BADLIST is

able to constrain the size of the search space dramatically, as noted by the

difference between the columns entitled "Number of Possible Structures" and

"Number of Plausible Structures", because more than one non-carbon atom is

present in ammo acids. This desirable reduction is lost in the other cases,

as indicated in the footnote to the third column of Tables 2-5.

l

II

For the ketones, shown in Table 2, planning was necessary to achieve the

search reduction noted between the columns entitled "Number of Plausible

Structures" and "Number of Structures Generated". Applying a few well-known

rules of mass spectrometry was almost solely responsible for this reduction.

Other rules about the mass spectrometric behavior of ketones allowed the evalu-

ation program to exclude some of the candidates generated and successfully rank

the remaining ones. As noted before, ketones are characterized by the presence

of the chemical substructure C~O .

ili

I Tables 3~5 show the results of the program's analysis of unringed compounds

containing the substructures

■N- (amines)

I 0- (ethers)OH (alcohols)

SH (thiols)S- (thioethers)

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IFor all of this work the planning program contained a much larger body of

theoretical knowledge than in the ketone case. Its theory about the mass

spectrometry of these classes of compounds, in fact, was as complete as .thetheory in the Predictor. And it included nuclear magnetic resonance (NMR)

theory which the Predictor does not. Thus, the plans which it was able to

construct were so detailed that the evaluation phase could make no further

improvements. In other words, there was no theory left to use for evaluation

which had not already been used in planning.

III

II

IV. CONCLUSION

The Heuristic DENDRAL program successfully explains experimental data for

many test problems in analytic organic chemistry. On a limited class of mole-

cules it performs at about the same level as a post-doctoral chemist. However,

the class of problems which can be solved is still very small relative to those

a practicing chemist may see. Much of our future work will be devoted to

extending the power of the program to cover, for example, compounds with several

functional groups and compounds containing an arbitrary number of rings . We

anticipate much work, also, on extending the program to cover more varied kinds

of scientific reasoning.

IIII

iI

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20I

BIBLIOGRAPHY

1. J. Lederberg and E.A. Feigenbaum, "Mechanization of Inductive Inferencein Organic Chemistry". In Formal Representation of Human Judgment .(B. Kleinmuntz- cd.), John Wiley & Sons, Inc., 1968. (Also StanfordArtificial Intelligence Project Memo No. 5k.)

2. J. Lederberg, G.L. Sutherland, B.G. Buchanan, E.A. Feigenbaum, A.V. Robertson,A.M. Duffield, and C. Djerassi, "Applications of Artificial Intelligence forChemical Inference I. The Number of Possible Organic Compounds: AcyclicStructures Containing C, H, 0 and N" . Journal of the .American ChemicalSociety, 91, 2973-2976 (1969).

3. A.M. Duffield, A.V. Robertson, C. Djerassi, B.G. Buchanan, G.L. Sutherland,E.A. Feigenbaum, and J. Lederberg, "Applications of Artificial Intelligencefor Chemical Inference 11. Interpretation of Low Resolution Mass Spectraof Ketones". Journal of the American Chemical Society, 91, 2977-2981 (1969) .

k. G. Schroll, A.M. Duffield, C. Djerassi, B.G. Buchanan, G.L. Sutherland,E.A. Feigenbaum, and J. Lederberg, "Application of Artificial Intelligencefor Chemical Inference 111. Aliphatic Ethers Diagnosed by Their LowResolution Mass Spectra and NMR Data". Journal of the American ChemicalSociety, 91, JkkO-'jkk 1? (1969).

5. A. Buchs, A.M. Duffield, G. Schroll, C. Djerassi, A.B. Delfino, B.G. Buchanan,G.L. Sutherland, E.A. Feigenbaum, and J. Lederberg, "Applications of ArtificialIntelligence for Chemical Inference IV. Saturated .Amines Diagnosed by TheirLow Resolution Mass Spectra and Nuclear Magnetic Resonance SpectraI. Journalof the American Chemical Society, Q2, 683l)(l970).

6. A. Buchs, A.B. Delfino, A.M. Duffield, C. Djerassi, B.G. Buchanan, E.A.Feigenbaum, and J. Lederberg, "Applications of Artificial Intelligence forChemical Inference VI. Approach to a General Method of Interpreting LowResolution Mass Spectra with a Computer"* Chemica Acta Helvetica, 53, 1394(1970)

7. B.G. Buchanan, G.L. Sutherland, and E.A. Feigenbaum, "Heuristic DENDRAL: AProgram for Generating Explanatory Hypotheses in Organic Chemistry". InMachine Intelligence k (B. Meltzer and D. Michie, eds . ) Edinburgh UniversityPress (1969). (Also Stanford Artificial Intelligence Project Memo No. 62.)

8. B.G. Buchanan,

G.L,

Sutherland, and E.A. Feigenbaum, "Toward an Understandingof Information Processes of Scientific Inference in the Context of OrganicChemistry". In Machine Intelligence 5, (B. Meltzer and D. Michie, eds.)Edinburgh University Press (1969). (Also Stanford Artificial IntelligenceProject Memo No. 99 ")

9. E.A. Feigenbaum, B.G. Buchanan, and J. Lederberg, "On Generality and ProblemSolving: A Case Study Using the DENDRAL Program". In Machine Intelligence 6(B. Meltzer and D. Michie, eds.) Edinburgh University Press (in press). (AlsoStanford Artificial Intelligence Project Memo No. 131.)

Page 23: COMPUTER SCIENCE DEPARTMENT STANFORD UNIVERSITYmp063pc2673/mp063pc2673.pdf · stanford artificialintelligenceproject memoaim-141 computer sciencedepartment report no. cs-203 the heuristicdendralprogram