COMMENT ⊗   VALID 00007 PAGES
C REC  PAGE   DESCRIPTION
C00001 00001
C00002 00002	.ASEC(Bibliography)
C00014 00003	.ASSEC(Books and Memos)
C00024 00004	Kac, Mark, and S. Ulam, 4Mathematics and Logic: Retrospects and Prospects*,
C00037 00005	.ASSEC(Articles)
C00045 00006	.ASSEC(Acknowledgements)
C00046 00007	.ASSEC(Documentation)
C00047 ENDMK
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.ASEC(Bibliography)

.ASSEC(Comparison to Other Systems)

One popular way to explicate a system's design ideas is to compare it to other,
similar systems, and/or to others' proposed criteria for such systems. There is
virtually no similar project known to the author, despite an exhaustive search
(see Bibliography). A couple tangential efforts will be mentioned, followed by
a discussion of how AM will measure up to the understanding standards set
forth by Moore and Newell in their MERLIN paper.
Next comes a listing of the books which were read, and finally a bibliography
of relevant
articles.

Several projects have been undertaken which comprise a small piece of the proposed
system, plus deep concentration on some area ⊗4not⊗* under study here. For example,
Boyer and Moore's theorem-prover embodies some of the spirit of this effort, but its
knowledge base is minimal and its methods purely formal.  Badre's CLET system worked
on learning  the decimal addition algorithm
$$ Given the addition table up to 10 + 10,
plus an English text description of what it
means to carry, how and when to carry, etc.* but the ⊗4mathematics discovery⊗*
aspects of the
system were neither emphasized nor worth emphasizing; it was an interesting natural
language communication study. 
The same comment applies to several related studies 
by IMSSS$$See [Smith], for example.*.
Gelernter has worked on using prototypical examples
as analogic models to guide search in geometry, and Bundy has used "sticks" to help
his program work with natural numbers.  
Kling has studied the single heuristic of analogy, and Brotz has written a
system which uses this to propose useful lemmata; both of these are set up as
theorem provers, again not as discoverers.
One aspect that each of these systems lacked
was size: they all worked in tiny toy domains, with miniscule, carefully prearranged
knowledge bases, with just enough information to do the job well, but not so much that
the system might be swamped. AM is open to all the advantages and all
the dangers of a non-toy system with a massive corpus of data to manage.  The other
systems did not deal with intuition, or indeed any multiple knowlege source (except
examples or syntactic analogy). 
Certainly none has considered the paradigm of ⊗4discovery and evaluation of
the interestingness of structure⊗*; the others have been "here is your task, try and
prove it,"  or, in Badre's case, "here is the answer, try and translate/use it."

There is very little thought about discovery in mathematics from an algorithmic
point of view; even clear thinkers like Polya and Poincare' treat mathematical 
ability as a sacred, almost mystic quality, tied to the unconscious.
The writings of philosophers and psychologists invariably attempt to examine
human performance and belief, which are far  more manageable than creativity
in vitro.  Belief formulae in inductive logic (eg., Carnap, Pietarinin) 
invariably fall back upon how well they fit human measurements. The abilities of
a computer and a brain are too distinct to consider blindly working for results
(let alone algorithms!) one possesses which match those of the other.

In an earlier section we discussed criteria for the system.
Two important criteria are final performance and initial starting point.
That is, what is it given (including the knowledge in the program environment),
and what does AM do with that information?  Moore and Newell have published some
reasonable design issues for any proposed understanding system, and we shall now
see how our system answers their questions$$
Each point of the taxonomy which they
provide before these questions is covered by the proposed system.*.

.BEGIN W(6) 

Representation: Families of BEINGs, simple situation/rules, opaque functions.
	Scope: Each family of BEINGs characterizes one type of knowledge. 
			Each BEING represents one very specialized expert.
			The opaque functions can represent intuition and the real world.
	Grain: Partial knowledge about a topic X is naturally expressed as an incomplete BEING X.
	Multiple representations: Each differently-named part has its own format, so, e.g.,
		examples of an operation can be stored as i/o pairs, the intuition points to an
		opaque function, the recognition section is sit/action productions, the
		algorithms part is a quasi-executable partially-ordered list of things to try.
Action: Most knowledge is stored in BEING-parts in a nearly-executable way; the remainder is
	stored so that the "active" segment can easily use it as it runs.  The place that
	a piece of information is stored is carefully chosen so that it will be evoked
	in almost all the situations in which it is relevant.  The only real action in the
	system is the selective completion of BEINGs parts (occasionally creating a new BEING).
Assimilation: There is no sharp distinction between the internal knowledge and the
	task; the task is really nothing more than to extend the given knowledge while
	maintaining interest and asethetic worth.  The only external entities are the
	user and the simulated physical world. Contact with the first is through a
	simpleminded translation scheme, with the latter through evaluation of opaque
	functions on observable data and examination of the results.
Accomodation: translation of alien messages; inference from (simulated) real-world examples data.
Directionality: The Environment gathers up the relevant knowledge at each step to fill
	in the currently worked-on part of the current BEING, simply by asking that part
	(its archetypical representative), that BEING, and its Tied BEINGs what to do.
	Keep-progressing: at each stage, there will be hundreds or thousands of unfilled-in
		parts, and the system simply chooses the most interesting one to work on.
Efficiency: 
	Interpreter: Will the contents of BEING's parts be compilable, or must they remain
		completely inspectable? One alternative is to provide two versions, one
		fast one for executing and one transparent one for examining. 
		Also provide access to a compiler, to recompile any changed (or new) part.
	Immediacy: There need not be close, rapidifire comunication with a human,
		but whenever communicating with him, time ⊗4will⊗* be important; thus the
		only requirement on speed is placed upon the translation modules, and
		they are fairly simple (due to the clean nature of the mathematical domain).
	Formality: There is a probabilistic belief rating for everything, and a descriptive
		"Justifications" component for all BEINGs for which it is meaningful.
		There are experts who know about Bugs, Debugging, Contradiction, etc.
		Frame problem: when the world changes, make no effort to update everything.
			Whenever a contradiction is encountered, study its origins and
			recompute belief values until it goes away.
Depth of Understanding:  Each BEING is an expert, one of whose duties is to announce his
	own relevance whenever he recognizes it. The specific desire will generally
	indicate which part of the relevant BEING is the one to examine. In case this loses,
	each BEING has a part which (on the basis of how it failed) points to alternatives.
	Access to all implications: The intuitive functions must simulate this ability,
		since they are to be analogic. The BEINGs certainly don't have such access.

.END

.ASSEC(Books and Memos)

All the references below have actually been read as background for AM.
They form 
a large yet far from comprehensive
list of publications dealing
with automated theory formation and with how mathematicians do research.$$
From a single author or project (e.g., DENDRAL), only one or two
recent papers will be listed.*
I actually relied upon those with an "α@" sign; the others proved to be merely
supplementary.

.BEGIN FILL SINGLE SPACE  PREFACE 1 INDENT 0,4,0 TURN OFF "@"; ONCE PREFACE 2

@Adams, James L., ⊗4Conceptual Blockbusting⊗*, W.H. Freeman and Co.,
San Francisco, 1974.

Allendoerfer, Carl B., and Oakley, Cletis O., ⊗4Principles of
Mathematics⊗*, Third Edition, McGraw-Hill, New York, 1969.

Alexander, Stephen, ⊗4On the Fundamental Principles of Mathematics⊗*,
B. L. Hamlen, New Haven, 1849.

Aschenbrenner, Karl, ⊗4The Concepts of Value⊗*, D. Reidel Publishing
Company, Dordrecht, Holland, 1971.

Atkin, A. O. L., and Birch, B. J., eds., ⊗4Computers in Number Theory⊗*,
Proceedings of the 1969 SRCA Oxford Symposium, Academic Press, New York, 
1971.

Avey, Albert E., ⊗4The Function and Forms of Thought⊗*, Henry Holt and
Company, New York, 1927.

@Badre, Nagib A., ⊗4Computer Learning From English Text⊗*, Memorandum
No. ERL-M372, Electronics Research Laboratory, UCB, December 20, 1972.
Also summarized in ⊗4CLET -- A Computer Program that Learns Arithmetic
from an Elementary Textbook⊗*, IBM Research Report RC 4235, February
21, 1973.

Bahm, A. J., ⊗4Types of Intuition⊗*, University of New Mexico Press,
Albuquerque, New Mexico, 1960.

Banks, J. Houston, ⊗4Elementary-School Mathematics⊗*, Allyn and Bacon,
Boston, 1966.

Berkeley, Edmund C., ⊗4A Guide to Mathematics for the Intelligent
Nonmathematician⊗*, Simon and Schuster, New York, 1966.

Berkeley, Hastings, ⊗4Mysticism in Modern Mathematics⊗*, Oxford U. Press,
London, 1910.

Beth, Evert W., and Piaget, Jean, ⊗4Mathematical Epistemology and
Psychology⊗*, Gordon and Breach, New York, 1966.

Black, Max, ⊗4Margins of Precision⊗*, Cornell University Press,
Ithaca, New York, 1970.

Blackburn, Simon, ⊗4Reason and Prediction⊗*, Cambridge University Press,
Cambridge, 1973.

Bongard, ⊗4Pattern Recognition⊗*, USSR

@Brotz, Douglas K., ⊗4Embedding Heuristic Problem Solving Methods in a
Mechanical Theorem Prover⊗*, dissertation published as Stanford Computer
Science Report STAN-CS-74-443, AUgust, 1974.

Brown, G. Spencer, ⊗4Laws of Form⊗*, The Julian Press, Inc., N.Y. 1972.

Bruner, Jerome S., Goodnow, J. J., and Austin, G. A., ⊗4A Study of
Thinking⊗*, Harvard Cognition Project, John Wiley & Sons,
New York, 1956.

Charosh, Mannis, ⊗4Mathematical Challenges⊗*, NCTM, Wahington, D.C., 1965.

Cohen, Paul J., ⊗4Set Theory and the Continuum Hypothesis⊗*,  W.A.Benjamin, Inc.,
New York, 1966.

Copeland, Richard W., ⊗4How Children Learn Mathematics⊗*, The MacMillan
Company, London, 1970.

Courant, Richard, and Robins, Herbert, ⊗4What is Mathematics⊗*, 
Oxford University Press, New York, 1941.

D'Augustine, Charles, ⊗4Multiple Methods of Teaching Mathematics in the
Elementary School⊗*, Harper & Row, New York, 1968.

Dodge, Clayton W., ⊗4Sets, Logic, and Numbers⊗*, Prindle, Weber & Schmidt, Inc.,
Boston, 1969.

Dornbusch, Sanford, and Scott, ⊗4Evaluation and the Exercise of Authority⊗*,
Jossey-Bass, San Francisco, 1975.

Douglas, Mary (ed.), ⊗4Rules and Meanings⊗*, Penguin Education,
Baltimore, Md., 1973.

Dowdy, S. M., ⊗4Mathematics: Art and Science⊗*, John Wiley & Sons, NY, 1971.

Dubin, Robert, ⊗4Theory Building⊗*, The Free Press, New York,  1969.

Dubs, Homer H., ⊗4Rational Induction⊗*, U. of Chicago Press, Chicago, 1930.

Dudley, Underwood, ⊗4Elementary Number Theory⊗*, W. H. Freeman and
Company, San Francisco, 1969.

Eynden, Charles Vanden, ⊗4Number Theory: An Introduction to Proof⊗*, 
International Textbook Comapny, Scranton, Pennsylvania, 1970.

Fuller, R. Buckminster, ⊗4Intuition⊗*, Doubleday, Garden City, New York,
1972.

Fuller, R. Buckminster, ⊗4Synergetics⊗*, ...

GCMP, ⊗4Key Topics in Mathematics⊗*, Science Research Associates,
Palo Alto, 1965.

George, F. H., ⊗4Models of Thinking⊗*, Schenkman Publishing Co., Inc.,
Cambridge, Mass., 1972.

Goldstein, Ira, ⊗4Elementary Geometry Theorem Proving⊗*, MIT AI Memo 280,
April, 1973.

Goodstein, R. L., ⊗4Fundamental Concepts of Mathematics⊗*, Pergamon Press, 
New York, 1962.

Goodstein, R. L., ⊗4Recursive Number Theory⊗*, North-Holland Publishing Co.,
Amsterdam, 1964.

@Green, Waldinger, Barstow, Elschlager, Lenat, McCune, Shaw, and Steinberg,
⊗4Progress Report on Program-Understanding Systems⊗*, Memo AIM-240,
CS Report STAN-CS-74-444,Artificial Intelligence Laboratory,
Stanford University, August, 1974.

@Hadamard, Jaques, ⊗4The Psychology of Invention in the Mathematical
Field⊗*, Dover Publications, New York, 1945.

Halmos, Paul R., ⊗4Naive Set Theory⊗*, D. Van Nostrand Co., 
Princeton, 1960.

Hanson, Norwood R., ⊗4Perception and Discovery⊗*, Freeman, Cooper & Co.,
San Francisco, 1969.

Hardy, G. H.,  and E. M. Wright, ⊗4An Introduction to the Theory of Numbers⊗*,
Oxford U. Press, London, 1938. (Fourth edition, 1960)

Hartman, Robert S., ⊗4The Structure of Value: Foundations of Scientific
Axiology⊗*, Southern Illinois University Press, Carbondale, Ill., 1967.

Hempel, Carl G., ⊗4Fundamentals of Concept Formation in Empirical
Science⊗*, University of Chicago Press, Chicago, 1952.

Hibben, John Grier, ⊗4Inductive Logic⊗*, Charles Scribner's Sons,
New York, 1896.

Hilpinen, Risto, ⊗4Rules of Acceptance and Inductive Logic⊗*, Acta
Philosophica Fennica, Fasc. 22, North-Holland Publishing Company,
Amsterdam, 1968.

Hintikka, Jaako, ⊗4Knowledge and Belief⊗*, Cornell U. Press, Ithaca, NY, 1962.

Hintikka, Jaako, and Suppes, Patrick (eds.), ⊗4Aspects of Inductive
Logic⊗*, North-Holland Publishing Company, Amsterdam, 1966.

Jouvenal, Bertrand de, ⊗4The Art of Conjecture⊗*, Basic Books, Inc.,
New York, 1967.

Kac, Mark, and S. Ulam, ⊗4Mathematics and Logic: Retrospects and Prospects⊗*,
Frederick A. Praeger, N.Y. 1968.

@Kershner, R.B., and L.R.Wilcox, ⊗4The Anatomy of Mathematics⊗*, The Ronald
Press Company, New York, 1950.

Klauder, Francis J., ⊗4The Wonder of Intelligence⊗*, Christopher
Publishing House, North QUincy, Mass., 1973.

Klerner, M., and J. Reinfeld, eds., ⊗4Interactive Systems for Applied Mathematics⊗*,
ACM Symposium, held in Washington, D.C., August, 1967. Academic Press, NY, 1968.

Kline, M. (ed), ⊗4Mathematics in the Modern World: Readings from Scientific
American⊗*, W.H.Freeman and Co., San Francisco, 1968.

@Kling, Robert Elliot, ⊗4Reasoning by Analogy with Applications to Heuristic
Problem Solving: A Case Study⊗*, Stanford Artificial Intelligence Project
Memo AIM-147, CS Department report CS-216, August, 1971.

Knuth, Donald, ⊗4The Art of Computer Programming⊗*, ...

Knuth, Donald, ⊗4Surreal Numbers⊗*, ...

Koestler, Arthur, ⊗4The Act of Creation⊗*,  New York, Dell Pub., 1967.

Korner, Stephan, ⊗4Conceptual Thinking⊗*, Dover Publications, New York,
1959.

Krivine, Jean-Louis, ⊗4Introduction to Axiomatic Set Theory⊗*, Humanities Press,
New York, 1971.

Kubinski, Tadeusz, ⊗4On Structurality of Rules of Inference⊗*, Prace
Wroclawskiego Towarzystwa Naukowego, Seria A, Nr. 107, Worclaw, 
Poland, 1965.

Lakatos, Imre (ed.), ⊗4The Problem of Inductive Logic⊗*, North-Holland 
Publishing Co., Amsterdam, 1968.

Lamon, William E., ⊗4Learning and the Nature of Mathematiccs⊗*, Science
Research Associates, Palo Alto, 1972.

Lang, Serge, ⊗4Algebra⊗*, Addison-Wesley, Menlo Park, 1971.

Lefrancois, Guy R., ⊗4Psychological Theories and Human Learning⊗*, 1972.

Le Lionnais, F., ⊗4Great Currents of Mathematical Thought⊗*, Dover
Publications, New York, 1971.

Margenau, Henry, ⊗4Integrative Principles of Modern Thought⊗*, Gordon
and Breach, New York, 1972.

Martin, James, ⊗4Design of Man-Computer Dialogues⊗*, Prentice-Hall, Inc.,
Englewood Cliffs, N. J., 1973.

Martin, R. M., ⊗4Toward a Systematic Pragmatics⊗*, North Holland Publishing
Company, Amsterdam, 1959.

Mendelson, Elliott, ⊗4Introduction to Mathematical Logic⊗*, Van Nostrand Reinhold
Company, New York, 1964.

Meyer, Jerome S., ⊗4Fun With Mathematics⊗*, Fawcett Publications,
Greenwich, Connecticut, 1952.

Mirsky, L., ⊗4Studies in Pure Mathematics⊗*, Academic Press, New
York, 1971.

Moore, Robert C., ⊗4D-SCRIPT: A Computational Theory of Descriptions⊗*,
MIT AI Memo 278, February, 1973.

Nagel, Ernst, ⊗4The Structure of Science⊗*, Harcourt, Brace, & World, Inc.,
N. Y., 1961.

National Council of Teachers of Mathematics, ⊗4The Growth of Mathematical
Ideas⊗*, 24th yearbook, NCTM, Washington, D.C., 1959.

Newell, Allen, and Simon, Herbert, ⊗4Human Problem Solving⊗*, 1972.

Nevins, Arthur J., ⊗4A Human Oriented Logic for Automatic Theorem
Proving⊗*, MIT AI Memo 268, October, 1972.

Niven, Ivan, and Zuckerman, Herbert, ⊗4An Introduction to the Theory
of Numbers⊗*, John Wiley & Sons, Inc., New York, 1960.

Olson, Robert G., ⊗4Meaning and Argument⊗*, Harcourt, Brace & World,
New York, 1969.

Ore, Oystein, ⊗4Number Theory and its History⊗*, McGraw-Hill, 
New York, 1948.

Parish, Charles, and Roy McCormick, ⊗4A Structral Approach to Arithmetic⊗*,
Van Nostrand Reinhold Co., N.Y., 1970.

Parker, Francis D., ⊗4The Structure of Number Systems⊗*, Prentice-Hall, Inc.,
Englewood Cliffs, N.J.,  1966.

Pietarinen, Juhani, ⊗4Lawlikeness, Analogy, and Inductive Logic⊗*,
North-Holland, Amsterdam, published as v. 26 of the series
Acta Philosophica Fennica (J. Hintikka, ed.), 1972.

@Poincare', Henri, ⊗4The Foundations of Science: Science and Hypothesis,
The Value of Science, Science and Method⊗*, The Science Press, New York,
1929. 
.COMMENT main library, 501  P751F, copy 4;

@Polya, George, ⊗4Mathematics and Plausible Reasoning⊗*, Princeton
University Press, Princeton, Vol. 1, 1954;  Vol. 2, 1954.

@Polya, George, ⊗4How To Solve It⊗*, Second Edition, Doubleday Anchor Books, 
Garden City, New York, 1957.

@Polya, George, ⊗4Mathematical Discovery⊗*, John Wiley & Sons,
New York, Vol. 1, 1962; Vol. 2, 1965.

Richardson, Robert P., and Edward H. Landis, ⊗4Fundamental Conceptions of
Modern Mathematics⊗*, The Open Court Publishing Company, Chicago, 1916.

Rosskopf, Steffe, Taback  (eds.), ⊗4Piagetian Cognitive-
Development Research and Mathematical Education⊗*,
National Council of Teachers of Mathematics, New York, 1971.

Rulison, Jeff, and... ⊗4QA4, A Procedural Frob...⊗*,
Technical Note..., Artificial Intelligence Center, SRI, Menlo
Park, California, ..., 1973.

Saaty, Thomas L., and Weyl, F. Joachim (eds.), ⊗4The Spirit and the Uses
of the Mathematical Sciences⊗*, McGraw-Hill Book Company, New York, 1969.

Schminke, C. W., and Arnold, William R., eds., ⊗4Mathematics is a Verb⊗*,
The Dryden Press, Hinsdale, Illinois, 1971.

Singh, Jagjit, ⊗4Great Ideas of Modern Mathematics⊗*, Dover Publications,
New York, 1959.

@Skemp, Richard R., ⊗4The Psychology of Learning Mathematics⊗*, 
Penguin Books, Ltd., Middlesex, England, 1971.

Slocum, Jonathan, ⊗4The Graph-Processing Language GROPE⊗*, U. Texas at Austin,
Technical Report NL-22, August, 1974.

Smith, Nancy Woodland, ⊗4A Question-Answering System for Elementary Mathematics⊗*,
Stanford Institute for Mathematical Studies in the Social Sciences, Technical
Report 227, April 19, 1974.

Smith, R.L., Nancy Smith, and F.L. Rawson, ⊗4CONSTRUCT: In Search of a Theory of
Meaning⊗*, Stanford IMSSS Technical Report 238, October 25, 1974.

Spivak, Michael, ⊗4Calculus on Manifolds⊗*,  W.A.Benjamin, Inc., N.Y. 1965.

Stein, Sherman K., ⊗4Mathematics: The Man-Made Universe: An Introduction
to the Spirit of Mathematics⊗*, Second Edition, W. H. Freeman and 
Company, San Francisco,  1969.

Stewart, B. M., ⊗4Theory of Numbers⊗*, The MacMillan Co., New York, 1952.

Stokes, C. Newton, ⊗4Teaching the Meanings of Arithmetic⊗*, 
Appleton-Century-Crofts, New York, 1951.

Streeter, Donald N., ⊗4The Scientific Process and the Computer⊗*, John Wiley & Sons,
New York, 1974.

Suppes, Patrick, ⊗4A Probabilistic Theory 
of Causality⊗*, Acta Philosophica Fennica,
Fasc. 24, North-Holland Publishing Company, Amsterdam, 1970.

Teitelman, Warren, ⊗4INTERLISP Reference
Manual⊗*, XEROX PARC, 1974.

Tullock, Gordon,  ⊗4The Organization of Inquiry⊗*, Duke U. Press, Durham, N. C.,
1966.

Venn, John, ⊗4The Principles of Empirical or Inductive Logic⊗*,
MacMillan and Co., London, 1889.

Waismann, Friedrich, ⊗4Introduction to Mathematical Thinking⊗*, 
Frederick Ungar Publishing Co., New York, 1951.

Watzlawick, P., John Weakland, and Richard Fisch, ⊗4Change: Principles of
Problem Formulation and Problem Resolution⊗*, W.W.Norton & Co., Inc., N.Y. 1974.

Wickelgren, Wayne A., ⊗4How to Solve Problems: Elements of a Theory of Problems
and Problem Solving⊗*, W. H. Freeman and Co., Sanf Francisco, 1974.

Wilder, Raymond L., ⊗4Evolution of Mathematical Concepts⊗*, John Wiley & Sons,
Inc., NY, 1968.

Winston, P., (ed.),
"New Progress in Artificial Intelligence",
⊗4MIT AI Lab Memo AI-TR-310⊗*, June, 1974. 

Wittner, George E., ⊗4The Structure of Mathematics⊗*, Xerox College Publishing,
Lexington, Mass, 1972.

Wright, Georg H. von, ⊗4A Treatise on Induction and Probability⊗*,
Routledge and Kegan Paul, London, 1951.

.END
.GROUP SKIP 2
.ASSEC(Articles)

.BEGIN FILL SINGLE SPACE  PREFACE 1 INDENT 0,4,0 TURN OFF "@"

Amarel, Saul, ⊗4On Representations of Problems of Reasoning about
Actions⊗*, Machine Intelligence 3, 1968, pp. 131-171.

Bledsoe, W. W., ⊗4Splitting and Reduction Heuristics in Automatic
Theorem Proving⊗*, Artificial Intelligence 2, 1971, pp. 55-77.

Bledsoe and Bruell, Peter, ⊗4A Man-Machine Theorem-Proving System⊗*,
Artificial Intelligence 5, 1974, 51-72.

Bourbaki, Nicholas, ⊗4The Architechture of Mathematics⊗*, American Mathematics
Monthly, v. 57, pp. 221-232, Published by the MAA, Albany, NY, 1950.

@Boyer, Robert S., and J. S. Moore, ⊗4Proving Theorems about LISP Functions⊗*,
JACM, V. 22, No. 1, January, 1975, pp. 129-144.

Bruijn, N. G. de, ⊗4AUTOMATH, a language for mathematics⊗*, Notes taken by
Barry Fawcett, of Lecures given at the Seminare de mathematiques Superieurs,
University de Montreal, June, 1971. Stanford University Computer Science
Library report number is 005913.

@Buchanan, Feigenbaum, and Sridharan, ⊗4Heuristic Theory Formation⊗*,
Machine Intelligence 7, 1972, pp. 267-...

@Bundy, Alan, ⊗4Doing Arithmetic with Diagrams⊗*, 3rd IJCAI, 
1973, pp. 130-138.

Daalen, D. T. van, ⊗4A Description of AUTOMATH and some aspects of its language
theory⊗*, in the Proceedings of the SYmposium on APL, Paris, December, 1973,
P. Braffort (ed). This volume also contains other, more detailed articles on this
project, by  Bert Jutting and Ids Zanlevan.

Engelman, C., ⊗4MATHLAB: A Program for On-Line Assistance in Symbolic Computation⊗*,
in Proceedings of the FJCC, Volume 2, Spartan Books, 1965.

Engelman, C., ⊗4MATHLAB '68⊗*, in IFIP, Edinburgh, 1968.

Gardner, Martin, ⊗4Mathematical Games⊗*, Scientific American, numerous columns,
including especially:  February, 1975.

@Gelernter, H., ⊗4Realization of a Geometry-Theorem Proving Machine⊗*,
in (Feigenbaum and Feldman, eds.) ⊗4Computers and Thought⊗*, Part 1, Section 3,
pages 134-152, McGraw-Hill Book Co., New York, 1963.

Goldstine, Herman H., and J. von Neumann, ⊗4On the Principles of Large Scale
Computing Machines,⊗* pages 1:33 of Volumne 5 of A. H. Taub (ed), ⊗4The
Collected Works of John von Neumann⊗*, Pergamon Press, NY, 1963.

Guard, J. R., et al., ⊗4Semi-Automated Mathematics⊗*, JACM 16,
January, 1969, pp. 49-62.

Halmos, Paul R., ⊗4Innovation in Mathematics⊗*, in
Kline, M. (ed), ⊗4Mathematics in the Modern World: Readings from Scientific
American⊗*, W.H.Freeman and Co., San Francisco, 1968, pp. 6-13. Originally in
Scientific American, September, 1958.

Hasse, H., ⊗4Mathemakik als Wissenschaft, Kunst und Macht⊗*,
(Mathematics as Science, Art, and Power), Baden-Badeb, 1952.

@Hewitt, Carl, ⊗4A Universal Modular ACTOR Formalism for
Artificial Intelligence⊗*, Third International Joint Conference on
Artificial Intelligence,
1973, pp. 235-245.
.COMMENT Maybe a better ACTORS reference?;

Menges, Gunter, ⊗4Inference and Decision⊗*, 
A Volume in ⊗4Selecta Statistica Canadiana⊗*,
John Wiley & Sons, New York,  1973, pp. 1-16.

Kling, Robert E., ⊗4A Paradigm for Reasoning by Analogy⊗*,
Artificial Intelligence 2, 1971, pp. 147-178.

Knuth,Donald E., ⊗4Ancient Babylonian Algorithms⊗*,
CACM 15, July, 1972, pp. 671-677.

Lee, Richard C. T., ⊗4Fuzzy Logic and the Resolution Principle⊗*,
JACM 19, January, 1972, pp. 109-119.

@Lenat, D., ⊗4BEINGs: Knowledge as Interacting Experts⊗*, 4th IJCAI, 1975.

McCarthy, John, and Hayes, Patrick, ⊗4Some Philosophical Problems
from the Standpoint of Artificial Intelligence⊗*, Machine Intelligence
4, 1969, pp. 463-502.

Martin, W., and Fateman, R., ⊗4The MACSYMA System⊗*, Second
Symposium on Symbolic and Algebraic Manipulation, 1971, pp. 59-75.

Minsky, Marvin, ⊗4Frames⊗*, in (Winston) ⊗4Psychology of Computer
Vision⊗*, 1974.

Moore, J., and Newell, ⊗4How Can Merlin Understand?⊗*, Carnegie-Mellon University
Department of Computer Science "preprint", November 15, 1973.

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.END


.ASSEC(Acknowledgements)

I owe a great debt of thanks to many people, both for the
input of new ideas and for the evaluation, channelling, and pruning of
my own. Let me mention, alphabetically:
B. Buchanan, A. Cohn, R. Davis,
E. Feigenbaum,
R. Floyd, C. Green, D. Knuth, M. Lenat,
A. Newell,
E. Sacerdoti, R. Waldinger,
and R. Weyrauch.
Let me also thank SRI,
SUMEX, and SAIL,
for providing the computer facilities needed for this research.

.ASSEC(Documentation)

.ONCE TURN OFF "@"
The application of BEINGs to an Automatic Programming task is described
in [Lenat].  The problems with the domain of concept-formation-program-writing,
studied therein and summarized here in Appendix 1,
led to the AM project. 
A more complete description of AM can be perused as SYS4[TLK,DBL]@SU-AI.
The full body of knowledge we expect to provide to AM  is found on 
file GIVEN[TLK,DBL]@SU-AI. The running AM program is stored at SUMEX.
From Interlisp, one need only load in the two files <LENAT>TOP5
and <LENAT>CON5.