To:        Dr. Eamon Barrett, NSF
From:      Dr. Douglas B. Lenat, Carnegie-Mellon University
Date:      July 7, 1978
Subject:   Update to Research Proposal


The research I intend to  pursue during the coming year (July 1, 1978
through June 30, 1979) is essentially unchanged from that outlined in
my previous proposal [10] (MCS-7704440:  "The use of informal rules to
guide the  search  for discoveries  in  Mathematics".).  How  can  we
account for the creative  syntheses of new mathematical concepts, for
the  facility  which  human  mathematicians  demonstrate  at  finding
proofs, deciding  quickly  the promise  of various  new  definitions,
noticing conjectures, etc.?

This  research followed closely  upon the construction  of a computer
program (AM) which carried on simple mathematical theory formation on
its  own.  This is summarized  in the proposal [10],  and discussed at
varying lengths in [1]-[9].

In my  two-year proposal,  I  intended to  (i) get  a handle  on  the
problem, (ii)  build a  prototypical system  to use  an  experimental
vehicle, (iii) re-design  from that experience, tentatively along the
lines of  change of representation.  By now  we have accomplished (i)
and  are well along on  (ii), although the "handle"  we discovered is
quite unlike what was expected  (as discussed in the annual report on
this  project):  We represent  each heuristic rule  as a full-fledged
concept  with facets  (a  frame  with  slots, a  property  list  with
properties), and  treat heuristics as if they were  a special sort of
mathematical operation, nothing more.

I am leaving Carnegie-Mellon  University to become an Asst. Professor
at Stanford  University.  Effective  August 1,  my research  will  be
conducted  from there.  The  primary function of this  document is to
discuss the changes -- and absence of changes -- necessitated by such
a transition.   I shall continue my current  line of investigation --
into  the mechanisms whereby  heuristic rules can  be synthesized and
modified  -- and  I  anticipate  no interruption  in  that  endeavor.
Activities (ii) and (iii) in the paragraph above will be continued.

The facilities at Stanford are,  for my purposes, equal to or surpass
those  at   CMU.   For  example,  Interlisp  is   present,  as  is  a
two-dimensional screen editor,  Xerographic printers, etc.  On a more
personal  level, the  valuable  interactions  I am  giving  up  (with
Herbert Simon) will be  replaced by other regular research discussion
meetings (with Ed Feigenbaum, Donald Knuth, Bruce Buchanan, and other
members   of   the  Stanford   Computer   Science   and   Mathematics
Departments).  The graduate student assistance I require can and will
be  met  by  Stanford  graduate  student  research  assistants.   The
equipment  I require is being  purchased by CMU from  this grant, and
those  funds will  be  used  by Stanford  to  re-purchase  equivalent
equipment for this project.

The  paramount  consideration  effecting  my  decision  to  shift  my
appointment to  Stanford was  the research  environment it  provided:
the increased expected yield of  my research.  The shift will cause a
delay in the  timetable, but not one of more  than a few weeks.  This
lack of trauma is due to the  fact that I spent the years 1972-6 as a
graduate student  at  Stanford, and  am  familiar with  the  systems,
languages, staff,  faculty, and many of  the graduate students there.
I am  receiving a great deal of support  from the department chariman
(Professor  E.  A. Feigenbaum),  department  administrators  (Ms.  B.
Scott), and others, to ease my transition as much as possible.
Published papers about the AM and Eurisko research projects


[1]  AM:   An   Artificial  Intelligence  Approach  to  Discovery  in
Mathematics  as Heuristic Search,  Ph.D.  Thesis, Stanford  A. I. Lab
Memo  AIM-286,   CS  Report   No.   STAN-CS-76-570,   and   Heuristic
Programming Project Report HPP-76-8, Stanford University, July, 1976.

[2] Designing a Rule System That Searches for Scientific Discoveries,
(Lenat  and  Harris),  invited  paper  for  the  PDIS  conference  in
Honolulu, May,  1977; published  in (Hayes-Roth  and Waterman,  eds.)
Pattern-Directed  Inference  Systems,  Academic  Press,  1977.   Also
issued as a CMU technical report, April, 1977.

[3]   Automated  Theory   Formation  in   Mathematics,  Fifth  IJCAI,
Cambridge, Mass., August, 1977.

[4] Less Than General  Production System Architectures, (Lenat and J.
McDermott,) Fifth IJCAI, Cambridge, Mass., August, 1977.

[5] The Ubiquity of Discovery, the 1977 Computers and Thought Lecture
(invited talk at the  Fifth IJCAI).  Preliminary version published in
the proceedings  of that  conference; final  version printed  in  the
Journal of  A.I.  Reprinted in New York's  The Sciences, and repeated
as an invited talk at NCC (Anaheim, June, 1978).

[6] On Automated Scientific Theory Formation:  A Case Study Using the
AM Program, invited paper presented at the Ninth Machine Intelligence
workshop in Leningrad, USSR, April, 1977.  Forthcoming publication in
(Michie, ed.) Machine Intelligence 9, 1978.

[7] Artificial Intelligence  and Natural Statistics, invited paper at
"Computer  Science and Statistics:  Eleventh  Annual Symposium on the
Interface", University of North Carolina at Raleigh, March 6, 1978.

[8] Unscripted interview on  AI & Problem Solving, broadcast over the
BBC,  as part of  the Open  University's 32 week  course on Cognitive
Psychology.  Taped  at CMU on Feb. 22, 1978,  by Clive Holloway, Open
University, Milton Keynes, England.

[9] Expert Systems, a section of the forthcoming COSERS report, 1978.

[10] The Use of Informal Rules to Guide the Search for Discoveries
in Mathematics,  Research Proposal MCS-7704440, submitted to NSF,
November 9, 1976.