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Dear Lucy,

Here is the  title and abstract  for my seminar  (Mon., Feb. 16).   A
nicer version (with  beautiful fonts, etc.) is winging its way to you
even now (via the  U.S. Mails).    It would probably be worth waiting
for that copy if you want to post the abstract somewhere.

Regards, 
Doug

*********************************************************************

Automating the Discovery of Mathematical Concepts


	Douglas B. Lenat
	Artificial Intelligence Lab
	Stanford University

We often face the difficult task of formulating new research problems
which must  be soluble and yet nontrivial.  Can such "originality" be
mechanized? Well, how about ⊗4partially⊗* mechanized?

This  seminar describes  one  approach  to partially  automating  the
development of new mathematical  concepts.  First, we consider how to
⊗4explain⊗* a  discovery, by  systematically  analyzing it  until  it
seems obvious. Inverting this reduction procedure, we obtain a simple
scheme  for ⊗4generating⊗* new discoveries.   Many powerful heuristic
rules  are  needed  for  guidance,  to  combat   the  combinatorially
explosive nature of this process.

An experimental  interactive LISP  program has been  developed, which
carries  out some of  the activities involved  in simple mathematical
research:  noticing   obvious   relationships  in   empirical   data,
formulating  new definitions  out  of existing  ones,  proposing some
plausible conjectures, and estimating the potential worth of each new
concept.

After explaining the  workings of this  program, we can  discuss such
issues as:

(i) Choice  of task domain: Why mathematics?   Suitability of various
other sciences.
(ii) Experiments one can perform on this program: What do we  hope to
learn?
(iii) The role of the human user: spectator ⊗4vs⊗* co-researcher.
(iv) How  can one judge  the performance of a  concept-proposer which
has no fixed goal?
(v) What kinds of discoveries are most difficult to mechanize?
(vi) Can the reasons for ⊗4considering⊗* X aid in ⊗4proving⊗* X?