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⊗2COLLOQUIUM:
Computer Science Department
University of Texas at Austin

Monday, February 23, 1976
4:00 pm⊗*



⊗5↓_Automating the Discovery of Mathematical Concepts_↓⊗*


⊗2Douglas B. Lenat⊗*
Artificial Intelligence Lab
Stanford University




.END

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 talk 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 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:

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(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?

.END