perm filename FAILED.TXT[NOT,DBL]1 blob
sn#200767 filedate 1976-02-08 generic text, type T, neo UTF8
Dear Professor Levy,
I imagine that Professor Amarel (or Bruce Buchanan) has told you who
I am, what my interests are, etc. Professor Amarel has informed me
that Friday, Feb. 20, would be a good day for me to give a talk at
Rutgers about my thesis research. That is fine with me. He indicated
that you would coordinate the final plans for my visit.
I am mailing to him a nicely-printed title and abstract for that
talk. A somewhat garbled version is appended to the end of this
note.
I will try to call you tomorrow (Monday, Feb. 9) around 1pm and 5pm
your time, and again Tuesday at those times. I will be at the A.I.
Lab (415-497-4971) off and on those days. Of course you can also
reach me via the Arpanet (DBL@SU-AI).
If you attend the ACM conference in Anaheim next week, perhaps we can
meet there. If not, I'll see you at Rutgers.
Sincerely,
Doug Lenat
*********************************************************************
*********************************************************************
Automating the Discovery of Mathematical Concepts
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:
(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?