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C00004 00003 We often face the difficult task of formulating new research problems
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⊗2LECTURE:
Computer Science Department
Rutgers University
Friday, February 20, 1976⊗*
⊗5↓_Automating the Discovery of Mathematical Concepts_↓⊗*
⊗2Douglas B. Lenat⊗*
Artificial Intelligence Lab
Stanford University
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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