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␈↓ ↓H␈↓␈↓ ε∀␈↓↓SEMINAR:
␈↓ ↓H␈↓↓␈↓ ¬0Monday, February 16, 1976␈↓



␈↓ ↓H␈↓␈↓ β
␈↓∧␈↓&Automating the Discovery of Mathematical Concepts␈↓)αβ␈↓


␈↓ ↓H␈↓␈↓ ¬m␈↓↓Douglas B. Lenat␈↓
␈↓ ↓H␈↓␈↓ ¬;Arti≡cial Intelligence Lab
␈↓ ↓H␈↓␈↓ ¬←Stanford University





␈↓ ↓H␈↓We␈αoften␈αface␈αthe␈αdi≠cult␈αtask␈αof␈αformulating␈αnew␈αresearch␈αproblems␈αwhich␈αmust␈αbe␈αsoluble␈αand␈αyet
␈↓ ↓H␈↓nontrivial.  Can such "originality" be mechanized? Well, how about ␈↓βpartially␈↓ mechanized?

␈↓ ↓H␈↓This␈α
seminar␈α
describes␈α
one␈α
approach␈α∞to␈α
partially␈α
automating␈α
the␈α
development␈α
of␈α∞new␈α
mathematical
␈↓ ↓H␈↓concepts.␈α
 First,␈α
we␈α
consider␈α
how␈α
to␈α
␈↓βexplain␈↓␈αa␈α
discovery,␈α
by␈α
systematically␈α
analyzing␈α
it␈α
until␈α
it␈αseems
␈↓ ↓H␈↓obvious.␈α↔Inverting␈α⊗this␈α↔reduction␈α⊗procedure,␈α↔we␈α⊗obtain␈α↔a␈α⊗simple␈α↔scheme␈α⊗for␈α↔␈↓βgenerating␈↓␈α⊗new
␈↓ ↓H␈↓discoveries.␈α∞ Many␈α∞powerful␈α∞heuristic␈α∞rules␈α∞are␈α∞needed␈α∞for␈α∞guidance,␈α∞to␈α∞combat␈α∂the␈α∞combinatorially
␈↓ ↓H␈↓explosive nature of this process.

␈↓ ↓H␈↓An␈α∩experimental␈α∩interactive␈α∩LISP␈α∩program␈α∩has␈α∩been␈α∩developed,␈α∩which␈α∩carries␈α∩out␈α∩some␈α∪of␈α∩the
␈↓ ↓H␈↓activities␈αinvolved␈α
in␈αsimple␈αmathematical␈α
research:␈αnoticing␈αobvious␈α
relationships␈αin␈α
empirical␈αdata,
␈↓ ↓H␈↓formulating␈αnew␈αde≡nitions␈αout␈αof␈αexisting␈α
ones,␈αproposing␈αsome␈αplausible␈αconjectures,␈αand␈α
estimating
␈↓ ↓H␈↓the potential worth of each new concept.

␈↓ ↓H␈↓After explaining the workings of this program, we can discuss such issues as:
␈↓ ↓H␈↓␈↓ αλ(i) Choice of task domain: Why mathematics?  Suitability of various other sciences.
␈↓ ↓H␈↓␈↓ αλ(ii) Experiments one can perform on this program: What do we hope to learn?
␈↓ ↓H␈↓␈↓ αλ(iii) The role of the human user: spectator ␈↓βvs␈↓ co-researcher.
␈↓ ↓H␈↓␈↓ αλ(iv) How can one judge the performance of a concept-proposer which has no ≡xed goal?
␈↓ ↓H␈↓␈↓ αλ(v) What kinds of discoveries are most di≠cult to mechanize?
␈↓ ↓H␈↓␈↓ αλ(vi) Can the reasons for ␈↓βconsidering␈↓ X aid in ␈↓βproving␈↓ X?