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⊗5↓_Discovery in Mathematics_↓⊗*
⊗5↓_as Heuristic Search_↓⊗*




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



.END

A program,  called  "AM", is  described which  models  one aspect  of
elementary  mathematics research:  developing new concepts  under the
guidance of  a  large body  of  heuristic  rules.   "Mathematics"  is
considered  as a  type of  intelligent  behavior, not  as a  finished
product.

The  local heuristics communicate  via an agenda  mechanism, a global
list of tasks for the system to perform and reasons  why each task is
plausible.  A single task might direct AM to define a new concept, or
to explore some  facet of  an existing  concept, or  to examine  some
empirical  data  for  regularities, etc.    Repeatedly,  the  program
selects from the  agenda the task having the best supporting reasons,
and then executes it.

Each concept is  an active, structured knowledge  module.  A  hundred
very   incomplete   modules   are  initially   provided,   each   one
corresponding  to an elementary  set-theoretic concept.
This provides  a  definite but  immense "space"  which  AM begins  to
explore.   AM  extends its  knowledge base,  ultimately rediscovering
hundreds of  common  concepts  (e.g., numbers)  and  theorems  (e.g.,
unique factorization).

This approach to plausible inference  contains some unexpected powers
and limitations.