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Can the process  of scientific research  be adequately modelled  as a
rule-directed  search  process? As  a  first step  in  answering that
question, a computer program called "AM" has been constructed which performs
elementary mathematics research. 

AM  develops new math
concepts under the guidance of a large body of heuristic rules.
The 250  local heuristic rules 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   a  recognizable  pattern,  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 a  simple 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 paper will emphasize the  control structure of AM, including  an
analysis of  its collection of  heuristic rules.   A brief  survey of
experimental  results  will  show that  this  rule-based  approach to
plausible inference contains great powers and great limitations.