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↓_AM:_↓ An Artificial Intelligence Approach to
Discovery in Mathematics as Heuristic Search
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Douglas B. Lenat, Ph.D.
Stanford University, l976
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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 (e.g., union).
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 great powers
and great limitations.
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