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C00002 00002	 \SSSEC{Diagram of Initial Concepts}
C00006 00003	 \SSSEC{An Illustration: Discovering Primes}
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 \SSSEC{Diagram of Initial Concepts}

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				    Anything
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	     ⊂∂∂∂∂∂∂∂∂∂Activity         Object
             }	       /   \  	        /  }  \
      Relation        /     \          /   }   \
         /     Predicate Operation  Atom Conjec Structure∂∂∂∂∂∂∂∂⊃
Logical-reln  /         \      }      }	       / }  }   }\       }
   Constant-pred Equality-pred } Truth-value  /  }  }   } \ Struc-of-strucs
.ONCE TURN OFF ``\``
     \       \        \        }             /   } Empty}  \
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     \       \        \        ∪	    /    }      }   \   
Const-T  Const-F  Obj-equal   ∩    Mult-eles  Non-mult  Ord  Unordered
		              ∪      \	   \   \     \  / } /	    /
                    Coalescing        \     \   \  Osets  }/       /
		Inverted-operation     \     \   \        /       /
		   Canonization         \     \   \      /}      /
       		    Composition          \     \    Sets  }     /
               Restricted-operation       \     \         }    /
			#                  \     \        ∪   /
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The diagram above represents the ``topmost" concepts
which AM had initially,
shown connected via
Specialization links (\8\\0) and Examples links (\8α\\0).
The only concepts not diagrammed are \4examples\0 of the concept Operation.
There are 47 such operations.

Also, we should note that many entities exist in the system
which are not themselves concepts. For example, the number ``3", though it
be an \4example\0 of many concepts, is not itself a concept.
All entities which \4are\0 concepts are present on the list called
CONCEPTS, and they all have property lists (with facet names as the
properties). In hindsight, this somewhat arbitrary scheme is regrettable.
A more aesthetic designer might have come up with a more uniform system
of representation than AM's.

 \SSSEC{An Illustration: Discovering Primes}


Here is a heuristic rule  that
results in a new concept being created:


\han2{{\it If the current task was {\6(Fill-in examples of F)},}}

\han3{{\it and F is an operation from domain space A into range space B,}}

\han3{{\it and more than 100 items are known examples of A (in the domain of F),}}

\han3{{\it and more than 10 range items (in B) were found by applying F to these
domain items,}}

\han3{{\it and at least  1 of these range items is a distinguished member (esp:
extremum)\foo{
This is handled as follows: AM takes the given list of range items. It eliminates
any which are not interesting (according to Interests(B))  or extreme (an entry
on B.Exs-Bdy, the boundary examples of B).
Finally, all those extreme range items are moved to
the front of this list. 
AM begins walking down this list, creating
new concepts according to the rule. Sooner or later,
a timer (or a storage-space-watcher) will terminate this costly activity. 
Only the frontmost
few range items on the list will have generated new concepts.
So ``especially" really just means priority consideration. }
of B,}}


\han2{{\it Then (for each such distinguished member
 `b'$\epsilon$B) create the following new concept:}}


\yskip

\han4{\6Name: {\it F\inv -of-b}}

\han4{\6Definition: \it $\lambda (x) \biglp F(x) = b \bigrp $}

\han4{\6Generalization: {\it A }}

\han4{\6Worth: \it $ Average \biglp Worth(A), Worth(F), Worth(B), Worth(b), $}

\han7{$100 \times max(10, \|Examples(B)\|)\bigrp $}

\han4{\6Interest: \it Any conjecture involving both this concept and either F or F\inv }

\han5{\it In case  the user  asks, the  reason for  doing this is:  
``Worthwhile
investigating those A's  which have an unusual F-value, namely, those
whose F-value is b"}

\yskip

\han3{\it and the total  amount of time  to spend  
right now  on all  of these  new
concepts is computed as: }

\han4{\it Half the  remaining cpu time in  the current
task's time quantum.}

\han3{\it and the total  amount of space to spend  right now  on each of these  new
concepts is computed as: }

\han4{\it 90{\rm \%} \ of the remaining space quantum for the current task.}

\noindent \1
Heuristics for the new concept are quite hard to fill in. This was one of AM's
most serious limitations, in fact (see Chapter 7).
Above, we see a trivial kind of ``heuristic schema" or template, which gets
instantiated to provide one new, specialized heuristic about the new concept.
That new heuristic tells how to judge the interestingness of any conjecture
which crops up involving this new concept. As new conjectures get proposed,
they are evaluated by calling on  a set of heuristics including this one.


Although some examples of \6F\inv -of-b\0 might be easily obtained
(or already known) at the moment of its creation, the above rule doesn't specifically
tell AM how to fill in that facet. The very last line of the heuristic indicates
that a few cpu seconds may be spent on just this sort of activity: filling in facets
of the new concept which, though not explicitly mentioned in the rule, are
easy to fill in now.
 Any facet {\it f} which didn't get filled in ``right now" will
probably cause a new task to be added to the agenda, of the form: ``\6Fillin
facet {\it f} of concept {\it F\inv -of-b}\1''.
Eventually, AM would choose that task, and spend a large quantum of time working
on that single facet.

Now let's look at an instance of when this heuristic was used. At one
point,  AM   was  working   on   the  task   ``\6Fill-in  examples   of
Divisors-of\0''.

This  heuristic's  IF-part was  triggered because: Divisors-of is  an
operation (from Numbers to Sets  of  numbers), and far more than 100  different
numbers  are  known, and  more than 10  different  sets  of  factors  were  found
altogether,  and some  of them  were  distinguished by  being extreme