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.require "memo.pub[let,jmc]" source
.bb WHAT IS A PATTERN?


	In many areas of programming and especially in artificial
intelligence, it is effective to create and use patterns.
The use involves determining that an object in a situation can be
obtained by instantiating a pattern in a particular way, i.e. that
the object can be obtained by replacing the variables in the pattern
by certain constants; after this the fact that the recognition was
successful and the values that had to be assigned to the variables
in the instantiation are used to determine an action.
More generally, the action taken may depend
on a set of patterns and other information as well.

	The most well developed forms of pattern and pattern
recognition occur in formal syntax of languages where both the
objects instantiating the variables and the object matched
are strings of symbols.  I want to define patterns
abstractly quite separately from language but hopefully in a way
that is applicable to language and in a way that will enable
some of the properties of linguistic patterns that have been
studied to carry over to %2abstract patterns%1.

	Besides the linguistic pattern recognition, there is also an
older study that involved solely determining which of a number of
patterns an object instantiated without giving the replacements
performed in making the instantiation.  In compensation, this study included
learning patterns from experience.  In my opinion, mere pattern
classification is a blind alley, but in compensation for not
identifying the instantiation required, patterns were sometimes
learned, and some patterns be recognizable in that way, which
have not been successfully studied as instantiations.

	Our goal is to generalize pattern recognition beyond it
linguistic origin and to illustrate some new kinds of pattern.

******

Examples:

	1. A pin in chess.

	2. A pine tree.

	3. A dog as an assemblage of parts with relations.

	4. The appearance of a dog (and its relation to the above
taking into account projection and occlusion).

	5. Considering an algebraic expression in which one of its subexpressions
occurs twice as an instance of a pattern.  (This can be done easily in the
string case as  axbxc  but then a, b, and c may be expressions with
unmatched parentheses).  The problem takes its true form in LISP where it is
an instance of F(x,x) where F is a substitution operator.

	6. Recognizing %23(cos%52%2x + 2y) + 3 sin%52%2x%1 as an example
of %2f(cos%52%2x + sin%52%2x)%1.  The best approach here may be to consider
that the actual object being recognized is the equivalence class of
an expression under a certain group of transformations.

This is patter.2[f75,jmc].