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PATTERNS AND CONCEPTS

by John McCarthy, Stanford University


	Papers reporting research in pattern recognition or concept
formation often use very limited notions of pattern or concept without
even hinting that there are patterns and concepts that don't fit
under their notions.  Some even give formal definitions of what
a concept is that are extremely limited in what they cover.

	This paper gives some examples of such limited notion, gives
some examples of patterns and concepts that don't fit them, and
gives a more general notion of pattern that includes all examples
that I know about.  However, since it has an arbitrary first order
language as a parameter, what patterns and concepts can be defined
depends on the language.  To some extent this passes the buck to
the inventor of the language, but we shall argue that this is the
way it should be.

	The works we shall criticize include (Bruner 1956), (Hunt 197x)
(Winston 197x) and (Mitchell 1981).

	None of the above notions can handle the following pattern
which we present in a form suitable for an intelligence or scholastic
aptitude test.

	Consider the following five groups of places:  Which one
differs from the other four in an interesting way?

California
San Francisco

U.S.A.
New York
Chicago

Buenos Aires
Argentina
South America

Toronto
Canada
North America
Ontario

the solar system
the Galaxy
Jupiter
The Great Red Spot

	The intended answer is that the second group of places is the
only one not totally ordered by inclusion.  A majority of people I
have asked find the odd group, but only a small minority can describe
the pattern they have in mind.
I have also given a geometric version of the problem with triangles,
circles and squares.  The most popular answer is that the four are
concentric and the fifth is not.  This is an approximate answer, since
the figures weren't well drawn enough to have definite centers, and
some of them were definitely eccentrically located.