creative sli

7/28/2019 Creative Sli

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CREATIVE SOLUTIONS TO PROBLEMS

John McCarthy

Computer Science Department

Stanford [email protected]

http://www-formal.stanford.edu/jmc/

started April 1, 1999; compiled May 18, 199

Almost all of my papers are on the web page.


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APPROACHES TO ARTIFICIAL INTELLIGE

biologicalHumans are intelligent; imitate huma

observe and imitate at either the psychological or

physiological level

engineeringAchieve goals in the worldso stu

world

1. Write programs using non-logical representatio2. represent facts about the world in logic and

what to do by logical inference

We aim at human level AI, and the key phenom

the common sense informatic situation.


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THE COMMON SENSE INFORMATIC SITUAT

Contrasts with the situation in a formal scientiory and most AI theories. Science is embed

common sense.

No limitation on what information may be re

Theories must be elaboration tolerant.

Needs non-monotonic reasoning.

Needs approximate entities.


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A LOGICAL ROAD TO HUMAN LEVEL A

Use Drosophilas that illustrate aspects of repr

tion and reasoning problems.

Concepts, context, circumscription, counterfa

consciousness, creativity, approximation

narrative, projection, planning

mental situation calculus

domain dependent control of reasoning


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IDENTIFYING CREATIVE SOLUTIONS T

PROBLEMS

Making creative programs will be hard.

Making a program that will recognize creativity

ier but still too hard for me now.

Distinguish the idea of a solution from the s

itself.


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IDENTIFYING CREATIVE SOLUTIONS T

PROBLEMS

I can identify, thinking by hand, creative solut

I can sometimes express the creative idea by a

formula.

The Drosophila for this research is the mutilate

board problem.

As much as possible, an idea should be one thi

it should be promising in itself.


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I know four creative solutions to the mutilated c

board problem, the standard solution, Marv

skys solution, Shmuel Winograds solution an

itri Stefanuks 17 similar solutions.

I tried to express each idea as concisely as wa

patible with leading a person to the solution.


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THE MUTILATED CHECKERBOARD


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DOMINO

MUTILATED CHECKERBOARD


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THE STANDARD SOLUTION

Whats the idea of the solution that a creative pe

program may come up with? This is distinct from

the detailed argument. English firstthen a form

Color the board as in a checkerboard.

A domino covers two squares of the opposite colo

Some people also need that the removed squares

the same color.


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THE COMMON FACTS IN SET THEORY

Board = Z8 Z8,

mutilated-board = Board {(0, 0), (7, 7)},

domino-on-board(x) (x Board) card(x) = 2(x1 x2)(x1 = x2 x1 x x2 x

adjacent(x1, x2))


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adjacent(x1, x2) |c(x1, 1) c(x2, 1)| = 1 c(x1, 2) = c(x2, 2)

|c(x1, 2) c(x2, 2)| = 1 c(x1, 1) = c(x2, 1).


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adjacent(x1, x2) |c(x1, 1) c(x2, 1)| + |c(x1, 2) c(x2, 2)| = 1,

partial-covering(z) (x)(x z domino-on-board(x))(x y)(x z y z x = y x y = {})

Theorem:

(

z)(partial-covering(z) z = mutilated-boar


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Makers of automatic or interactive theorem prov

ten dont like set theory because of the compre

principle. They had better get used to it.


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THE UNMATHEMATICAL REQUIRE MANY H

Take into account the colors.

What are the colors of the diagonally opposite

squares?

How many of each color does a domino cover?

How many of each do n dominoes cover? huh?

What about 7 dominoes?

How many of each do n dominoes cover? Equa

Two blacks left over, but maybe a more clever. . . .


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MARVIN MINSKYS IDEA

Starting with the two square diagonal next to

excluded square, successively compute how m

dominoes must project from each diagonal to

next diagonal.

Good enough hint for a horse doctor.

Not a sentence, but a program fragmentwit

termination condition.


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SHMUEL WINOGRADS IDEA

Note that an odd number of dominoes project fr

top row to the second and continue.

A movie showed a math teacher rejecting this id

Socratically leading the student to the standard so

Winograd showed the student was on the righ

but most people need something like

Starting with the top row, compute the parity

number of dominoes projecting down out of eac

Consider the parity of the sum. Repeat going h

tally. Compute the parity of the total number o

noes compared to the sum of the two parities.


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DIMITRI STEFANUKS IDEA

The idea seems to involve two program fragment

Label an arbitrary square 1, label its rectilin

neigbors 2, their neighbors 3, etc.

Starting with n = 1, successively compute hmany dominoes must project from the set of sq

labelled n to the squares labelled n + 1.


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FORMULAS FOR MINSKY SOLUTION

diag(n) = {x Board|c(x, 1) + c(x, 2) = n}

covering(u) partial-covering(u)

u = Boa

covering(u) 2 n 13dominoes-into(n, u) = {x u|x diag(n 1) = {} x diag(n) = {}}

card(dominoes-into(n, u)) + card(dominoes-into(n= card(diag(n))


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covering(u) card(dominoes-into(2, u)) = 2


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REALITY BEHIND APPEARANCE

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