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Artificial Intelligence in Action Wednesday, September 6

Two Open Lectures NC 1511

7:00 am – 8:15 am LINGUISTIC GEOMETRY FOR DEFENSE SYSTEMS

8:30 am – 9:45 am LINGUISTIC GEOMETRY:

A HISTORICAL PROSPECTIVE

Both lectures will be given by Professor Boris Stilman www.stilman-strategies.com

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Assignment 2. Due 09/13/10.

1. Analyze problems Tower of Hanoi and Missionaries and

Cannibals with respect to the seven problem characteristics discussed in class.

2. Construct heuristic functions and apply

a) simple hill climbing b) steepest-ascent hill climbing

to 3 problems Tower of Hanoi, Monkey and Bananas, Missionaries and Cannibals.

Show search trees and explain how your functions help to reduce search. Do they really work? If your functions do not work properly explain what happened.

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Problem Characteristics

1. Is the problem decomposable? 2. Can solution steps be ignored or undone? 3. Is the problem's universe predictable? 4. Is good solution absolute or relative? 5. Is the desired solution a state of the world or a path to a

state? 6. Is a large amount of knowledge absolutely required to solve

the problem, or is it important only to constrain the search? 7. Must problem-solving be interactive?

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1. Decomposable and Non-Decomposable Problems

(x2 + 3x + sin2x cos2x) dx

x2dx 3xdx sin2x cos2xdx

x3 3xdx (1—cos2x) cos2xdx 3

3x2 cos2xdx cos4xdx 2

Recursive Decomposition

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1. Decomposable and Non-Decomposable Problems

A Simple Blocks World Problem

C

A B

ON(C, A)

C

A

B

ON(B, C) ON(A, B)and

Start Goal

1. CLEAR(x) —> ON(x, Table) pick up x and block x has put it on table nothing on it 2. CLEAR(x) and CLEAR(y) —> ON(x, y) put x on y

ON(B, C) and ON(A, B)

ON(A, B)ON(B, C)

ON(B, C) CLEAR(A) ON(A, B)

CLEAR(A) ON(A, B)

Move C to tablePut A on B

Put B on C

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1. Decomposable and Non-Decomposable Problems

A Digital Lock Problem (decomposable)

1 3 2 7

10 windows

. . . .

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2. Ignorability

8-Puzzle

2 8 3

1 6 4

7 5

1 2 38 4

7 6 5

Start Goal

— Ignorable (theorem proving) can be ignored — Recoverable (8-puzzle) solution steps can be undone — Irrecoverable (chess) cannot be undone

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3. Is the Universe predictable?

What about 8-Puzzle?

— Playing bridge. We do not know the current state. But we can do fairly well

since we have available accurate estimates of the probabilities of each of the possible outcomes.

— Controlling a robot arm. The outcome is uncertain for a variety of reasons. Someone

might move into the path of the arm. The gears of the arm might stick. A slight error could cause the arm to knock over a whole stack of things.

— Helping a lawyer decide how to defend his client against

a murder charge. Here we probably cannot even list all possible outcomes,

much less assess their probabilities. The worst scenario: Irrecoverable, uncertain-outcome problem

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4. Absolute or relatively good solution

Facts about Marcus

1. Marcus was a man. 2. Marcus was a Pompeian. 3. Marcus was born in 40 A.D. 4. All men are mortal. 5. All Pompeians died when volcano erupted in 79 A.D. 6. No mortal lives longer than 150 years. 7. It is now 2009 A.D.

Is Marcus alive?

Solution 1 7. It is now 2009 A.D. axiom 7 5. All Pompeians died in 79 A.D. axiom 5 11. All Pompeians are dead now. 7, 5 2. Marcus was a Pompeian. axiom 2 12 Marcus is dead. 11, 2

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4. Absolute or relatively good solution

Facts about Marcus

1. Marcus was a man. 2. Marcus was a Pompeian. 3. Marcus was born in 40 A.D. 4. All men are mortal. 5. All Pompeians died when volcano erupted in 79 A.D. 6. No mortal lives longer than 150 years. 7. It is now 2009 A.D.

Is Marcus alive?

Solution 2

1. Marcus is a man. axiom 1 4. All men are mortal axiom 4 8. Marcus is mortal. 1, 4 3. Marcus was born in 40 A.D. axiom 3 7. It is now 2009 A.D. axiom 7 9 Marcus' age is 1969 years. 3, 7 6. No mortal lives longer than 150 years axiom 6 10. Marcus is dead 8, 6, 9

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4. Absolute or relatively good solution An Instance of the Traveling Salesman Problem

Boston New York

Miami Dallas S. Francisco

Boston 250 1450 1700 3000 New York 250 1200 1500 2900 Miami 1450 1200 1600 3300 Dallas 1700 1500 1600 1700 S. Francisco

3000 2900 3300 1700

Boston

San Francisco New York

Dallas Miami

New York Dallas

Miami San Francisco

Boston Boston

(3000) (250)

(1700) (1200)

(1500) (1600)

(1700)

(3000)

Total: 7750

(1200)

(1450)

Total: 8850

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5. Is the solution a State or a Path to the State?

Consider the problem of finding interpretation of the following statement?

The bank president ate a dish of pasta salad with fork. — The word "bank" may refer either to a financial institution

or to a side of a river. But only one of these may have a president.

— The word "dish" is the object of the verb "eat". It is

possible that a dish was eaten. But it is more likely that the pasta salad in the dish was eaten.

— Pasta salad is a salad containing pasta. But there are other

ways meanings can be formed from pairs of nouns. For example, dog food does not normally contain dogs.

— The phrase "with the fork" could modify several parts of

the sentence. In this case, it modifies the verb "eat". But, if the phrase had been "with vegetables" then the modification structure would be different. And if the phrase had been "with her friends," the structure would be different still.

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5. Is the solution a State or a Path to the State?

Boston

San Francisco New York

Dallas Miami

New York Dallas

Miami San Francisco

Boston Boston

(3000) (250)

(1700) (1200)

(1500) (1600)

(1700)

(3000)

Total: 7750

(1200)

(1450)

Total: 8850

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6. What is the role of knowledge?

— The names of the candidates in each party. — The fact that if the major thing you want to see done is

have taxes lowed, you are probably supporting the Republicans.

— The fact that if the major thing you want to see done is

improved education for minority students, you are probably supporting the Democrats.

— The fact that if you are opposed to big government, you are

probably supporting the Republicans. — And so on . . . — What can we say about the game of chess?

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7. Does the task require interaction?

Two types of problems:

— Solitary, in which the computer is given a problem description and

produces an answer with no immediate communication and with no demand for an explanation of the reasoning process.

— Conversational, in which there is intermediate communication between a

person and the computer, either to provide additional assistance to the computer or to provide additional information to the user, or both.

(Geometry theorem proving).