[PPT] - Logic and Knowledge Representation P r o b l e m T y p e PowerPoint Presentation

SLIDE 1

Logic and Knowledge Representation

G i

v

a n n i S i l e n

g

s i l e n

@e

n s t . f r

T é l é c

m

P a r i s T e c h , P a r i s

D

a u p h i n e U n i v e r s i t y

P r

b

l e m T y p e s , a n d P r

b

l e m s

l

v i n g m e t h

d

s

2 7 A p r i l 2 1 8

SLIDE 2

Problem solving

SLIDE 3

Well-defined problems

P r

b

l e m s a r e w e l l

d

e fj n e d w h e n t h e r e i s a s i m p l e t e s t t

c
n

c l u d e w h e t h e r a s

l

u t i

n

i s a s

l

u t i

n

.

J . M c C a r t h y ( 1 9 5 6 ) T h e i n v e r s i

n
f

f u n c t i

n

s d e fj n e d b y T a r i n g m a

c

h i n e s . A u t

m

a t a S t u d i e s , A n n a l s

f

M a t h e m a t i c a l S t u d i e s , 3 4 : 1 7 7 – 1 8 1 .

SLIDE 4

Well-defined problems & problem spaces

P r

b

l e m s a r e w e l l

d

e fj n e d w h e n t h e r e i s a s i m p l e t e s t t

c
n

c l u d e w h e t h e r a s

l

u t i

n

i s a s

l

u t i

n

.

J . M c C a r t h y ( 1 9 5 6 ) T h e i n v e r s i

n
f

f u n c t i

n

s d e fj n e d b y T a r i n g m a

c

h i n e s . A u t

m

a t a S t u d i e s , A n n a l s

f

M a t h e m a t i c a l S t u d i e s , 3 4 : 1 7 7 – 1 8 1 .

P e

p

l e s

l

v e p r

b

l e m s b y s e a r c h i n g t h r

u

g h a p r

b

l e m s p a c e , c

n

s i s t i n g

f

t h e i n i t i a l s t a t e , t h e g

a

l s t a t e , a n d a l l p

s

s i b l e s t a t e s i n b e t w e e n .

N e w e l l , A . , & S i m

n

, H . A . ( 1 9 7 2 ) . H u m a n p r

b

l e m s

l

v i n g .

SLIDE 5

Problem and solution spaces P S

p r

b

l e m s s p a c e s

l

u t i

n

s p a c e s

l

u t i

n

s p

solution(s, p)

c a n b e i n t e r p r e t e d a s s s a t i s fj e s p

SLIDE 6

Problem and solution spaces P S

p r

b

l e m s s p a c e s

l

u t i

n

s p a c e s

l

u t i

n

s p

solution(s, p)

c a n b e i n t e r p r e t e d a s s s a t i s fj e s p p r

b

l e m : h

w

t

g

e n e r a t e s

l

u t i

n

s ?

SLIDE 7

Problem and solution spaces P S

p r

b

l e m s s p a c e s

l

u t i

n

s p a c e s

l

u t i

n

s p

solution(s, p)

c a n b e i n t e r p r e t e d a s s s a t i s fj e s p p r

b

l e m : h

w

t

g

e n e r a t e s

l

u t i

n

s ?

p r

b

l e m t y p e a b s t r a c t s

l

u t i

n

a b s t r a c t i

n

r e fj n e m e n t

SLIDE 8

Defining the problem...

An old lady wants to visit her friend in a neighbouring village. She takes her car, but halfway the engine stops after some

hesitations. On the side of the

road she tries to restart the engine, but to no avail.

B r e u k e r , J . ( 1 9 9 4 ) . C

m

p

n

e n t s

f

p r

b

l e m s

l

v i n g a n d t y p e s

f

p r

b

l e m s . A F u t u r e f

r

K n

w

l e d g e A c q u i s i t i

n

, 8 6 7 , 1 1 8 – 1 3 6 .

SLIDE 9

Defining the problem...

An old lady wants to visit her friend in a neighbouring village. She takes her car, but halfway the engine stops after some

hesitations. On the side of the

road she tries to restart the engine, but to no avail.

B r e u k e r , J . ( 1 9 9 4 ) . C

m

p

n

e n t s

f

p r

b

l e m s

l

v i n g a n d t y p e s

f

p r

b

l e m s . A F u t u r e f

r

K n

w

l e d g e A c q u i s i t i

n

, 8 6 7 , 1 1 8 – 1 3 6 .

Wh i c h i s t h e p r

b

l e m h e r e ?

SLIDE 10

from ill-defined to well-defined problems...

B r e u k e r , J . ( 1 9 9 4 ) . C

m

p

n

e n t s

f

p r

b

l e m s

l

v i n g a n d t y p e s

f

p r

b

l e m s . A F u t u r e f

r

K n

w

l e d g e A c q u i s i t i

n

, 8 6 7 , 1 1 8 – 1 3 6 .

SLIDE 11

Suite of problem types

m

d

e l l i n g

B r e u k e r , J . ( 1 9 9 4 ) . C

m

p

n

e n t s

f

p r

b

l e m s

l

v i n g a n d t y p e s

f

p r

b

l e m s . A F u t u r e f

r

K n

w

l e d g e A c q u i s i t i

n

, 8 6 7 , 1 1 8 – 1 3 6 .

SLIDE 12

Suite of problem types

m

d

e l l i n g d e s i g n

B r e u k e r , J . ( 1 9 9 4 ) . C

m

p

n

e n t s

f

p r

b

l e m s

l

v i n g a n d t y p e s

f

p r

b

l e m s . A F u t u r e f

r

K n

w

l e d g e A c q u i s i t i

n

, 8 6 7 , 1 1 8 – 1 3 6 .

s t r u c t u r a l v i e w : s y s t e m

SLIDE 13

Suite of problem types

m

d

e l l i n g p l a n n i n g d e s i g n

B r e u k e r , J . ( 1 9 9 4 ) . C

m

p

n

e n t s

f

p r

b

l e m s

l

v i n g a n d t y p e s

f

p r

b

l e m s . A F u t u r e f

r

K n

w

l e d g e A c q u i s i t i

n

, 8 6 7 , 1 1 8 – 1 3 6 .

s t r u c t u r a l v i e w : s y s t e m b e h a v i

u

r a l v i e w : s y s t e m + e n v i r

n

m e n t

SLIDE 14

Suite of problem types

m

d

e l l i n g p l a n n i n g d e s i g n a s s i g n m e n t

B r e u k e r , J . ( 1 9 9 4 ) . C

m

p

n

e n t s

f

p r

b

l e m s

l

v i n g a n d t y p e s

f

p r

b

l e m s . A F u t u r e f

r

K n

w

l e d g e A c q u i s i t i

n

, 8 6 7 , 1 1 8 – 1 3 6 .

s t r u c t u r a l v i e w : s y s t e m b e h a v i

u

r a l v i e w : s y s t e m + e n v i r

n

m e n t

SLIDE 15

Suite of problem types

m

d

e l l i n g p l a n n i n g d e s i g n a s s i g n m e n t

B r e u k e r , J . ( 1 9 9 4 ) . C

m

p

n

e n t s

f

p r

b

l e m s

l

v i n g a n d t y p e s

f

p r

b

l e m s . A F u t u r e f

r

K n

w

l e d g e A c q u i s i t i

n

, 8 6 7 , 1 1 8 – 1 3 6 .

b e h a v i

u

r a l v i e w : s y s t e m + e n v i r

n

m e n t s t r u c t u r a l v i e w : s y s t e m s c h e d u l i n g c

n

fj g u r a t i

n

SLIDE 16

Suite of problem types

m

d

e l l i n g p l a n n i n g d e s i g n a s s i g n m e n t a s s e s s m e n t

B r e u k e r , J . ( 1 9 9 4 ) . C

m

p

n

e n t s

f

p r

b

l e m s

l

v i n g a n d t y p e s

f

p r

b

l e m s . A F u t u r e f

r

K n

w

l e d g e A c q u i s i t i

n

, 8 6 7 , 1 1 8 – 1 3 6 .

s t r u c t u r a l v i e w : s y s t e m b e h a v i

u

r a l v i e w : s y s t e m + e n v i r

n

m e n t

SLIDE 17

Suite of problem types

m

d

e l l i n g p l a n n i n g d e s i g n a s s i g n m e n t a s s e s s m e n t m

n

i t

r

i n g

B r e u k e r , J . ( 1 9 9 4 ) . C

m

p

n

e n t s

f

p r

b

l e m s

l

v i n g a n d t y p e s

f

p r

b

l e m s . A F u t u r e f

r

K n

w

l e d g e A c q u i s i t i

n

, 8 6 7 , 1 1 8 – 1 3 6 .

s t r u c t u r a l v i e w : s y s t e m b e h a v i

u

r a l v i e w : s y s t e m + e n v i r

n

m e n t

SLIDE 18

Suite of problem types

m

d

e l l i n g p l a n n i n g d e s i g n a s s i g n m e n t a s s e s s m e n t m

n

i t

r

i n g d i a g n

s

i s

B r e u k e r , J . ( 1 9 9 4 ) . C

m

p

n

e n t s

f

p r

b

l e m s

l

v i n g a n d t y p e s

f

p r

b

l e m s . A F u t u r e f

r

K n

w

l e d g e A c q u i s i t i

n

, 8 6 7 , 1 1 8 – 1 3 6 .

s t r u c t u r a l v i e w : s y s t e m b e h a v i

u

r a l v i e w : s y s t e m + e n v i r

n

m e n t

SLIDE 19

Agent problem-solving cycle

SLIDE 20

Agent problem-solving cycle

w h e r e i l l

d

e fj n e d p r

b

l e m s c

m

e u p

SLIDE 21

Agent problem-solving cycle

w h e r e i l l

d

e fj n e d p r

b

l e m s c

m

e u p w h e r e w e l l

d

e fj n e d p r

b

l e m s a r e s e t u p

SLIDE 22

Agent problem-solving cycle

w h e r e i l l

d

e fj n e d p r

b

l e m s c

m

e u p w h e r e w e l l

d

e fj n e d p r

b

l e m s a r e s e t u p w h e r e t a s k s a r e a s s i g n e d a n d s c h e d u l e d

SLIDE 23

Forward and backward reasoning

SLIDE 24

J . L a r k i n , J . M c D e r m

t

t , D . P . S i m

n

, H . A . S i m

n

( 1 9 8 ) , E x p e r t a n d N

v

i c e P e r f

r

m a n c e i n S

l

v i n g P h y s i c s P r

b

l e m s , S c i e n c e , 2 8 ( 4 4 5 )

How do we approach a problem?

SLIDE 25

J . L a r k i n , J . M c D e r m

t

t , D . P . S i m

n

, H . A . S i m

n

( 1 9 8 ) , E x p e r t a n d N

v

i c e P e r f

r

m a n c e i n S

l

v i n g P h y s i c s P r

b

l e m s , S c i e n c e , 2 8 ( 4 4 5 )

How do we approach a problem?

N

v

i c e s t u d e n t s s t a r t f r

m

t h e g

a

l .

T h e y l

k

f

r

a f

r

m u l a r e t u r n i n g t h e g

a

l , a n d t h e n f

r

f

r

m u l a s r e t u r n i n g w h a t i t i s n e e d e d b y t h e p r e v i

u

s

n

e , u p t h e y f

r

m u l a s s a t i s fj e d w i t h t h e g i v e n d a t a .

SLIDE 26

J . L a r k i n , J . M c D e r m

t

t , D . P . S i m

n

, H . A . S i m

n

( 1 9 8 ) , E x p e r t a n d N

v

i c e P e r f

r

m a n c e i n S

l

v i n g P h y s i c s P r

b

l e m s , S c i e n c e , 2 8 ( 4 4 5 )

How do we approach a problem?

N

v

i c e s t u d e n t s s t a r t f r

m

t h e g

a

l .

T h e y l

k

f

r

a f

r

m u l a r e t u r n i n g t h e g

a

l , a n d t h e n f

r

f

r

m u l a s r e t u r n i n g w h a t i t i s n e e d e d b y t h e p r e v i

u

s

n

e , u p t h e y f

r

m u l a s s a t i s fj e d w i t h t h e g i v e n d a t a .

E x p e r t s s t a r t f r

m

t h e d a t a .

T h e y a p p l y f

r

m u l a s d i r e c t l y t

d

a t a , a c c

r

d i n g t

s
m

e h e u r i s t i c s .

SLIDE 27

J . L a r k i n , J . M c D e r m

t

t , D . P . S i m

n

, H . A . S i m

n

( 1 9 8 ) , E x p e r t a n d N

v

i c e P e r f

r

m a n c e i n S

l

v i n g P h y s i c s P r

b

l e m s , S c i e n c e , 2 8 ( 4 4 5 )

How do we approach a problem?

N

v

i c e s t u d e n t s s t a r t f r

m

t h e g

a

l .

T h e y l

k

f

r

a f

r

m u l a r e t u r n i n g t h e g

a

l , a n d t h e n f

r

f

r

m u l a s r e t u r n i n g w h a t i t i s n e e d e d b y t h e p r e v i

u

s

n

e , u p t h e y f

r

m u l a s s a t i s fj e d w i t h t h e g i v e n d a t a .

E x p e r t s s t a r t f r

m

t h e d a t a .

T h e y a p p l y f

r

m u l a s d i r e c t l y t

d

a t a , a c c

r

d i n g t

s
m

e h e u r i s t i c s .

a n d P r

l
g

?

SLIDE 28

Example of diagnosis task

“ e x p e r t ” k n

w

l e d g e

SLIDE 29

Example of diagnosis task

“ e x p e r t ” k n

w

l e d g e

leak_in_bathroom :- hall_wet, kitchen_dry. problem_in_kitchen :- hall_wet, bathroom_dry. no_water_from_outside :- window_closed ; no_rain. leak_in_kitchen :- problem_in_kitchen, no_water_from_outside. hall_wet. bathroom_dry. window_closed.

p r

l
g

p r

g

r a m

SLIDE 30

Some technical detail

p r

l
g

p r

g

r a m

:- dynamic(kitchen_dry/0, no_rain/0). leak_in_bathroom :- hall_wet, kitchen_dry. problem_in_kitchen :- hall_wet, bathroom_dry. no_water_from_outside :- window_closed ; no_rain. leak_in_kitchen :- problem_in_kitchen, no_water_from_outside. hall_wet. bathroom_dry. window_closed. ?- leak_in_bathroom. FALSE ?- leak_in_kitchen. TRUE n e c e s s a r y t

d

e fj n e fm u e n t s , i . e . f a c t s t h a t m i g h t c h a n g e a l

n

g t h e e x e c u t i

n

SLIDE 31

Some technical detail

p r

l
g

p r

g

r a m

:- dynamic(kitchen_dry/0, no_rain/0). leak_in_bathroom :- hall_wet, kitchen_dry. problem_in_kitchen :- hall_wet, bathroom_dry. no_water_from_outside :- window_closed ; no_rain. leak_in_kitchen :- problem_in_kitchen, no_water_from_outside. hall_wet. bathroom_dry. window_closed. ?- leak_in_bathroom. FALSE ?- leak_in_kitchen. TRUE n e c e s s a r y t

d

e fj n e fm u e n t s , i . e . f a c t s t h a t m i g h t c h a n g e a l

n

g t h e e x e c u t i

n

H

w

? … u s i n g assert a n d rectract

SLIDE 32

Generalization

U

s i n g P r

l
g

' s

w

n s y n t a x f

r

r u l e s m a y g a v e c e r t a i n d i s a d v a n t a g e s h

w

e v e r :

– t

h i s s y n t a x m a y n

t

b e t h e m

s

t s u i t a b l e f

r

a u s e r u n f a m i l i a r w i t h P r

l
g

; e . g . e x p e r t s

– t

h e k n

w

l e d g e b a s e i s n

t

s y n t a c t i c a l l y d i s t i n g u i s h a b l e f r

m

t h e r e s t

f

t h e p r

g

r a m

L

e t u s c r e a t e a s m a l l D S L ( d

m

a i n s p e c i fj c l a n g u a g e ) !

SLIDE 33

A simple interpreter for rules

% symbols of DSL and priority :- op(800, fx, if). :- op(700, xfx, then). :- op(300, xfy, or). :- op(200, xfy, and).

p r i

r

i t y t y p e

f

c

m

p

s

i t i

n

( u n a r y , b i n a r y , . . . ) s y m b

l

SLIDE 34

A simple interpreter for rules

% symbols of DSL and priority :- op(800, fx, if). :- op(700, xfx, then). :- op(300, xfy, or). :- op(200, xfy, and). % knowledge base if hall_wet and kitchen_dry then leak_in_bathroom. if hall_wet and bathroom_dry then problem_in_kitchen. if window_closed or no_rain then no_water_from_outside. if problem_in_kitchen and no_water_from_outside then leak_in_kitchen. fact(hall_wet). fact(bathroom_dry). fact(window_closed).

SLIDE 35

Backward chaining

% backward chaining rule interpreter is_true(P) :- fact(P). is_true(P) :- if Condition then P, is_true(Condition). is_true(PI and P2) :- is_true(PI), is_true( P2). is_true(PI or P2) :- is_true(PI) ; is_true( P2).

SLIDE 36

for forward chaining we need to materialize the (partial) conclusions!

% necessary with SWI-Prolog. :- dynamic(sunshine/0, raining/0, fog/0). nice :- sunshine, not(raining). funny :- sunshine, raining. disgusting :- raining,fog. raining. fog. ?- nice. ?- disgusting. ?- retract(fog). ?- disgusting. ?- assert(sunshine). ?- funny.

SLIDE 37

Forward chaining

% forward chaining rule interpreter forward :- new_derived_fact(P), !, write('Derived:'), write(P), nl, assert(fact(P)), forward ; write('No more facts'). new_derived_fact(Concl) :- if Cond then Concl, not(fact( Concl)), composed_fact( Cond). composed_fact(Cond) :- fact(Cond). composed_fact(Cond1 and Cond2) :- composed_fact(Cond1), composed_fact( Cond2). composed_fact(Cond1 or Cond2) :- composed_fact(Cond1) ; composed_fact( Cond2).

SLIDE 38

Backward vs Forward chaining

G
i

n g f r

m

a n i n i t i a l s t a t e t

a

g

a

l s t a t e c a n b e u n s u i t a b l e f

r

p r

b

l e m s w i t h a l a r g e n u m b e r

f

r u l e s ( a l l f a c t s a r e d e r i v e d , e v e n t h e n

t

u s e f u l

n

e s ) .

SLIDE 39

Backward vs Forward chaining

G
i

n g f r

m

a n i n i t i a l s t a t e t

a

g

a

l s t a t e c a n b e u n s u i t a b l e f

r

p r

b

l e m s w i t h a l a r g e n u m b e r

f

r u l e s ( a l l f a c t s a r e d e r i v e d , e v e n t h e n

t

u s e f u l

n

e s ) .

S

e a r c h i n g b a c k w a r d s f r

m

t h e g

a

l s t a t e u s u a l l y e l i m i n a t e s s p u r i

u

s p a t h s .

SLIDE 40

Backward vs Forward chaining

G
i

n g f r

m

a n i n i t i a l s t a t e t

a

g

a

l s t a t e c a n b e u n s u i t a b l e f

r

p r

b

l e m s w i t h a l a r g e n u m b e r

f

r u l e s ( a l l f a c t s a r e d e r i v e d , e v e n t h e n

t

u s e f u l

n

e s ) .

S

e a r c h i n g b a c k w a r d s f r

m

t h e g

a

l s t a t e u s u a l l y e l i m i n a t e s s p u r i

u

s p a t h s . b u t i t d

e

s n

t

e n j

y

c a c h i n g a b i l i t i e s !

SLIDE 41

Types of reasoning (with rules)

SLIDE 42

Types of reasoning (Pierce) - 1

D e d u c t i

n

R u l e : A l l t h e b e a n s f r

m

t h i s b a g a r e w h i t e . F a c t : T h e s e b e a n s a r e f r

m

t h i s b a g .  R e s u l t : T h e s e b e a n s a r e w h i t e .

T h i s c

n

c l u s i

n

i s c e r t a i n l y t r u e , i f t h e p r e m i s e s a r e t r u e .

SLIDE 43

Types of reasoning (Pierce) - 2

I n d u c t i

n

F a c t : T h e s e b e a n s a r e f r

m

t h i s b a g . F a c t : T h e s e b e a n s a r e w h i t e .  H y p . r u l e : A l l t h e b e a n s f r

m

t h i s b a g a r e w h i t e .

T h i s c

n

c l u s i

n

i s t r u e u n t i l p r

v

e d

t

h e r w i s e .

SLIDE 44

Types of reasoning (Pierce) - 3

A b d u c t i

n

R u l e : A l l t h e b e a n s f r

m

t h i s b a g a r e w h i t e . O b s e r v e d f a c t : T h e s e b e a n s a r e w h i t e .  H y p . f a c t : T h e s e b e a n s a r e f r

m

t h i s b a g .

T h i s c

n

c l u s i

n

i s p l a u s i b l y t r u e .

SLIDE 45

Resuming...

D e d u c t i

n

A s s e r t e d R u l e + A s s e r t e d F a c t = A s s e r t e d F a c t

I n d u c t i

n

O b s e r v e d F a c t + O b s e r v e d F a c t = H y p

t

h e t i c a l R u l e

A b d u c t i

n

O b s e r v e d F a c t + K n

w

n R u l e = P l a u s i b l e F a c t

SLIDE 46

Planning

SLIDE 47

Monkeys and bananas

A

h u n g r y m

n

k e y i s i n a r

m

. S u s p e n d e d f r

m

t h e r

f

, j u s t

u

t

f

h i s r e a c h , i s a b u n c h

f

b a n a n a s . I n t h e c

r

n e r

f

t h e r

m

i s a b

x

. T h e m

n

k e y d e s p e r a t e l y w a n t s t h e b a n a n a s b u t h e c a n ’ t r e a c h t h e m . Wh a t s h a l l h e d

?

SLIDE 48

Monkeys and bananas

A

f t e r s e v e r a l u n s u c c e s s f u l a t t e m p t s t

r

e a c h t h e b a n a n a s , t h e m

n

k e y w a l k s t

t

h e b

x

, p u s h e s i t u n d e r t h e b a n a n a s , c l i m b s

n

t h e b

x

, p i c k s t h e b a n a n a s a n d e a t s t h e m .

SLIDE 49

Planning

T
s
l

v e t h i s p r

b

l e m t h e m

n

k e y n e e d e d t

d

e v i s e a p l a n , a s e q u e n c e

f

a c t i

n

s t h a t w

u

l d a l l

w

h i m t

r

e a c h t h e d e s i r e d g

a

l .

P

l a n n i n g i s a t

p

i c

f

t r a d i t i

n

a l i n t e r e s t i n A I .

T
b

e a b l e t

p

l a n , a s y s t e m n e e d s t

b

e a b l e t

r

e a s

n

a b

u

t t h e i n d i v i d u a l a n d c u m u l a t i v e e fge c t s

f

a s e r i e s

f

a c t i

n

s .

T

h i s i s a s k i l l t h a t i s

n

l y

b

s e r v e d i n a f e w a n i m a l s p e c i e s a n d

n

l y m a s t e r e d b y h u m a n s .

SLIDE 50

Ingredients

A

c t i

n

s , w i t h c

n

d i t i

n

s a n d c

n

s e q u e n c e s :

action(InitialState, Action, ObtainedState)

SLIDE 51

Ingredients

A

c t i

n

s , w i t h c

n

d i t i

n

s a n d c

n

s e q u e n c e s :

action(InitialState, Action, ObtainedState)

S

t a t e s

f

t h e w

r

l d

state(middle, onbox, middle, not_holding)

monkey horizonal position monkey vertical position box horizonal position hand with banana relation

SLIDE 52

Ingredients

A

c t i

n

s , w i t h c

n

d i t i

n

s a n d c

n

s e q u e n c e s :

action(state(P, floor, P, T), climb, state(P, onbox, P, T)).

S

t a t e s

f

t h e w

r

l d

state(middle, onbox, middle, not_holding)

monkey horizonal position monkey vertical position box horizonal position hand with banana relation

SLIDE 53

action(state(middle, onbox, middle, not_holding), grab, state(middle, onbox, middle, holding)). action(state(P, floor, P, T), climb, state(P, onbox, P, T)). action(state(P1, floor, P1, T), push(P1, P2), state(P2, floor, P2, T)). action(state(P1, floor, B, T), walk(P1, P2), state(P2, floor, B, T)). success(state(_, _, _, holding)). success(State1) :- action(State1, A, State2), write("Action : "), write(A), nl, write(" --> "), write(State2), nl, success( State2).

Cooking everything

?- success(state(door, floor, window, not_holding)). goal condition

SLIDE 54

Another exercise: the tower of Hanoi

SLIDE 55

Recursion

SLIDE 56

Recursion

R

e c u r s i

n

i s a c

n

c e p t w i d e l y u s e d i n c

m

p u t e r s c i e n c e a n d l i n g u i s t i c .

– a

n

b

j e c t d e fj n e d i n t e r m s

f

i t s e l f

– a

p r

c

e d u r e i n v

k

i n g i t s e l f

SLIDE 57

Recursion

H

y p

t

h e s i s : n a t u r a l l a n g u a g e i s r e c u r s i v e , a s ( s

m

e ) s y n t a x i c c a t e g

r

i e s a r e r e c u r s i v e .

J
h

n t h i n k s E m i l y p l a y s w e l l . s t a t e m e n t s t a t e m e n t

SLIDE 58

Recursion

T

h r e e p h a s e s : d e s c e n t , s t

p

a t b

t

t

m

, a s c e n t . even([ ]). even([_,_|L]) :- even(L).

SLIDE 59

Recursion

T

h r e e p h a s e s : d e s c e n t , s t

p

a t b

t

t

m

, a s c e n t . even([ ]). even([_,_|L]) :- even(L). ?- even([3, 5, 3]).

SLIDE 60

Recursion

T

h r e e p h a s e s : d e s c e n t , s t

p

a t b

t

t

m

, a s c e n t . even([ ]). even([_,_|L]) :- even(L). ?- even([3, 5, 3]). S e e k f

r

a n e n t r a n c e

SLIDE 61

Recursion

T

h r e e p h a s e s : d e s c e n t , s t

p

a t b

t

t

m

, a s c e n t . even([ ]). even([_,_|L]) :- even(L). ?- even([3, 5, 3]). P r

p

a g a t e r e c u r s i v e l y

SLIDE 62

Recursion

T

h r e e p h a s e s : d e s c e n t , s t

p

a t b

t

t

m

, a s c e n t . even([ ]). even([_,_|L]) :- even(L). ?- even([3, 5, 3]). R e a c h t h e b

t

t

m
f

t h e r e c u r s i

n

SLIDE 63

Recursion

T

h r e e p h a s e s : d e s c e n t , s t

p

a t b

t

t

m

, a s c e n t . even([ ]). even([_,_|L]) :- even(L). ?- even([3, 5, 3]). R e t r a c e b a c k

SLIDE 64

Recursion

T

h r e e p h a s e s : d e s c e n t , s t

p

a t b

t

t

m

, a s c e n t . even([ ]). even([_,_|L]) :- even(L). ?- even([3, 5, 3]). P r

p

a g a t e t h e r e s u l t b a c k

SLIDE 65

Recursion

T

h r e e p h a s e s : d e s c e n t , s t

p

a t b

t

t

m

, a s c e n t . mirror(Left, Right) :- invert(Left, [], Right). invert([X|L1], L2, L3) :- invert(L1, [X|L2], L3). invert([], L, L).

SLIDE 66

Conclusions

SLIDE 67

Conclusions

S

y m b

l

i c A I p r e s e n t s r e l e v a n t t e c h n i q u e s t

s
l

v e p r

b

l e m s t h a t c a n b e d e s c r i b e d i n s y m b

l

i c t e r m s , t h a t i n m a n y c a s e s

u

t p e r f

r

m h u m a n s .

h t t p s : / / e n . w i k i p e d i a .

r

g / w i k i / D e e p _ B l u e _ v e r s u s _ G a r r y _ K a s p a r

v

SLIDE 68

Conclusions

S

y m b

l

i c A I p r e s e n t s r e l e v a n t t e c h n i q u e s t

s
l

v e p r

b

l e m s t h a t c a n b e d e s c r i b e d i n s y m b

l

i c t e r m s , t h a t i n m a n y c a s e s

u

t p e r f

r

m h u m a n s .

A

I m e t h

d

s a r e t

d

a y i m p l e m e n t e d i n n e w g e n e r a t i

n

s

f

e x p e r t s y s t e m s a n d a l l I T i n f r a s t r u c t u r e s

f
r

g a n i z a t i

n

s .

SLIDE 69

Conclusions

S

y m b

l

i c A I p r e s e n t s r e l e v a n t t e c h n i q u e s t

s
l

v e p r

b

l e m s t h a t c a n b e d e s c r i b e d i n s y m b

l

i c t e r m s , t h a t i n m a n y c a s e s

u

t p e r f

r

m h u m a n s .

A

I m e t h

d

s a r e t

d

a y i m p l e m e n t e d i n n e w g e n e r a t i

n

s

f

e x p e r t s y s t e m s a n d a l l I T i n f r a s t r u c t u r e s

f
r

g a n i z a t i

n

s .

H
w

e v e r , m a n y p r

b

l e m s c a n n

t

b e a d e q u a t e l y h a n d l e d b y s y m b

l

i c t e c h n i q u e s , a s e . g .t h

s

e f a c e d b y s e n s

r

y

m
t
r

m

d

u l e s :

– v

i s i

n

, a c t i

n

SLIDE 70

Conclusions

I

n r

b
t

i c s , s t a r t i n g f r

m

t h e 8 s , a r a d i c a l l y d i fg e r e n t p a r a d i g m s t a r t e d t

b

e c

n

s i d e r e d , r e n

u

n c i n g t

s

y m b

l

i c r e p r e s e n t a t i

n

s .

A

s R

d

n e y B r

k

s f a m

u

s l y p u t i t : “ E l e p h a n t s d

n

' t p l a y c h e s s ”

– o

v e r l a p w i t h m a c h i n e l e a r n i n g

SLIDE 71

Conclusions

I

n r

b
t

i c s , s t a r t i n g f r

m

t h e 8 s , a r a d i c a l l y d i fg e r e n t p a r a d i g m s t a r t e d t

b

e c

n

s i d e r e d , r e n

u

n c i n g t

s

y m b

l

i c r e p r e s e n t a t i

n

s .

A

s R

d

n e y B r

k

s f a m

u

s l y p u t i t : “ E l e p h a n t s d

n

' t p l a y c h e s s ”

– o

v e r l a p w i t h m a c h i n e l e a r n i n g

S

i m i l a r l y , f a i l u r e s

f

s y m b

l

i c A I e x p l a i n s t

d

a y i n t e r e s t f

r

d e e p l e a r n i n g t e c h n i q u e s .

SLIDE 72

Conclusions

H
w

e v e r , w e s h

u

l d n

t

f

r

g e t , t h a t a g

d

d e a l

f
u

r i n t e r a c t i

n

s w i t h

t

h e r p e

p

l e i s n

t

t

f

a r f r

m

p l a y i n g c h e s s .

– e

x p r e s s i n g h

w

a n d w h y i s f u n d a m e n t a l f

r

h u m a n s , a n d f

r

t h i s w e n e e d s y m b

l

s .

S

y m b

l

i c A I a n d S t a t i s t i c a l A I

c

c u p y d i fg e r e n t s i d e s

f

t h e s p e c t r u m

f

i n t e l l i g e n t b e h a v i

u