31 2:

2.3:

.

.

1.

2.

1. Modus Ponens

2.

2 , 31, 2.3:

3.

.

1.

2.

3.

4.

5.

.

.

(-)

(-)

3 , 31, 2.3:

(-)

.

1. ,

.

4 , 31, 2.3:

1: parent(tom,x) parent(y,bob): bob/x tom/y( )

4: parent(tom,x) parent(y,z): tom/y x/z( )

2:

person(x,date(11,10,1954)) person(tom,date(y,z,w)): tom/x, 11/y, 10/z, 1954/w( )

3:

person(tom,date(11,10,1954)) person(x,y): tom/x, date(11,10,1954)/y( )

: Q(f(x)) Q(x): !!( )

5: Q(f(x)) Q(y): y/f(x)( )

.

2. ( ),

( )

5 , 31, 2.3:

Modus Ponens ( )

: )}()({ xxx )( )( :

:

)}()({ xxx )( )(

)(xx )(

C~ CB

.

1. .

6 , 31, 2.3:

:

:

TSSSS n ...321

TSSSS n ~...321

( , )

TSSSS n ~...321

:

( ) . : .

.

.

2. :.

7 , 31, 2.3:

() :

.

.

::

() :

)]()([.3)](~)([.2

)]()([.1

xNxxxxx

xxx

)(.3)(.3

)(~)(~.2)()(~.1

ba

yyxx

.

2. :.

8 , 31, 2.3:

() :

:

)](~)([ xxx

:

:

)()(~.4)(.3)(.3

)(~)(~.2)()(~.1

zz

ba

yyxx

)](~)([~ xxx

)()(~ zz

.

2. :.

9 , 31, 2.3:

:

)(.3)(.3

)(~)(~.2)()(~.1

ba

yyxx

(3,4)

(5,1)

)(.5 /z)(.6 /x

)()(~.4)(.3

zz

b

(5,1)(6,2)

(7,3)

)(.6 /x)(~.7 /y

.

2. :.

10 , 31, 2.3:

:

)(.3 b

/z

)()(~.4 zz

)(.5

)(.6 /x

)(~.7 /y

)()(~.1 xx

)(~)(~.2 yy

)(.3 a

.8

. 3. ( ) :

11 , 31, 2.3:

1. _=S /* S= */

2. :

2.1 _

2.2

2.3 _

( NP-Complete)

. 4.

:

: - -.

- .

12 , 31, 2.3:

.

: ,

.

:

.

. 5.

.

2 : ( ) .

13 , 31, 2.3:

( OR )

.

: . . ,

.

.

5. :.

14 , 31, 2.3:

.

5. :.

15 , 31, 2.3:

.

5. :

16 , 31, 2.3:

x1/, x3/

. ~, . ~ ,

. ~ . ~

x2/

. ~ . ~

. ~ .

.

5.

17 , 31, 2.3:

x1/, x3/

. ~, , . ~ ,

x2/

". ,

. ~ , . ~

. ~ , .

1 :

.

()

18 , 31, 2.3:

() 19 , 31, 2.3:

() .20 , 31, 2.3:

2( 2 2.2) .

21 , 31, 2.3: