(-)

. .-. . ,. . . ,. . ., . () 09-07-00066, (2.3 ) 15 ( 4.3 " ")

1. : ()2. (): 3. 4. 5 6. 7. 8.

*

( ) , XIX

( )

, .

. .. . . ,

, , , ;; ..

1. ?+2. +3.

+4. --5. -+-

1. : ()2. (): 3. 4. 5 6. 7. 8.

*

( )=

XY

= ( )=

XY

() . : , :C; C-; D-; D. -. - .

: (, , \ ) ( ) : ; ; (+Atr); (Atr). : , , . : () () (G, G, \G , G, G )

: (-)C- R[XY...Z] = [A B ... C], A, B, ..., C C-;A X, B Y, ..., C Z, .. . : R[XY...Z] = [A B ... C] = AB ... C.:R [XY...Z] = [{a,c} {c,d,f} {b}] = {a,c} {c,d,f} {b} =

XYZacbadbafbccbcdbcfb

C-C- . C- : P(x) Q(y) R(z) -:

C-: [A B ... C] [A1 B1 ... C1] = [A A1 BB1 ... C C1]. :[A B ... C] [A1 B1 ... C1], AA1, BB1, , CC1.

C- -- C- .

: C- [P Q R ] P(x) Q(y) R(z), P(x), Q(y) , R(z) , P, Q, R . C- :

(P1(x) Q1(y) R1(z)) (P2(x) Q2(y) R2(z)) .

: (-)

C-

. C C-. - D- D-, X = {a, b, c, d}, Y = {f, g, h}, Z={a, b, c}:Q[XYZ] = [ {f, g} {a, c}] = [{a, b, c, d} {f, g} {a, c}] - , X. T= [{b, d} * {a, b}], = ]{a, c} {c}[. A X, - . = A; A = ; = ; = .

: ( )

C-:D- C. D- ]P Q R[ [XYZ] : P(x) Q(y) R(z). C- [ {, , , , } {, , } ] D- ] {, , } {, } [ ( ) C- : (D-)

R = ,

D- .

, C- Q[XYZ] = [A C]

D- [XYZ] = ] [ : (D-) C- ( ) - D- .

C- R , D- .

( ). -). (+Atr) , -. : A x(A) ( , x A)4. ( Atr) . TC - C-, TD D- D-, X. X(TC) x(TC); X(TD) x(TD).

: ,

: , ( )

: , ( ) R1[V] R2[W]. V W V W. X, Y, Z :X = W\V; Y = WV; Z = V\W. V = Y Z W = XY. : R1[V] = R1[YZ] R2[W] = R2[XY]. : R1[YZ] R2[XY] = +X(R1) +Z(R2) = x(R1) z(R2). : R1[YZ] R2[XY] = Y(+X(R1) +Z(R2)) = Y(R1 R2) = = y(x(R1) z(R2)). Q[YZ] =P[XY] = P Q , Q1[XYZ] = x(Q[YZ]) = , P1[XYZ] = z(P[XY]) = PQ =

, , , , .. P[XY] Q[YZ] = +Z(P[XY]) +X(Q[YZ]) , P[XY] G Q[YZ]. .

: , ( ) G=[{a},{b,d}] G[{a},{k,l}]X YX Z=[{a},{b,d},*]X Y Z [{a},*,{k,l}] =X Y Z=[{a},{b,d},{k,l}] X Y Z=

XYabad

XZakal

XYZabkabladkadl

X1, X2, , Xn . X1 X2 Xn ;[Xi Xj Xk] (i, j, , k 1 n) ;Xi Xj Xk ; , X1 X2 Xn. - - - . Xi Xj Xk F(xi, xj, , xk), xi, xj, , xk , Xi Xj Xk. , .

( ) 2.1. - C- P=[P1P2Pn] Q=[Q1Q2Qn]. 2.2. PQ=[P1Q1 P2Q2 PnQn]. : [{b,d}{f,h}{a,b}][{f,g}{a,c}]=[{b,d}{f}{a}]; [{b,d}{f,h}{a,b}][{g}{a,c}]=[{b,d}{a}]=. 2.3. PQ, PiQi i=1,2,,n. 2.4. PQ[P1Q1 P2Q2PnQn], : PQ QP; Pi=Qi , . 2.7. C- P=[P1 P2 Pn] D- =] [. ( 30 ) -. -, , .

1. : ()2. (): 3. 4. 5 6. 7. 8.

*

G2[XY] = G [XY] G [XY] = Y(G[XY] G[YZ]) : :

=

Y: G2 =

G, n , :G+ = G G2 G 3 G k, k n.G[XY] =

R1[XY] = R2[XY] =

R3[XY] = [{K} {L}]; R4[XY] = [{A} {A}]. :(R1[XY] [{D} ]) (R2[YZ] [ {K}]) == [{D} {F, G, H} {K}] . : [{F, G, H} {M}] .

() . : , , . . . , isa(a1, S1); isa(a2, S1); isa(a3, S1); isa(a4, S2);prop(S1, c1, d1); prop(S1, c2, d2); prop(S2, c1, d3). : isa prop. C-:

isa[XY] = ; prop[YZV] =

: isa[XY] prop[YZV] property[XZV] , X = a1 V = d2, Q[XV] = [{a1} {d2}]. : isa[XY] G prop[YZV] G Q[XV].

()

C- D- C- ()D- () - -, () -

()

+Y(R) - R[X1X2Xn]+Y(R) = y(R)X(R) C- R[X] ( X)x(P) X(R) D- R[X] ( X)x(P) G G (A G B) ( A B)

1. : ()2. (): 3. 4. a) b) ) 5 6. 7. 8.

*

( ) : (. . ) (. ) (. . ) 1. F1, ..., Fn G. G F1, ..., Fn , ((F1 ... Fn) G) . 2. F1, ..., Fn G. G F1, ..., Fn , (F1 ... Fn G) .

: 1. - F1, ..., Fn G. G F1, ..., Fn , (F1 G ... G Fn) (F1 G ... G Fn) GG. 2. - F1, ..., Fn G. G F1, ..., Fn , (F1 G... G Fn) F1 G ... G Fn G = .

( ) 4.1. AB SA SB, AB SASB. . , AB , B A. (1) , , , , , .

( ) () A1, A2, , An B. :1) . (A1 G G An) G B.2) . - A = A1 G G An, Bi, A G Bi. - A = A1 G G An C-. A ( Pi(A) A G Pi(A) ). , . -, , -. -, 1-4, .

( : ):

: C-

Up[ABC] = ,

C- Down[C] = [{1}] Down[ABC] = [ * * {1}] , Up[ABC] G Down[C].

( : ):

: -Up[ABC] = ,

: [XA] [XB], .

:

-: , : - , : , - , . ?

-: P1[ABC] = P11 P12 = [{1} * *] [* {0} *] = [{1} {0} *] ; : P2[ABC] = P21 P22 = [{0} * *] [* * {1}] = [{0} * {1}] ; : P3[ABC] = P31 P32 = [* * {0}] [{1} * *] = [{1} * {0}].

: ::

1 (- ) : 2 ( ) : 3 ( ) : , , -.

P1 (

(

= [{1} {0} *] (

(

=

= [{1} {0} *] (

(

= [{1} {0} {1}].

_1362404904.unknown

_1362404979.unknown

_1362406197.unknown

_1362407190.unknown

_1362404913.unknown

_1362240107.unknown

( P2 (

=

( [{0} * {1}] (

=

=

( [{0} * {1}] (

=

_1362404913.unknown

_1362405003.unknown

_1362405718.unknown

_1362407190.unknown

_1362408496.unknown

_1362406197.unknown

_1362405012.unknown

_1362404979.unknown

_1362241338.unknown

_1362404904.unknown

_1362240107.unknown

(

( P3 =

(

( [{1} * {0}] =

=

(

( [{1} * {0}] = [{1} {1} {0}].

_1362404904.unknown

_1362405012.unknown

_1362406197.unknown

_1362406772.unknown

_1362406935.unknown

_1362407190.unknown

_1362406915.unknown

_1362406763.unknown

_1362405718.unknown

_1362404979.unknown

_1362405003.unknown

_1362404913.unknown

_1362241338.unknown

_1362242045.unknown

_1362240107.unknown

- 1: ,

2: , -

123M1=[{,}{,}]M2=[{,}{,}]

- 1 ( , - ) : 2 ( , - ) :

M1(

=[({,}{,}](

=[{}{,}{,}]=

=

_1362404913.unknown

_1362406197.unknown

_1362411099.unknown

_1362412016.unknown

_1362407190.unknown

_1362404979.unknown

_1362240107.unknown

_1362404904.unknown

_1351418670.unknown

(M2=

([{,}{,}(]=[{,}{,}{}]=

=

_1362404904.unknown

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_1362411316.unknown

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_1362412233.unknown

_1362411099.unknown

_1362404979.unknown

_1362406197.unknown

_1362404913.unknown

_1351418702.unknown

_1362240107.unknown

_1351418670.unknown

(A) (B) () (D): , .

, : [* {2} * *]=[{1} * * *] ==P1=P2=P3=: 1- - , 2- - , 3- , 4- .

, () , .

:, " A A" (A ) , , A ;, AA, , ;, .

: :1. 2. .3. . " ", , ( ).

:

() , 1)"" - ( - );2) , ( );3) ( - );4) , (, ). 5) , , : " ; " , "

R = A B; Ri , R Ri; Hi = ( Ri ) ; Hi A ; , 2, .A :

: 1

2 AC AB C. , . . AC P1[XA XB XC] = . AB P2[XA XB XC] = . C B[XA XB XC] = [ * * {1}]. .R = (P1P2)\B = P1P2 = [{0} {1} {0}]. [ XB XC] ( ), Ri [ XB XC] = [{1} {0}]; [ XB XC] = ]{0} {1}[, BC .

: 2 [.. , .. ] , . x6 (x2 x3). , . x7 x5. , . x1 (x2 x3 x5) , . x5 (x8 x9 x10) , x4 (x9 x10) : , . (x3 x1 x7) x9

2 A =

D-

D- B[X1 X4 X7 X9] = ]{0} {0} {0} {1}[.

2

R 1) ;2) , , , ;3) - ., R.

2 [X1X9], C- Ri[X1X9] = [{1} {0}]. : 1) ( C Ri); 2) ; 3) .( 2 3 , C- Ri) ..

1. : ()2. (): 3. 4. 5 6. 7. 8.

*

-

:1) , ;2) , ;3) , ;4) , , ;5) . : ( , ) ; / ().

1) , ;2) , ;3) , ;4) ;5) - , - :6) .

, () , .

: P1 P2 Pn, Q., (x,y) (y,z), (x,z). P1 G P2 G G Pn, Q , , . ( , -) .

- 1) -: , ?2) : ? ? ? ..

3) -4) -5) -

.. . .: "", 1994.

. . . .: , 1989.

- 1) . : ( , ) , , (, ..), ( ), . .

2) ; .

: Z R[XYZ], X = a Y = b ?Q[XYZ] = [{a} {b} ]R[XYZ]GQ[XYZ]

Z R[XYZ], X = a Y = c, X = a b, Y = e, Z D?Q1[XYZ] =R[XYZ]G Q1[XYZ] P[XYZ] R[YVW]. X V, , Z=a?Q2[XVZ] = [ {a}]P[XYZ] GR[YVW] GQ2[XYZ]

1. : ()2. (): 3. 4. 5 6. 7. 8.

*

= {a,b,c} {b,c} {b,c,f} {a,b,c,d} {a,c,d} {b,c,d} = ??? 1 .

= 18 36 3 = 19442 . -C[XYZ] D[XYZ] = = [{a,b,c} {b,c} {b,c,f}] [{a,b,c,d} {a,c,d} {b,c,d}]= =[{a,b,c} {a,b,c,d} {b,c} {a,c,d} {b,c,f} {b,c,d}]= = [{a,b,c} {c} {b,c}] . = 3 4 + 2 3 + 3 3 = 27

XYZabbabcabfacbaccacfcbbcbccbfccbcccccfdbbdbcdbfdcbdccdcf

XYZaabaacaadacbaccacdadbadcaddbabbacbadbcbbccbcdbdbbdcbddcabcaccadccbcccccdcdbcdccdddabdacdaddcbdccdcdddbddcddd

+ , . , (NP- ). , .

C- C- D-D- ++++ C- +++ C- +++ D- +++ D-

- D- , . D- , . D- , . D- , D- . :

[XYZ] =

C =[XYZ] = [{A} {c}]

- () 6. D- Q , .

Q = , T11 Q, D-

, T21 Q D-, . 7. D- Q , Q , D, T22.:

Q = =

, (. ) F1 F2 Fn, (Fi, Fj ) . - -, - . -

Q1, Q2, ..., Qm-1, Qm . 5. D- ]Q1 Q2 ... Qm-1 Qm[

C- .

6. P Q C-, , C-, C.

1. : ()2. (): 3. 4. 5 6. 7. 8.

*

: A B: 1) 0;2) ( A, B) (AB)=(A)+(B)(AB). - (-) , , , . - . . . : E3={c,d,e,f,(c,d),(d,e),(e,f)} Ei= , (Ei)=

5.1. C- , C- . 5.2. C- C-.

: - -, , 1: () C- C- 1; 1; - [0,1]; - 0; - A 1(A); - A B (AG B)=(A)+(B)(AG B); - , .

:

Xi 2 (0 1) : F = (X1 X4) (X2 X5) (X2 X3 X4) (X1 X3 X5) . , . .

R1 = , 3 : : RF =

- -, , , , . 1 -

p1(1p3)+(1p2)p3+(1p1)p2.

2 - (p(a1) + p(a2))(1 p(b2))+(1 p(a1) p(a2))(p(b1)+ p(b2)).

- () : ; , - ( ). : ; . , .

1 (Nilsson N. J. Probabilistic Logic // Artificial Intelligence, 28, 1986, pp. 71-87): : p(A) = p1 p(A B) = p2. : p(B). : AB = {0, 1}2. A = [1 ]; B = [ 1]; A B = B = ]0 1[ = . p(A) = p1; (1 p(A)) + p(A) p(B) = p2.

p(B) =

. p2 + p1 1 p(B) p2.

2

2

, - . . , , , , . . . .

: , ; :1) ,2) , ; - ; , .

;- ; ; - .

.. // . . . 1993. 3. . 226-239. .. // . 1995. 2. . 111-124. .. . 1. // . 1997. 1. . 126136. .., . . . 2. // . 1997. 2. . 169179. .. - . IV " ". , 25-28 2005 . , 2005 . - .1075-1108. .., .. . // -2008 (28 - 3 2008 ., , ): . .1. .: , 2008. .298-304. .., .. // . 2008. 3. .41-51. .., .. // . . 2009. 2. .95-103. .., .., .. / . (-2009) // - . - : - , 2009. - .86-88.

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