4 1 2 3 4

1. ?4? ??????1?????2???????3???????4??/?????? ???68??,???????????,???68??,???????????,

2. ???? ????? ????????,????????(?????)????????????(??????)??????????????????????,?????????? 1 ????: ?????????? ?????????????,???????????? 2. ????? ?????,????? ???C J, Date 3 ????? 4 ??????1 ????: ?????????? ?????????????,???????????? 2. ????? ?????,????? ???C J, Date 3 ????? 4 ??????

3. ???????? ??????????????,???????????: 1??????????????? 2????????????? 3??????????? 4????????????? 5??????????????????? ??????:

4. 1??????????????? ??????????????????????,????????????????????,???: ???:???????????; ???:?????????; ??:????????????????????? ?????: ?????: ????:?????: ?????: ????:

5. 1??????????????? ?????????: (1)?????????????; (2)??????????; (3)??,?????????? ??(1)????,(2)???? (3)?????????? ?????????????,????????????????

6. 1??????????????? ???????????????????,??????????????,???????????? ???????? ????,???????????????,???????? ????? ????,???DBA??? ??? ???????? ????,???????????????,???????? ????? ????,???DBA??? ???

7. 1??????????????? ??????????????????????????,???????????????,??????????,??????????????,???????,??????:??????????????????????????

8. 1??????????????? ????????????,????????,??????????????,?????????????? ???????????,???????????????????????????????,???A???????,??????????????B???,???B??,???????????,?? ???????,????????????????????,?????????????

9. 1??????????????? ?????????????????????????,????????????????????????,???????????????????????????,???????????????????,????????????????,????????????

10. 2????????????? ??????????????????????,??????????,???????????????????? ??????????????????????,?????????????,??????????,?????????? ?????IT???????:????????????????IT???????:???????????

11. 2????????????? ??,?????????????????,?????????????????????????????????????,??????????????,?????????????????

12. 3??????????? ???????????????????????????????,?????????????,?????????,?????????????,????????????????????,??????????????????????????????

13. 4????????????? ????????????????????,?????????????????? ???????????????????????????????????

14. 5?????????????????? ????????????,??????????????????????? ????,???????????????????,??????????? ???????????????????????,???????????,???????????,???

15. 5?????????????????? ???????????????????? ???????????,?????????????,???????????,??????????,??????????????,?????,????????????????????????????????????

16. ??????? ??????????????????????????????????????? ???????????????,?????????????????????????

17. ???? ????????????,??????????????????? ?????????????: 1??????????????????DB; 2??????DB?????????,???????,????;???????;

18. ???? 3?????DB??????,?????KB,??KB??????????,????4,???6; 4?KB????????????,?????????KS; 5?KS??,??????????????????????,??????????DB?,???2;?KS?,?6;

19. ???? ?????????????????,????,?????????DB?,?3,????????,????. ?????????P115??4-1??. ????????,????????????,???????.

20. ???? ????????????????,????????????,??????????,?????????;?????????,????????,???????.???????????.

21. ???? 1????????(????); 2?????????????,??,??????,???????????????;??,????; 3??????????,???????????????,??,?????;?????? 4??????????????????,???????KS,????;

22. ???? 5?KS???????,?????? ????????????,???2. ???????P116??4-2??.

23. ???? ??????????????????????????. ???????????P119??4-4??.

24. ????????? ???????????????????????????. ???????????,?????????????????????,????????????????,????????????????????

25. ???? ???????????????????,??????????????????????????,??????? ?????????????????????? ?????????????????,???????????????????????????????????,??????????????????????? ???????? ???????????????????

26. ???? ????????????: P1:father(??,???)and man(???) P2:father(x,y)and man (y) ??????x,??????y,?P1? P2???????.?????????????,???????,???????????.

27. ???? ???????????: ????? {t1/x1,t2/x2,�,tn/xn}????????, t1, t2, �,tn??, x1. ,x2,�, xn????????; ti/xi????ti????xi,???ti ?xi??,????xi?????????tj??

28. ???? ?????? ?????,???????,??????????

29. ???? ??{a/x,f(b)/y,w/z}??????,?? {g(y)/x,f(x)/y}???????,???????????????????????????????,??????????,?{g(y)/x,f(x)/y}?x?y????????????,??????x,?????y?

30. ???? ??????{g(a)/x,f(x)/y}????,???????x???g(a),y???f(g(a)),???????x?y?

31. ???? ????????????????: ?F?????, ??????,?F ????F????????,?????F?????????????????????F=P(x,y,f(y))????={a/x,b/y} ??F ?=P(a,b,f(b))

32. ???? ??????????? ?????????,?? ? = {t1/x1,t2/x2,�,tn/xn} ? = {u1/y1,u2/y2,�,um/ym}? ??????????????,????= {t1 ? /x1,t2 ? /x2,�,tn ? /xn, u1/y1,u2/y2,�,um/ym} ?????????: ti ? /xi ?ti ? = xi ? ui/yi ?yi? {x1. ,x2,�, xn}?,???????????,??? � ??

33. ???? ????????: ? ={f(y)/x,z/y} ?={a/x,b/y,y/z} ?? �??? � ? ?:??????

34. ???? ? ={f(y) ? /x, z ? /y, a/x,b/y,y/z} ={f(b) /x, y /y, a/x,b/y,y/z}????????: y /y(??1) a/x,b/y(??2) ??? �?= {f(b) /x,y/z}

35. ???? ???? � ?,????? ?={a ?/x, b ?/y, y ?/z, f(y)/x,z/y} ={a /x, b /y,z/z, f(y)/x,z/y} ????????z/z,f(y)/x,z/y? ? � ?={a /x, b /y} ??????????????????????????????,?? ? � ?= ? � ?=?

36. ???? ???????????: ?????F={F1,F2,�,Fn},??????????F1 ?= F2 ?=�= Fn ? ???????F?????,?? F1,F2,�,Fn??????

37. ???? ??F=P(x,y), ?={a/x,g(a)/y} ???F??????? F ? = P(a,g(a)) ?????F={P(x,y,f(y)),P(a,g(x),z)}? ?={a/x,g(a)/y,f(g(a))/z}???F??????

38. ???? ?????????????????? ?????F?????,??????????????????:?= ? � ?????????????

39. ???? ??????????????????????????????,??????????????????,???????????,????????????????

40. ???? ????????????????(???????)?????????????? F1:P(x,y,z) F2: P(x,f(a),h(b)) ???F1 ?F2????????,??????,????F1??y?F2??f(a)??,??????????:D1={y,f(a)},

41. ???? ????????,???F1??F2??h(b)??,??????????: D2={z,h(b)}??????????????: (1)?K=0, Fk=F,?k=???,F?????????????, ?????,???????? (2)?Fk???????,????,?k??????????

42. ???? (3)??Fk????Dk? (4)?Dk?????xk?tk,??xk???,tk??,?xk??tk???,??: ?k+1= ?k�{tk/ xk} Fk+1= Fk{tk/ xk} K = k + 1?(2) (5)???,F??????????

43. ???? ??,? F = {P(a,x,f(g(y))),P(z,f(z),f(u))}???????. (1)??0=?, F0=F,?F0????????,???0???????? (2)???D0= {a,z}, (3) ?1= ?0? {a/z}, F1 = {P(a,x,f(g(y))),P(a,f(a),f(u))}

44. ???? (4) D1={x,f(a)} (5) ?2= ?1? {f(a)/x}={a/z, f(a)/x}, F2=F1 {f(a)/x} = {P(a, f(a),f(g(y))),P(a,f(a),f(u))}? (6) D2={g(y),u}? (7)?3= ?2? {g(y)/u}={a/z, f(a)/x, g(y)/u}?

45. ???? (8) F3=F2 {g(y)/u} = {P(a, f(a),f(g(y))),P(a,f(a),f(g(y)/u))} = {P(a, f(a),f(g(y)))} ??F3????????,???3???????,? {a/z, f(a)/x, g(y)/u}???????

46. ?????? ????????????????: ???????,???????????????????????,????????????: (1)????????????????????? (2)?????????????????????

47. ?????? (3)???????????????????? ???????,???????????????,??????????,?????????????

48. ?????? ????????????,??????????????,????????: 1??????? ???????????: r1:IF A1 and A2 and � An THEN H1 r2:IF B1 and B2 and � Bm THEN H2

49. ?????? ?????????,??r1????Ai???????Bi ,?r2?????r1?????A1,A2, �, An?,???????,??r2 ? r1???????, r1 ?r2 ???????? ????????????????(????r2)??????????,?????? ????,??????,????????

50. ?????? 2???????????? ???????????,?????????????????????,???????????????????????? ?????,??????????????????????????r1?????A????,??r2?????B????,?A?B??????????????????????

51. ?????? 3?????? ????????,????????????????,??????????????,???????????????,?????????????????????????,???????????????

52. ?????? 4???????????? ?????????????????,????????????????????????????????

53. ?????? 5????????? ?????????????????????,???????,??????????????????????????????

54. ?????? 6???????? ???????????????????,????????????? 7???????? ?????????????????,??????????????????

55. 4.2?????? ??????????,??????????????????????????????,????????P???T????????????????????????? P,P?Q ? Q ????????? P?Q,?Q? ? P

56. 4.2?????? ????????????: ?1:A,B,A?C,B?C ?D,D ?Q ?Q 1?A P?? 2? A?C P?? 3? C T??1?2 4?B P?? 5? B?C T??3?4

57. 4.2?????? 6? B?C ?D P?? 7? D T??5?6 8?D ?Q P?? 9? Q T??7?8 ????

58. 4.2?????? ?2???????; (1)?????????(Wang)???? (2)C?????????? (3)ds?C?????? ??????ds?????

59. 4.2?????? ??:????????: Easy(x): x???? Like(x,y): x??y C(x): x?C?????? ?????????:

60. 4.2?????? ?x(Easy(x) ? Like(Wang,x)) ?x(C(x) ? Easy(x)) C(ds) ? Like(Wang,ds).

61. 4.2?????? 1??x(Easy(x) ? Like(Wang,x)) P?? 2? Easy(ds) ? Like(Wang,ds) US???1 3? ?x(C(x) ? Easy(x)) P?? 4? C(ds) ? Easy(ds) US???3 5? C(ds) ? Like(Wang,ds) T??2?4 6? C(ds) P?? 7? Like(Wang,ds) T??5?6 ?????ds????.

62. 4.2?????? ????????????????????,????,?????????,??????,????????????????????????????,?????????????????????,?????????????????,??????????

63. 4.3?????? ??????????????????,????????????????????????,???????(?????????????????)?????????????????????????P???Q??P ?Q?????????????????????????????????????,(??????????????????)??????????????

64. 4.3?????? ??????,??????????????????????,????????????????? ?????????????????????,?????????

65. 4.3?????? ??:??????,??????????????;???????????? ??,P(x) ?Q(x), ?P(x,f(x)) ?Q(x,g(x))??????P(x) ? Q(x,g(x))? ?P(x,f(x))????????????????????????

66. 4.3?????? ????????????,???????????,?????????,?????? ?????????????????????????????????????????????

67. 4.3?????? ?????????: 1??????????????????�?� ?�?�: P ?Q?P?Q P ?Q ?(P?Q)?(?P ? ?Q)

68. 4.3?????? 2????????????�?�???????? ? ? P ? P ? (P ?Q)? ?P ? ?Q ? (P ? Q)? ?P ? ?Q ? (?x)P ?(?x) ? P ?(?x)P ? (?x) ? P

69. 4.3?????? 3????????,???????????????? 4???????????????:?????????????????????,??????????????????????????????????;?????????????????????????,?? (?x1) (?x2)�(?xn)( ?y)P(x1,x2,�,xn,y) ?????Skolem??f(x1,x2,�,xn)?????????????,???????????

70. 4.3?????? 5???????????????? 6??????? P?(Q?R) =( P? Q) ? ( P? R)????? Skolem????

71. 4.3?????? Skolem?????????: (?x1) (?x2)�(?xn)M ??,M???????,??Skolem??????? 7??????? 8??????,?????????????

72. 4.3?????? 9????????,???????????????????????????????,????????????,?????

73. ????? ??????????????????????????????????????? ??????? ????????????????,????????????????,????????????????????????,???????

74. ????? ??????????????????,????????,???????? ????? *?S????,??????????H????????:

75. ????? 1??H0?S??????????,?S????????,??H0 ={a},??a????????????? 2??Hi+1 = Hi?{S???n???f(x1,x2,�,xn) | xj(j=1,2,�,n)?Hi????},??, i = 0,1,�???????????????

76. ????? ?1????S={P(x)?Q(x),R(f(y))}?H?? ?:??S???????,????a??????,????: H0 = {a}, H1 = {a, f(a)}, H2 = {a, f(a),f( f(a))}, H3 = {a, f(a),f( f(a)), f(f( f(a)))}, ? H? = {a, f(a),f( f(a)),�}

77. ????? ?2 ????S={P(a),Q(b),R(f(x))}?H? ?:??H??????: H0 ={a,b} H1={a,b,f(a),f(b)} H2={a,b,f(a),f(b), f(f(a)), f(f(b)) } ?

78. ????? ?3:????S={P(x),Q(y)?R(y)}?H?? ?:?????????????,????,???????????a??????,????H0 = H1=�= H?= {a} ????:???S???????????S?H???????????????????????S????D???????S,??H???????????S???????,S?H???????:

79. ????? ???S?H?????????????: 1????I?,???????; 2?S?????n????Hn?H?????,?h1,h2,�,hn?H,?f(h1,h2,�,hn) ?H;

80. ????? 3?S????n????Hn?{T,F}??????????????T????F? ?????????????????????????,?????????????????????1965???????????,?????????

81. ??????? ??????????,??????????????????,????????????????? ??????????????????,?????????????????,?????????????,????????????,???????????????,????????????,?????????

82. ??????? ???????????????????????,??,????S????,????????????????,????????????????????????

83. ??????? ?????????????????? ??P???????,??P??P???????????????????: P?Q,Q ? R? P? R? ? P ? Q, ? Q ? R ? ? P ? R c1 c2 c12

84. ??????? ????????????????c1 ?????Q,???c2???Q????? Q,??????????,????????????? c1 ?c2?????c12???c12?c1 ?c2????, c1 ?c2???c12??????

85. ??????? ??: 1?C1=? P ?Q ?R C2=? Q ?S ??????c12?? P ?R ?S 2?C1=? P C2=P ??????c12?NIL?????

86. ??????? 3?C1=? P ?Q C2=? Q ?R C3=P ??????c123?R???????????????????????????

87. ??????? ?P?Q ?Q?R ?P?R P R ??????????

88. ??????? ????????????????????: ?c1?c2????S??????,c12???????,??c12??c1?c2???????S1,??S1??????????S???????????????,?????S??? ?????,?????????S1???????,�??????Sn ??????????

89. ??????? ??????,?????????,?????????????????????,???????????????????????????????????????????,??????????????????

90. ??????? ?C1?C2????????????,L1?L2 ???C1?C2????,???L1??L2??????,?? C12= ( C1 ? -{L1 ?})?( C2 ? - {L2 ?})?C1?C2??????, L1?L2?????????????P132???4.10??4.11?

91. ??????? ???C1=P(a)? ?Q(x) ?R(x) C2= ? P(y)? Q(b) ??L1= P(a), L2= ? P(y),??={a/y}?L1 ?? L2??????. ???C12=(C1 ?-{L1 ?})?(C2 ? -{L2 ?}) ={?Q(x) ?R(x)} ?{Q(b) } ={?Q(x),R(x), Q(b) }.

92. ??????? ??L1= ? Q(x), L2= Q(b),??={b/x}?L1 ?? L2??????. ???C12=(C1 ?-{L1 ?})?(C2 ? -{L2 ?}) ={?Q(x) ?R(x)} ?{Q(b) } ={P(a),R(b), ? P(y) }.

93. ??????? ?????????: C1=P(x)?Q(a),C2=?P(b)?R(x) ??C1?C2 ?????????????????????C1?C2???.???????,???C2 ??????.

94. ??????? ?C2=?P(b)?R(y),??,L1=P(x), L2= ?P(b),??????????={b/x}.??? C12=({P(b),Q(a)}�{P(b),}) ?({?P(b)?R(y),}-{?P(b)}) ={Q(a), R(y)}. ???????????????????,???????????????,???:

95. ??????? ????:C1=P(x) ?P(f(a)) ?Q(x) C2= ?P(y) ?R(b)???C1???????P(x) ?P(f(a)),?????????? ?={f(a)/x}????,?? C1?= P(f(a)) ?Q(f(a)) ????C1??C2????,????C1?C2??????.?C1??C2??? L1=P(f(a)), L2= ?P(y),?????????

96. ??????? ?={f(a)/y}???????????: C12=R(b)?Q(f(a)) ????C1??C1??,??C1???????,????C1?????. ???????,???????????????????.

97. ??????? ??;??C1?C2??????????????: (1)C1?C2??????; (2)C1?C2???C2 ?2??????; (3)C1???C1 ?1?C2??????; (4)C1???C1 ?1?C2???C2 ?2? ?????;

98. ??????? ?????????,???????????????,?????????S??????????????S????????S??????.

99. ???? ??????:?? P1,P2,?, Pn?Q (1) P1??P2,?, ? Pn?Q=T (2) ?(P1??P2,?, ? Pn)?Q=T (3) (P1??P2,?, ? Pn) ? ? Q=F (4) ???????????????,??(4)?????(3),?(3)?????(2),?(2)?????(1) .

100. ???? ?????????,????????????????,???????????: (1)?????????�?�, ???? A?B = ?A?B (2) ?????????????????,???? ?(A?B)= ?A??B ?(A?B)= ?A??B ?((?x)A(x)) = (?x) ? A(x) ?( (?x) A(x)) = (?x) ?A(x)

101. ???? (3) ?????? ????????,?????????????(????),??????????????????????????????,?????????????????????????????????????????????? ??? (?x)(A(x) ?(?x)(B(x))) ???? (?x)(A(x) ?(?y)(B(y)))

102. ???? (4) ?????? ??? (?x)( (?y)P(x,y))?,??????????????,????????x?????y???????????????g(y)???,????y?????????x???????skolem??????skolem???????x,?????????????,???(?y)(P(g(y),y))

103. ???? ??? (?x)( (?y)P(x,y))?,??????????????,????????x?????y???????????????g(y)???,????y?????????x???????skolem??????skolem???????x,?????????????,???(?y)(P(g(y),y))

104. ???? ????????????????????skolem??????????????????,???skolem??????????????????????????,??????????????????????????skolem???????????????,?????????????????????: (?y) (?x) P(x,y)?(?y)(P(g(y),y))??,??g(y)??skolem???

105. ???? ????????????????????????,???????????skolem????????,(?x) P(x)??P(A),??????A??????????????A??????????,???????????????

106. ???? (5)????? ??????????????,??,????????????????????????????,???????????????????????????????????

107. ???? ?????????????,?????????,????????????,? ???=(??) (??) ????? ?????

108. ???? (6)????????? ????????????????(?)??????????????????????????????????????????????,??????????????, A?(B?C)=(A?B)?( A? C)

109. ???? (7)?????? ?????,???????????????????,???????????????????????????

110. ???? (8)????????,?A,B??A?B??????????,?????????,????????????????????????????????????? (9)?????? ???????????,?????????????????????????????????????????:

111. ???? ?1??:G?F1?F2?????,?? F1:(?x)( P(x)? (?y)(Q(y) ??L(x,y))) F2:(?x)( P(x)? (?y)(R(y) ??L(x,y))) G: (?x) (R(x) ?? Q(x)) (?x)(P(x)?(?y)(Q(y)??L(x,y))), (?x)( P(x)? (?y)(R(y) ??L(x,y))) ?(?x) (R(x) ?? Q(x))

112. ???? ??:???F1 ,F2 ??G??????: F1=(?x)(P(x)?(?y)(Q(y)??L(x,y))) =(?x)(?P(x)?(?y)(?Q(y) ? ?L(x,y))) =(?x) (?y) (?P(x)? ?Q(y) ? ?L(x,y)) =?P(x)? ?Q(y) ? ?L(x,y).

113. ???? F2=(?x)( P(x)? (?y)(R(y) ??L(x,y))) =(?x)( P(x)? (?y)( ?R(y) ? ?L(x,y)) =( P(a)? (?y)( ?R(y) ? ?L(a,y)) =(?y) ( P(a)? ( ?R(y) ? ?L(a,y)) P(a), ?R(z) ? ?L(a,z)

114. ???? ?G=? (?x) (R(x) ?? Q(x)) =(?x)? (?R(x) ? ?Q(x) = (R(x) ?Q(x)) R(b), Q(b) ????????: 1. ?P(x)? ?Q(y) ? ?L(x,y) 2. P(a) 3. ?R(z) ? ?L(a,z) S 4. R(b) 5. Q(b)

115. ???? 6. ?Q(y) ? ?L(a,y) 1?2??a/x? 7. ?L(a,b) 5?6??b/y? 8. ?R(b) 3?7??b/z? 9.? 4?8?? ?=? ?S??????,G?F1?F2??????

116. ???? ?2???:??????????,??????????,Mary?Bill???,???????????Mary??Tom???? ?:???????????????: brother(x,y):x?y???; sister(x,y): x?y???; woman(x): x????

117. ???? ?????????: (?x)(?y)(brother(x,y)??woman(x)), (?x)(?y)(sister(x,y)? woman(x)), sister(Mary,Bill) ? ?brother(Mary ,Tom)

118. ???? ?????????????????: (?x)(?y)(brother(x,y)?? woman(x)) = ?brother(x,y)? ? woman(x); (?x)(?y)(sister(x,y)?woman(x))= ? sister(x,y) ? woman(x); ??brother(Mary,Tom)= brother(Mary,Tom); sister(Mary,Bill).

119. ???? ???????S??: 1?sister(Mary,Bill) 2?brother(Mary ,Tom) S 3??brother(x,y)??woman(x) 4?? sister(z,w) ? woman(z)

120. ???? 5??woman(Mary)?3??Mary/x,Tom/y? 6?woman(Mary)1?4??Mary/z,Bill/w? 7?��������� ? 5?6????? ? ????.

121. ???? ?3???,John???Paul???(wine), Paul?????(cheese)???Paul?????John????????????,???????,??????????????????????John????????

122. ???? ?:?????????????: thief(x): x?? like(x,y): ??x????y may-steal(x,y):??x???????y

123. ???? ?????????: thief(John), like(Paul,wine), like(Paul,cheese ), (?y)(like(Paul,y)?like(John,y)), (?x)(thief(x)?(?y)(like(x,y)?may-steal(x,y))) ? may-steal(John,Z).

124. ???? ?????????????????: (?y)(like(Paul,y)?like(John,y))= ?like(Paul,y)?like(John,y ); (?x)(thief(x)?(?y)(like(x,y)?may-steal(x,y))= thief(John)?(?y)(like(John,y)? may-teal(John ,y))= (?y)(thief(John)?(?like(John,y)? may-steal(John ,y)))= thief(John)?(?like(John,y)?may-steal(John,y)).

125. ?may-steal(John,Z). ???????S?: 1? thief(John ) 2? ?like(John ,y)? may-steal(John ,y) 3?like(Paul, wine ) 4?like(Paul, cheese ) 5??may-steal(John,Z) 6??like(Paul,X)?like(John,X) 7?like(John,wine) 3?6??wine/x? 8?may-steal(John,wine) 2?7??wine/y? 9?? 5?8?? ? ?????

126. ????????????? ?????????????????,?????????.???????: 1???????????????,??????????S; 2??????????????????,??????????ANSWER?????, ANSWER???????????????,????????????????????;

127. ????????????? 3??????????,????????????S?,?????? S?; 4??S???????????; 5???????ANSWER,?????ANSWER??

128. ????????????? ?: F1:???(wang)?????(li)??? . F2:?????(zhang)?????. F3:??x?y?????,?x?????y???. ?????????

129. ????????????? ?:??????: T(x,y):x?y???. C(x,y):x?y?????. ???????????????????: F1: T(wang ,li) F2: C(li,zhang) F3: (?x) (?y) (?z)(C(x,y) ?T(z,x) ? T(z,y)).

130. ????????????? G:?(?x)T(x,zhang)?ANSWER(x) ??????????: (1)T(wang ,li) (2) C(li,zhang) S? (3) ? C(x,y) ? ?T(z,x) ? T(z,y). (4) ?T(u,zhang) ?ANSWER(u)

131. ????????????? ??????????: (5) ? C(li,y) ? T(z,y). (1)?(3)?? (6) ? C(li,zhang) ?ANSWER(wang) (4),(5) (7) ANSWER(wang) (2)?(6)?? ?????P137??4-9??

132. ????????????? ?:?A,B,C??????????,????????,???????????????:??????A?:�B?C????�;B?:�A?C????�;C?:�A?B?????????�.???????,??????

133. ????????????? ?:?T(x):??x??? ??A?????,?? T(A)??T(B)??T(C) ??A?????,?? ?T(A)?(T(B) ?T(C)) ?B?C??????????: T(B)??T(A)??T(C) ?T(B)?(T(A) ?T(C))

134. ????????????? T(C)?(?T(A) ? ?T(B)) ?T(C)?(T(A) ?T(B)) ???????????S?: (1) ?T(A) ? ?T(B) (2) ?T(A) ? ?T(C ) (3) ?T(B) ? ?T(C ) (4) T(B) ?T(A) ?T(C) (5) ? T(C) ??T(A) ? ?T(B) (6) T(A) ? T(C )

135. ????????????? (7) T(B) ?T(C ) ??????????. ??T(x) ?ANSWER(x)??S?S1 (8) ?T(x) ?ANSWER(x) ?S1?????? (9) ?T(A) ?T(C ) (1)?(7)

136. ????????????? (10)T(C) (6)?(9) (11) ANSWER(C) (8)?(10)?{C/x} ?C????. ???S1???????ANSWER(B) ?ANSWER(A) .???????A?B?????. ?A?????,???T(A)???????S??S2

137. ????????????? ?S2??S?????? (8) ? (?T(A)) (9) ?T(A) ?T(C ) (1)?(7) (10) ?T(A) (2)?(9) (11)NIL (8)?(10) ??A?????,????B?????.

138. ???? ????????????????????,??S???????????,???????????????? .??????????????????????????????????????.?????????????????.

139. ???? ????????,?????????S????????,???????????????????,???????????,??:????,????,????,??????

140. ???? ????????,?????S????????????,??????????S??????,????????????????????????? ???: ??????C?D,????(???)?,??C? ? D ??,????C???D??,??D?C??,? ???D???S????

141. ???? ??:C?????C????????,????C????????????????? ?? C=p(x) D=p(a) ?Q(a) ??=?a/x????C?= p(a)??? ? p(a) ? ? ? p(a),Q(a) ? ???????????

142. ???? ?????C1,C2,?,Ck??S??Ck???,?????????????????????????,???????????????????????????,????????????S??,???????????????,?????????????Sn ?

143. ???? ????????(Subsumption Algorithm) ?D=L1?L2??? Lm,?? =?a1/x1 , a2/x2, ? ,an/xn?,??x1 ,x2,?, xn?D????????, a1 ,a2,? ,an?C?D??????????????? ?1 ?W = ? ?L1 ?,? , ?Lm ??,K = 0,U0 = ?C?; ?2 ??? Uk????,C??D? ?3 ?Uk+1=?R(C1,C2)? C1? Uk , C2 ?W?; ?4 ?Uk+1=?,????,C???D? ?5 ?K=K+1,??2

144. ???? ??U0 ,U1,? , Uk,????,?????????????????????????????????,???????????,??,????????n?Uk=???? Un???????.???????,???C????D,???????????2? ?????????????????????????????,??????????????????????????,??????????????????????????????????????????????????(???????)? ?????????????????????????????,??????????????????????????,??????????????????????????????????????????????????(???????)?

145. ???? ???? C=?P(x)?Q(f(x),a) D= ?P(h(y))? Q (f(h(y)),a) ??P(z) ???C?????D? ?:?? = ?b/y,c/z? W = ? P(h(b)), ?Q (f(h(b)),a), P(c) ?, K = 0 U0 =?? P(x)?Q (f(x),a)? K=0:??? U0

146. ???? U1= ?Q(f(h(b),a),?P(h(b)), Q(f(c),a) ? ?U1??,K=K+1, K=1: ??? U1, ?U2=???, ?U2??,K=K+1, K=2: ?? U2 ???,C??D?D??????

147. ???? ? ?C = P(x,x),D = P(f(x),y)?P(y,f(x))???C????D? ?:?? = ? a/x,b/y? W = ? ?P(f(a),b), ?P(b), f(a)? K = 0 U0 = ?P(x,x) ? K = 0:??? U0,?U1=?, ?U1 = ?,???,C???D?

148. ?????? ???????????,???????S?????????????C0?????,???????????????Ci???????Bi????????Ci+1?Bi??S??????????Cj(j?i)

149. ?????? ? S=?P?Q,? P?Q,P?? Q, ? P?? Q ? ?????C0 = P?Q ?????? 1? P?Q 2?? P?Q 3?P?? Q 4?? P?? Q 5?Q 1?2 6?P 5?3 7?? Q 6?4 8?? 7?5 ????????? ???????????????????????????????DBMS?????????? ????????? ???????????????????????????????DBMS??????????

151. ?????? ?????????????????????C0?S-? C0 ??????? ????????????????,???????.????,???????????,?????????????????.?????? S ={P(x)?Q(x),?P(y)?Q(y),P(u)?? Q(u), ?P(t) ?? Q(t) }???????????????.

152. ??????? ?????????????,?????????. ????????????????????????????????. ??:?????: S={?I(x)?R(x),I(a), ?R(y) ? ?L(y),L(a)} ???I(x)?R(x)??????????????.??????????????

153. ???????? (1)?I(x)?R(x) (2) I(a) S S1 (3) ?R(y) ? ?L(y) (4) L(a) (5) R(a) (1)?(2)???{a/x} (6) ?R(a) (3)?(4)???{a/y} S2 (7)?I(a) (1)?(6)???{a/x} (8) ?L(a) (3)?(5)???{a/y} S3 (9)NIL

154. ??????? ??????????????????,????????,???????????????????????.

155. ?????? ????????????????????: (1)C1?C2????????????????. (2)??????????????????,???????????.??????(??C1)??????(??C2 ) ?????C2 ??C1??????????????.

156. ?????? ?????????. ?????? S={P(x)?Q(x),?P(y)??Q(y),P(u)? Q(u), P(t)?? Q(t) }

157. ?????? ????????????: ? P(x)?Q(x) ?P(y)??Q(y) S 3. P(u)? Q(u) P(t)?? Q(t) ? P(x) 1?2???{x/y} Q(x) 3?5???{x/u} P(t) 4?6???{x/t} NIL 5?7????{}

158. ?/?????? ????????????,??????????????????,?????????/??????????????.??????????????,????????????????????/??????,???????????????,??????????.

159. ?/?????? ?/???????????????????????,??????: 1??/???????? ??????????,????????(F??)??????,???????????????? ??????????????F?????????????????????

160. ?/???????? 1????????/?????????? ???????/?????????????,???????????????,?????????

161. ?/???????? ?????????????/??: (?x)(?y){Q(y,x)? ?[(R(y)?P(y)) ?S(x,y)]} ???=)(?y){Q(y,a)? ?[(R(y)?P(y)) ?S(a,y)]} /*??????*/ = Q(z,a)?[(?R(y)??P(y)) ? ? S(a,y)] /*??????,?????????????*/

162. ?/???????? ???????/???? { Q(z,a)?[(?R(y)??P(y)?? S(a,y)]} Q(z,a) [?R(y)??P(y)?? S(a,y)] ?R(y)??P(y) ? S(a,y) ?R(y) ?P(y)

163. ?/???????? ???????????????????????,????????????,????????,?????????.

164. ?/???????? ????/?????????????????,???????????????,????????????: Q(z,a) ?R(y)?? S(a,y) ?P(y)?? S(a,y) ??????????????.

165. ?/???????? 2?F??????? ??/?????????,????F????????: L?W ??,L????,W??/?? ??F????????,???????????,??F???????????/??,???/???????????,????F?????

166. ?/???????? ??????(??).???????????????????,??????????????,?????: 1)????????�?� 2)?????�?�?????????? 3)??skolem???????? 4)?????? 5)?????:??? P?Q=P?Q

167. ?/???????? 3?????????? ??/????????????????????? 4????? ??F?????????????????????????????/????,????F???????????????,??????

168. ?/???????? 1)????/???????????; 2)?F???????/??????????,???????F??????/???; 3)???2?,???????????????????????.

169. ?/???????? ??????? A?B F??? r1:A?C?D r2:B?E?G ?????: C?G ????????:

170. ?/???????? C G C D D G A B A B A?B

171. ?/???????? ?????????????????,???????/??????,?????????.???????????????F??,?????????????????.

172. ?/???????? ??????? ?P(a)?{Q(a)?R(a)} F???: R1: ?P(x)??S(x) R2: Q(y)?N(y) ???????: ?S(z)?N(z) ??????:

173. ?S(z) N(z) N(a) ?S(a) Q(y) ?P(x) Q(a) R(a) ?P(a) Q(a)?R(a) ?P(a)?{Q(a)?R(a)}

174. ?/???????? ?/????????????????(??)??,??????????(B??)??????,?????????????????. ?????????,???????????????B?????????

175. ?/???????? 1???????/???? ???????????,???????????????????????. ??????????: (?y)(?x){P(x)?[Q(x,y)??(R(y) ?S(y))]} ??????:

176. ?/???????? (?y)(?x){P(x)?[Q(x,y)??(R(y) ?S(y))]} =(?y){?P(f(y))?[Q(f(y),y)?(?R(y)??S(y))]} =?P(f(y))?{Q(f(y),y)?[?R(y)??S(y)]} =?P(f(z))?{Q(f(y),y)?[?R(f(y)??S(y)]}

177. ?/???????? ???????????????????(??????). ??????/?????????????/??????,???????????,?????????. ????/??????.

178. ?P(f(z))?{Q(f(y),y)?[?R(f(y)??S(y)]} ?P(f(z)) Q(f(y),y)?[?R(f(y)??S(y)] Q(f(y),y) ?R(f(y)??S(y) ?R(f(y) ?S(y)

179. ?/???????? ???????????????????????,?????????????? ?P(f(z)) Q(f(y),y)? ?R(f(y) Q(f(y),y)? ?S(y) ?????????.

180. ?/???????? 2?B????? B???????? W?L ??W????/????;L???? ????????????????,?????F??????????,??? W?L1?L2

181. ?/???????? ?????B????????: W?L1 W?L2 3???????? ???????????,??? F1?F2? ? Fn ??????,??Fi???????,???????????????? {F1,F2,? , Fn}

182. ?/???????? 4????? 1)????/???????????; 2)?B???????/?????????,???????B??????/???; 3)?????2?,?????????????????????.??????????????????????????.

183. ?/???????? ?????????? ??: f1:DOG(fido) fido?? f2:?BARKS(fido) fido??? f3:WAGS-TAIL(fido) fido??? f4:MEOWS(myrtle) myrtle???

184. ?/???????? ??: r1: (WAGS-TAIL(x1)?DOG(x1))? FRENDLY(x1) /*?????????*/ r2: (FRENDLY(x2) ? ?BARKS(x2)) ? ? AFRAID(y2,x2) /*???????????*/ r3: DOG(x3) ?ANIMAL(x3)

185. ?/???????? r4: CAT(x4) ?ANIMAL(x4) r5: MEOWS(x5)?CAT(x5) ??????:?????????????,??????????? ?????????: (?x)(?y)[CAT(x) ?DOG(y) ? ?AFRAID(x,y)]

186. CAT(x) ?DOG(y) ? ?AFRAID(x,y) CAT(x) DOG(y) ?AFRAID(x,y) CAT(x5) DOG(fido) ?AFRAID(y2,x2) MEOWS(x) ?BARKS(y) FRENDLY(y) MEOWS(myrtle) ?BARKS(fido) FRENDLY(x1) WAGS-TAIL(y) DOG(y) WAGS-TAIL(fido) DOG(fido)

187. ?/???????? ????????????.????????,???????????? ???????????? {myrtle/x}?{fido/y }??????????,?????????: CAT(myrtle)?DOG(fido) ??AFRAID(myrtle, fido) ??????myrtle???????fido????????????.

188. ??????????? 1??????? ???????????????????????????????????????????: ?????? ?={?1 ,?2,?, ?n}??i????i? ?i={ti1/xi1, ti2/xi2, ?, tim(i)/xim(i)} ??tij??xij???(j=1,2 , ?, m(i))

189. ??????????? ???????????????????? T={t11,t12,?,t1m(1),t21, t22,?,t2m(2),?,tnm(n)} X={x11,x12,?,x1m(1),x21,x22,?,x2m(2),?,xnm(n)} ???.

190. ??????????? 1)??1={x/y}, ?2={y/z},??1??2????. 2)??1={f(g(x1))/x3 ,f(x2)/x4}, ?2={x4/x3,g(x1)/x2 },??1??2????.

191. ??????????? 3)??1={a/x}, ?2={b/x},??1??2?????. 4)??1={g(y)/x}, ?2={f(x)/y},??1??2?????. ??????????,????????????????,????????????,?????,????????.

192. ??????????? 2????? ??/?????????????F?????(????)?B?????(????)??/??????????(??),?????????????????,????????,??????,????????????,?????.

193. ??????????? ??????????:??????????????????,?????????????,???????,???????????????????.?????????????????????????,???????????????.????????????????????,?????????.

194. ??????????? ??,?????/????a??,???B??? r1:S(z)?P(b) r2:R(y)?P(y) ?????r1??????{a/x,b/y} ????????.??????????.???r2?????{a/x,x/y},?????,???r2????,?????????/???.??b??.

195. ??????????? P(x)?Q(x) P(x)?Q(x) P(x) Q(x) P(x) Q(x) Q(a) P(y) Q(a) a? R(x) b?

196. ??????????? ?/????????????????????,???????,?????????????,????. ??????????????????????????,??????????????????????.

197. ??:P153 4.14 P154 4.15,4.16,4.17