BAI HQC QUOC GIA THANH PHO HO CHI MINH.
TRUdNG BAI HQC KHOA HQC TV NHIEN

BO VAN NHcJN
XA Y D{jNG HI:: TINH TOAN THONG MINH
XAYDVNG &PHAT TRlftN cAe M6 HINHBlftU
DlitN TRI TIHJ'CClIO CAC Ht GIAI TOANTV DONG
Chuyen nganh: Dam baa toao hQc cho may Hnh
Va cac h~ tho'ng Hnh toaD
Mii so': 1.01.10
TOM TAT LUh-N AN TIEN SI TO AN HQC
Thanh pho'H6 Chi Minh - 2001
PHAN Md DAD
Tri tu~ Nhan t<;lOla mQt lInh vlfe eua khoa hge may tinh
nh~m nghien CUllphat tri6n cae h~ th6ng ngay cang thong mint
hon h6 trel tcJt hon cho h()~\t dOng xlt ly thong tin va XL(ly tri
thue, tint loan va diSH khi6n, v.v Trong qua trlnh philo tich va
thiSt kS cae M th6ng Tri tu~ Nhan t<;lO,d~e bi~t la cae M
ehuyen gia va cae h~ giai loan thong minh, nguoi ta ph~Uquan
tam uSn 2 va'n dS co ban nha't la:
(I) Bi6u diGn tri thae, va
(2) Phlwng phap va ky thuOtt1mk16m hay SHYdiOn,
Ngl1i<3nel(U vi\ pl1~llridll de l1\t\1111111bidu di~n lri lhac vi\ suy
di€:n tlf dQng tren tri thue gilt mOt dia vi ra't quan tr9ng trang
khoa 11(.)Cmay linh cOng nlu( lrong 'I'd lll\; Nhan l<.lo.
M~le lieu ct'1adS tai Iii xfiy d\1'ng,phat tri6n mOt sO'mo hint
bi6u di~n tri thue va cae thu~t giai d6 giai tlf dOng cae d<;lngbEd
loan khae nhau dlfa tren tri thue.
Cach ti6p c~n duQc slt d\1ng Iii kC't hQp cae phuong phap
bi6u di~n tri thUe da e6 vdi nhung phat lri6n nha't dint d6 t<;lOra
mQt sO'mo hint bi6u di€:n tri thue mdi th6 hi~n duQe nhiSu d<;lng

BIJ'fUDIEN TRI TRUC vA
Rt GIAI TOAN D{jA TREN TRI TRUC
Chuang n~y trlnh bay t6ng quan v~ cac phuong phap bi6u
di€n tri thUc va cac cang trlnh lieu bi6u vS cac chuang trlnh giai
cac bai loan dt!a tren tri thUc. Cac ke't qua nghien cliu oa co n~y
cling ouQc nh?n d~nhva oanh gia.
1.1 Cae va'n d~ cd ban trong thie't ke' m{)t h~ giai b~li toan
dQ.'atren tri thue
1.1.1 Ca'u true eua m{)t h~ giai b~lito:1n dQ.'atren tri thue
Ca'u truc co ban cua M th6ng bao g6m cac thanh ph~n ouQc
chi ra tren blah 1.1 bell dUai.
2
di<$n
Giao
N gu'~l 511'dllng
moh 1.1 Cffu true eua mQth~ giiii loan thong minh
C6 th~ n6i rAng trai tim eua h~ th6ng la phh co sd tri thue,
trong d6 ehua cae kie'n thue dn thie't eho vi~e giiii cae bai loan.
BQ soy di1;n (con gQi 1£1mo-tel soy di1;n) se ap d\;lng kie'n thUc
trong co sd tri thue M tlm Wi giiii eho bai loan.
1.1.2 Va-o d~ Bi~u di~o Tri thuG
Bi~u di1;n tri thue d6ng vai tro rfft quail tn;mg trong thie't ke'
va xfiy dlfng mQt M giai bai loan thong minh. George F. Luger
([26]) va Gerhard Lakemeyer ([41]) oa t6ng ke't cae phuong
phap bi6u diGn tri thue khae nhau va philn lam 4 lo~i: bi6u diGn
dlfa tren logic hlnh thue, bi~u di1;n tri thue thu tl,1e,bi~u di~n
d[~ng \11l,1ng,va hiGHdiGn CrIlltruc. MOi phuong phap chI biGu
di1;n ou<;leffiQtkhia e~nh eua kie'n thue trong khi tri thue dn
du<;lebi~u di€n trong cae Mung dl,1ngrfftda d~ng.
1.1.3 Va-n d~ Soy di~n Tt! dQng

hlnh bi&udi~n tri thuc co Hnh tfl/Cquail , tinh mo dun hoa cao va
cMa d1!ngnhi~u thanh ph§n tri tMc da d<;lng.
1.2.3 MQt s6 phu'dng phIlp chung minh dinh ly hlnh hQc
Nhi~u phuong phap chung minh djnh 19hlnh hQc da dlt<;JCd~
xufft nhu phuong phap di~n tich va phuong phap "full angle".
Cac phuong phap nay chua cho ta mQt mo hlnh bi6u di~n tri thuc
4
t6t d~ co th~ xiiy dl!ng m(>tco s0 tri thuG va m(>tligon ngG'khai
bao bai loan mOt cach tl! nhien.
1.2.4 Phu'dng phIlp Wu
Phuong phap Wu la mN phuong phap chung minh dinh 1:9
hlnh hQc theo cach liSp c~n d~i so'.Phuong phap nffy cho ta mOt
bi~u dii;n kha dyp v~ m~t 1:9thuySt loan hQC.Tuy nhien no cling
co nhi~u h~n chS nhu cac phuong phap "di~n tich" va ':f'ull
angle" trong nhu du xiiy dl!ng mOt M giiii bai loan dl!a tren tri
thuG.
1.2.5 Cac phtidng philp chung minh hinh hQc biing may Hnh
T(ing kG! cae nghicn Call VOcl~((ng l1linh t\( dOng cae bid
loan hlnh hQC,S.C. Chou va cac d6ng lac giii oil li<$tke cae
phuong phap khac nhau co th6 sa dl,mg06 chung minh cac bili
loan hlnh hQc b~ng may tinh. H~n chS ldn nha't cua cac phuopg
phap nffy la chUng khong cho ta nhG'ng mo hlnh bi~u dii;n tri
thUGt6t giup xiiy dl!ng mOt co s0 tri thuG, b(>suy dii;n va cac
thanh pMn khac cila M th6ng.
1.2.6 MQt s(f nghien CUllxfiy d1;ingh~ ghii toan hinh hQc
M(>t so' nghien CUllxiiy dl!ng h~ giiii loan hlnh hQc GOng
du<;icd~ c~p dSn va GOngco nhG'ng h~n chS tuong tl! nhu cac
phuong phap da c1u<;iclieUd tren.
1.2.7 MQt s(f san phii'm phftn m~m giai toan
Trong m1,1cnffy u~ c~p uSn mOtso'phffm m~m Cl,lth~ co lien

r6ng cua M sao eho u(f) n v(f) =0.
D6i vdi m6i f E F, ta kg hi~u M(f) la t~p cae bie'n e6 lien M
trong quaD h~ f, nghla la M(f) =u(f) u v(f).
2.2.3 Cae va-n d~ eo'ban tren m~ng suy di~n
6
Tren m(;lngsuy di6n (M,F) gicisa c6 mQt t~p bie'n A ~ M da
du<;Jcxac dinh vft B 1ftmQt t~p bie'n ba't ky trong M.
. Va'n d~ 1: C6 th€ xac dinh du<;Jc(hay suy fa) t~p B tU t~p A
nho cac quail M trong F hay khong?
. Va'n d~ 2: Ne'u c6 tItS suy ra du<;JcB tU A thl qua trlnh suy
di6n nhu the' nfta? Cach suy di6n khac nhau thl cach suy
di0n nao la t6t nhflt'l
. Va'n d~ 3: Trang truong h<;Jpkhong tItS xac dinh du<;JcB, 'thl
dn cho them di~u ki~n gl M c6 th~ xac dinh du'<;JcB.
Biii loan xac djnh B tU A tren m(;l~gsuy di6n (M,F) du<;Jcvie't
dlfdi d~ng A -t B.
Dinh nghia 2.2: Cho D = {1'" 1'2, , 1'd c F va A eM. Ky hi<$u
D(A) 1fts1,1'ma rQng clia A nho ap dl,lllgday quail h~ D.
Dinh nghia 2.3: D ={fl, f2, , fd c F 1ft mQt liJi giai cua bfti
loan A -t B khi D(A) ::) B. Bfti loan A -t B du<;JcgQi 1ftgidi
du(/ckhi n6 c6 mQtWigicii.Loi gicii{f10f2o , fd 1ftliJi gidi t6't
ne'u khong tItS bo bot mQt s6 quail h~ trong Wigicii.
2.3 TIm lui giai
Xet bfti loan A -t B tren m(;lngsuy di6n (M,F). Trang m1,1c
n~y ta khao sat tinh ghli dtiQc cua b~1iloan suy di~n, tlm mQt loi
gicii t6t cho bfti loan suy di6n vft phan tkh qua trlnh suy di6n.
2.3.1 nnh giai duQc
Dinh nghia 2.4: Cho m(;lngsuy di6n (M,F), vft A 1ftmQt t~p con
cua M. Bao dong cua A 1ftt~p B lOn nha't ~ M sao cho bfti loan
A-tB la giciidu<;Jc.Ky hi~u baa d6ng cua A la A.

MSDT,1iimQtmo hlnh(A, D, w) bao g6m:
(1) mQtt~phQpcac thuQctinh A,
(2) mQtt~phQpcac 1u~tsuydi~nD, vii
(3) mQt ham trQng s6 du'dng w: D ~ R+
M6i lu~t dfin r thuQc D co d~ng r: U=:>v, vdi U va vIa cac t~p
hQp con khac r6ng va roi nhau cua A.
Bioh oghia 2.6: Neu len khai ni~m v~ Wi giiii t6i u'u d1!a tren
cac trQng s6.
2.4.2 L<1igiai va dQ phuc t~p cua qua trinh Hm loi giai
Thu~t toaD 2.4: TIm mQt Wi giiii cho bai loan H ~ G tren mQt
MSDT (A, D, w).
Meoh d~ 2.5 Thu~t loan 2.4 cho Wi giiii la dung va co dQ phuc
t~p la O(IAI.IDl.min(IAI,IDI).
2.4.3 Tim liYigiiii t6i lill
vein d~ tlm Wi giiUlo'i u'u cho btd loan H~G lren MSDT (A,
D, w) du'Qcgiiii quye't d1!atren thu~t giiii A. b~ng cach xay d1!ng
d6 thj co trQng so' Grapgh(H~G).
Meoh d~ 2.6:
(1) MQt day S g6m cac lu~t la mQt loi giiii cua H~G khi va chi
khi S la mQt 1(>trlnh tren Graph(H~G) n6i tU H de'n S(H) va
S(H) =:>G.
(2) D(>diU cua m(>l1(>lrlnh S lrcn <16lhj Graph(H~G) Hi w(S),
trQng s6 cua danh sach lu~t S tren MSDT (A, D, w).
Thu~t toaD 2.5: TIm Wi giiii t6i u'u cho bfli tmin H~G.
Meoh d~ 2.7 Thu~t loan 2.5 cho Wi giiii la dung va co dQ phuc
t~p 1ftO(IAI2.IDI2).
2.5 TS)phqp sinh va vit:CKi~m djnh, bOsung gia thie't
2.5.1 Khai ni~m t~p hqp sinh
Bioh oghia 2.7: Cho(A,D)la mQtm~ngsuy di~n. M9t t~p thu9C
tinh SeA du'QcgQila m(>ttgp h(!psinh cua m~ngsuydi~n khi ta

d~t cae ph5n tlt cua H a muc O.
10
Thui,H toaD 2.8: Cho m<;lngsuy di~n (A, D) va bai loan H +G
khong gilli dU<;1C(khong co Wi gilli). TIm H' sao cho H n H' =0
va bai loan (H u H') +G la gilli dU<;1c.
Menh d~ 2.9: Thui,ltloan 2.8 d~ tlm s1,1'b5 sung gill thi~t cho bai
suy di~n la dung va co dQphuc t~p la O(IAI.IDI).
2.6 M~ng Suy di~n - Tinh toaD
2.6.1 Mo hlnh
Dinh nghia 2.10: MQt m~ng suy di~n-tinh loan g6m:
(1) T~p h<;1pA g6m cac thuQctinh.
(2) T~p h<;1pD g6m cac lu~t suy dit;n (hay cac quan h9 suy
di~n) In~ncite Ihll0c Ifnh.
(3) T~p h<;1pF gOm cac Gong thuG Hnh loan hay cac lhii ll,lc~inh
loan tu'dng ung vdi cae lu~t suy di~n. S1,1'tu'dng ung nfly lhS
hi<$nboi mQt anh x<;lf: D + F.
(4) T~p h<;1pR g6m mQt s6 qui t~c hay di@ukic$nrang buQc tren
cac thuQc tinh.
M~ng suy di~n Hnh loan du<;1cky hic$uboi bQ b6n (A, D, F, R).
Theo dinh nghla, ta co (A, D) la mQt m<;lngsuy di€n va Wi gilli
cho bai loan H + G tren m~ng suy di€n n§y se xac dinh cac
Gong thuG hay cac thii t,=,cHnh loan cac ph§n ta thuQCG ti'tcac
phh ta thuQc H.
2.6.2 Giai bili toaD tren m~ng guy di~n-tinh toaD
Ta co th€ gilli quy~t cac bai loan suy dit;n Hnh loan va tlm
Wi gilli t6i u'u d1,1'atren cac thu~t gilli dii trlnh bay a tren. Ngoai
fa, con tlm ra du<;1ccae GongthuGLuongminh qua cac buGCgilli
bai loan va rUt gQn cae Gong thuG du'oi d~ng ky hil$u. Nhu lhe'
tren m~ng suy di€n-Hnh loan ta eo th~ chi ra mQt cach t1,1'dQng
cac Gong thUGLuongminh d~ Hnh mQt s6 y~u t6 n§y ti't mQt s6

d5i tU<;1ng,va Rules la t~p h9P cae lu~t suy di~n tren cac s\1'
ki~n.
12
3.2 M6 hlnh tri thuc cae d6i tu'qng tinh toan
Ma hlnh tri thue cae C-objeet co th~ dung bi~u dien eho mQt
d~ng co sO tri thue bao g6m cae khai ni~m v~ cae d6i tu'<;1ngco
diu true cling voi cae lo~i quan h~ va cae eang thue Hnh loan
lien quan.
3.2.1 M6 hlnh tri thuc
Ta gQi mQt ma hlnh tri thue cae C-Objeet , vie't t1{tla mQt
ma hlnh COKB (Computational Objects Knowledge Base), la
mi)t h9 th6ng (C, H, R, Ops, Rules) g6m:
1. Mot tap hop C cae khai niem v~ cae C-Obieet.
M5i khai ni9m la mQt lOp C-Objee't co du true bell trong nhu'
san:
Ki~u d6i tu'<;1ng.
Danh saeh cae thuQe Hnh.
Quan h9 tren du true thie't l~p.
T~p h<;1pcae di~u ki9n rang buQe tren eae thuQe Hnh.
T~p h<;1peae tinh eha't nQit~i tren cae thuQe Hnh.
T~p h<;1peae quan h~ soy dien - Hnh loan.
T~p h<;1peae lu~t soy dien eo d~ng:
{cae SIfki~n giil thie't}:::>{caes11ki9n ke't lu~n}
Cung voi du true tren, d6i tu'<;1ngeon du'<;1etrang bi eae Mnh vi
trong vige giili quye't eae bai loan soy di~n va Hnh loan.
2. Mot tap H eae quan he phan dp giua cae loai d6i tu'ong.
Tren t~p C ta eo mQt quan h~ phan dp theo do eo th~ eo
mQt so' khai ni9m la st;l d~e bi9t hoa eua eae khai ni9m
khae. C6 th~ n6i rhng H 11\mOtbi~u d6 Hasse khi xem quan
M phan dp tren la mQtquan M thU t11tren C.

hQccling co th<5dU<;iCbi6u diGn theo ma hInh nay.
3.3 T6'chuc cd sd tri thuc COKB
Co so tri thUc COKB co th6 duQc t6 chlic boi mQt M th6ng
t~p tin van ban co ca'u truc nhu sail:
14
[1] T~p tin "Objeets.txt" lu'u tru cae dinh danh eho cae lo<;ti
d6i tU<;1ngC-Objeet.
[2] T~p tin "RELATIONS.txt" lu'u tru thong tin v€ cae lo<;ti
quan h~ khae nhau tren cae lo<;tiC-Objeet.
[3] T~p tin "Hierarehy.txt" lu'u l<;ticae bi~u d6 Hasse th~
hi~n quan h~ phan ea'p tren cae khai ni~m.
[4] Cae t~p tin voi ten t~p tin d~ lu'u tru ea'u true eua lo<;ti
d6i tu<;1ng.
[5] T~p tin "Operators.txt" lu'utru cae thOng tin v~ cae roan
t\i'tren cae d6i tu<;1ng.
[6] T~p tin "FACTS.txt" lu'u tru thOng tin v~ cae lo<;tisl!
ki~n khae nhau.
[7] T~p tin "RULES.txt" lu'u h~ lu~t cua cd sa tri thUG.
M6i lien h~ v€ ca'u truc thong tin trong cd sa tri thUGc6 th~ ou<;1c
minh hQa trcn so d0 sau day:
cofu truc 661 tu'<!ng
Cifu tnJc 661 tu'<!ng
mnh 3.3 Bi~u 06 lien M giua cac thanh phgn trong COKB
Cach tes chuG cci so tri thUG cho ta mQt cau truc tri thuG
ro rang va tach bc;tChvoi day du cac thong tin clIng voi cac
lien h$ khac nhau rat da dc;lng.Mo hlnh COKB dLiQCxay
dljng co cac Liudi§m sau day:
. Thfch hQp cho vi~c thie't ke' ml;Jtcd sa trl thuc vdl cae
khai ni$m co th§ dLiQCbi§u dien bai cac C-Object.
15

3.4.2 Giai quye't va'n d~ cd ban 2
D~ tlm mOt Wi giai eho bai loan GT => KL, ta e6 th~ thl/e
hiQn mQt thu tl,1cg6m 2 giai do,!-nnhu dudi day.
16
Thu(H giai 3.2: TIm mQt Wigiai cho bfd toclnGT ~ KL.
. Giai doan 1: TIm mQt loi giai (neu c6) cho bai loan.
. Giai doan 2: Tht/c hi~n lo~i bo cac bo'oc do' thlta trong Wi
. ghli (nSu c6) Om do'Qcd giai do~n 1 bhg cach troy ngo'Qc
theo Wi giai, ung voi m6i bo'oc giai ma st/ ki~n moi do'Qc
sinh ra nho'ng kh6ng dn thiet thllo~i boo
Vi du 3.3: Giai bai toclnGT ~ KL tren d6i to'Qng"TAM_GIAC"
voi GT = {a, b=5, GocA = m*(b+c), GocA = 2*GocB,
a"2=b"2+c"2}, KL = { GocB, GocC }.
Thu~t giai 3.2 se cho ta m9t Wi giai nho'sau:
1. Soy ra {GaeE '= ~GaeA } tlt {GocA =2 GocR}
2
2. Soy ra {GocA '= ~ 1t} tlt {a2 =';2 + C2}
3. Soy ra {GoeB '= ~ 1t} tlt {GoeE '= ~ GoeA ,GoeA = ~ 1t} ,
4. Soy ra {GocB} lU' {CoeE =~1t }
1 1 1
5. Soy ra {CaeC ==41t} tlt {CacA =2:1t, GacB=~rt}
6. Soy ra {GoeC } tlt {GoeC '=L1t }
4
3.4.3 Giai quye't vfi'n d~ cd ban 3
Thu~t giai 3.3: cho ta m9t thii tt,1ctht/c hi~n tinh loan cac thu9c
Hnh trong t~p hQp KL tlt cac st/ ki~n trong GT trong tru'ong hQp
bai loan GT~KL giai do'Qc.
Vi du 3.5: Tren m9t d6i to'Qng "TAM_GIAC", cho bai loan
{o, b = 1, GacA = ~ 1t} ~ {R, S, c} .
Thu~t giiii 3.3 tren se OmWigiai r6i tht/c hi~n tinh loan va cho

3. TIm mQt Wi giai t6t nha't (hay Wi giai t6i u'u) eua b~d roan
. tinh roan B tu gia thie'tA?
B~d roan xae djnh B tU A tren m~ng (0, M, F) dU<;Ievie't duoi
d~ng A~B.
Dlnh nghia 4.2: neu khai ni~m Wi giai eua b~liroan A~B.
4.2 Cac thu~it giai
4.2.1 Tinh giai duQc cua bai tmin
Dlnh nghia 4.3: baod6ng A cua A tren m(lng.
M~nh d~ 4.1 neu ten mQt tint ehfft eua bao d6ng.
Dinh Iv 4.1: Tren mQt m~ng cae a6i tu<;lng(0, M, F), bai roan A
~ B Ia giai dlt<;lekhi va chi khi B ~A .
M~nh as 4.2 va 4.3 phat bitSu mOt tinh eha't lien quail de'n ky
hi~u D(A) voi AS;;;;M, va day D = {tJ, t2, , tm}s;;;;F u O.
Dinh I" 4.2. Cho mN m~ng cae d6i tu<;Ing(0, M, F), A va B la
hai t~p con eua M. Ta e6 cae di@usail day la tudng dUdng:
(1) B S;;;;A.
(2) C6 D S;;;; F u a sao eho D ap aU<;letren A va D(A) ~ B.
Thuat toaD 4.1: tlm bao d6ng eua t~p AS;;;;M tren m~ng cae d6i
tu<;lngtinh roan (0, M, F).
4.2.2 Tim IOigiai cua bai toaD
Menh d~ 4.4: Day D c F u a la mQt Wi giai eua bai roan A~B
khi va chi khi D ap dl,1ngdu<;letren A va D(A) ~ B.
Thuat giai 4.2: tlm mi)t Wi giai eho bai roan A ~ B.
4.2.3 Dinh Iy v~ srf phan tich qua trinh giai
Dinh IV 4.3. Cho {tl, t2, , tm} la mi)t Wi giai t6t eho bai roan
A~B tren m~ng (0, M, F). f)~t :
Ao =A, Ai= {tJ, t2, , t,}(A), voi mQi i=l, ,m.
Khi d6 e6 mQt day {Bo,BJ, , Bm-I,Bm}cae t~p con eua M, thoa
cae diSu ki~n sail day:
19

giiii eua con ngu'oi. Du'oi day la mQt s6 heuristic e6 th~ du'<;1esU'
dl,1ng:
(HI) UU tieD sU'dl,1ngcae qui t~e xae djnh d6i tu'Qng va cae
thuQe Hnh eua d6i tu'Qng.
(H2) Chuy~n d6i d6i tu'Qng (nMn d~ng d6i tu'Qng thuQe khai
ni~m mue eao hdn) sang khai ni~m mue eao hdn trong
bi~u d6 phan ca'p cae khai ni~ljll.
(H3) SU'dl,JOgcae qui t~e phat sinh d6i tu'<;1ngmoi d~ lien k€t cae
y€u t6 tren mc;tngcae d6i tu'<;1ng.
(H4) Khi phat sinh d6i tu'<;1ngthl u'utieD t~o ra d6i tu'Qnge6 lien
quail d6n cae d0i tlf<;lngdang e6 nhfllia lien quail d€n cae
sl,[ki9n 1111,Ielicu.
(H5) Uu tieD sU'dl,JOglu~t hay d<;\ngsoy lu~n d~ phcit sinh ra slf
ki~n lien quail d€n cae slf ki~n ml,1etieu.
(H6) N€u khong th~ phat sinh slf ki~n moi hay cae d6i tu'Qng
moi ta e6 thS d~t tham bi€n va giiii cae phu'dng trinh hay
h~ phu'dng trinh. .
(H7) Luon luau e6 slf ki~n moi khi thi€t l~p d6i tu'Qngmoi.
4.4 TIl giac vUi Hnh Dang md rC)ng
Trang ph~n n~y trlnh bay slf mC1rQng khii Dang giai tmin
eua mQt C-Objeet thong qua vi~e b6 sung cae lu~t nQi bQ lien
quail d€n cae d6i tu'<;1ngthi€t l~p tren daub saeh cae d6i tu'Qng
n~n eua tU giae: 4 di~m CJ4 dinh eua tu giae. MQt m<;\ngd6i
tu'<;1ngnQi bQ eGng du'<;1edu'a vao dS lien k€t cae thuQe Hnh eGng
nhu' cae d6i tu'Qnglien quail lrang tu ghk Ky thu~t n~y lam eho
d6i tu'Qng "tU giae" e6 khii Dang xU'ly va giiii quy€t nhi~u bai
toaD hdn so voi phu'dng phap giiii C-Objeet dl1 du'Qe trinh bay
tru'oe day trang ehu'dng 3.
21
Chu'dng5.

<ml,1clieu cua bai loan>
end_goal
5.1.3 Mc)t s6 tho tl,lCchlnh
Ml,1cn§y trlnh bay mOt sO'thu tl,1Cchinh du<;iCvie't trong moi
truong MAPLE d~ giiii loan C-objcc~.
5.1.4 LOi ghH
Ml,1cn~y trlnh bay mOt vi d~lv~ 101ghH cila bal loan uu<;ic
tIm thffy bdi chuang trlnh.
5.2 Chu'dng trlnh ghli tmin hlnh hQc phiing
Ph§n nfty trlnh bay v6 mOt ling dl,1ngcila mo hlnh COKB va
mi,lng cac C-Objcct: package ghli cac bi'ii loan hlnh hQCphhg.
Ky thu~t thie't ke' cac thu~t giiii dil du<;ictrlnh bay trong chuang 3
va chuang 4. Phfln cai d~t cl,1th~ tuang tl! nhu phfln cai d~t
backage giiii loan C-Object. Duai day se lieU len phftn ligon ngu
d~c ta cho bai loan va trlnh bay mQt sO'vi dl,1minh hQa.
5.2.1 Ngon ngii d~c tit bai tmln
Bid toan du<;ickhai bao theo diu truc sau day:
begin_hypothesis
parameters: <cac thalli bie'n>
objects:
<cae 06i tu<;ing> : <ki~u 06i tu<;ing>
facts:
<cac sl! ki~n>
end_hypothesis
23
begin_goal
<ml,lclieu cua bai loan>
end_goal
5.2.2 Cac VIdQ
Vi du 5.3: Cho tam giac din ABC, din t<;tiA, va cho bie't tru'dc

: TAM_GIAC_CAN[A,B,C];
: TAM_GIAC[A,G,E];
: HINH_VUONG[A,E,D,B] i
: HINH_VUONG[A,C,F,G];
24

Trích đoạn KET LU!.N

---