Mo Hinh ONTOLOGY-COKB Va Ung Dung

8/12/2019 Mo Hinh ONTOLOGY-COKB Va Ung Dung

1/49

1

M UVic biu din tri thc ng vai tr ht sc quan trng trong vic khng nh kh

nng gii quyt vn ca mt hc stri thc. hiu r iu ny ta stm hiu mi

quan hgia tri thc lnh vc v biu din tri thc

Tri thc l shiu bit vmt vn no td vhiu bit vy khoa. Tuy nhin

trong thc ttri thc ca hchuyn gia gn lin vi mlnh vc xc nh. Mc h

trca mt hchuyn gia phthuc vo min hot ng ca n. Nhng vi cch t

chc cc tri thc nh thno squyt nh lnh vc hot ng ca chng .Vi cch biu

din hp l ta c thgii quyt vn a vo theo cc c tnh lin quan n tri thc

c

Da vo cch thc con ngi gii quyt vn , cc nh nghin cu xy dng cc

kthut hiu din cc dng tri thc khc nhau trn my tnh. Cc kthut phbin

nht hiu din tri thc.

Logic: dng hiu din tri thc cin nht trong my tnh, vi hai dng phbin l

logic mnh v logic vt. chai kthut ny u dng k hiu thhin tr thc v

cc ton tp ln cc k hiu suy lun Iogic.

Cc lut dn: l cu trc tri thc dng lin kt thng tin bit vi cc thng

tin khc gip a ra cc suy lun, kt lun tnhng thng tin bit.

Mng ngngha: l phng php biu din tri thc dng thtrong nt biu

din i tng v cung hiu din quan hgia cc i tng.

Frames, m l cu trc liu thhin tri thc a dng vkhi nim hay i

tng no .

Cc kthut trn u pht trin ngn ngc ttri thc hiu din tri thc mc

hnh thc .chi quan tm n hnh thc m khng quan tm n ni dung bn trong

ca cch hiu din.


2/49

2

V d: Cho lut Sau: nu tam gic c 3 cnh bng nhau th l tam gic u. Cho 3

im

A, B, C c khong cch ln lt tmt im n hai im cn li bng nhau. Hi

ABC l hnh g?V dny cho ta thy: phi c cc khi nim im, on, tam gic, tam gic u

th mi c thsuy lun c ABC l tam gic u nu khng ta phi bsung mt s

lng ln cc lut. iu ny dn n hn chkhi hiu din cc tri thc phc tp trong h

gii ton tng da trn tr thc v thng l hiu din khng c ththc hin

trn my tnh.V vy cc kthut hiu in trn vn cn hn ch.Vo khong thp nin

1990 cc nh khoa hc xem xt li cch hnh thnh tri thc ca con ngi. Qu trnh

hnh thnh tri thc ca con ngi.

Khi nim> Phn on -> Suy lun

Khi nguyn ca tr thc l khI nim qua v dtrn nu ta c khi nim vim,

on, tam gic, tam gic u th ta c thsuy lun ngay ABC l tam gic u iu ny

n n ssuy lun cc k n gin. Nn nhu cu cn mt hthng nh ngha cc khI

nim hiu c ni dung bn trong ca tng cch hiu din.Ontology l hthng

nh ngha cc khi nim v c pht trin mnh t.

Trn c scc phng php hiu din tri thc bit cng vi vic khc st cc

ontology khc c xut. li ny xy dng mt ontology biu din mt dng

c str thc phc vcho vic thit kc str thc hgii bi tan tng da trn tr

thc. Nhm tin ti tip cng vic chun ho c str thc c th khai thc phc v

cho nhiu ng dng.

V d: hgii ton tng hnh hc phng a trn tr thc, hhi p thng tinhnh hc phng, hqun trcoi stri thc hnh hc phng, u sdung mt ontology).


3/49

3

CHNG 1 :TNG QUAN ONTOLOGY1.1 NH NGHA

Theo trit hc th ontology c nh ngha nh Sau: "ontology l mt siu hnh hc

nghin cu vstn ti v hin thn ca tnhin" [AristoteleS].

Theo tin hc th ontology c nhng nh ngha nh Sau:

Gruber (l993), "Ontology l mt thuyt minh hnh thc, rrng ca mt nhn thc

chung. nh ngha ca ng c phn lm 4 khI nim chnh: m hnh tru tng cahin tng (nhn thc), din at r rng bng ton hc (hnh thc), cc khi nim v

quan hgia chng phi c nh ngha mt cch chnh xc v rrng (rrng), tn

ti mt sng thun ca nhng ngi sdng ontology (chung).

RuSsell & Norving (1995), Ontology l mt m t hnh thc ca cc khi nim v

quan hm c thtn ti trong mt cng ng cth".

1.2 CC THNH PHN CHNH CA ONTOLOGY

1.2.1. Cc khi nimNhng khi nim c tchphn loi nh ngha tp hp cc thuc tnh

hoc tp hp cc thao tc vn c trLmg ca bt cthnh phn no ca khi nim.

V d: trong ontology vhnh hc, tam gic v tgic l 2 khi nim.

1.2.2 quan h (relation)

Ku tng tc gia cc khi nim. V d: khi nim tam gic cn l khi nim conca khi nim tam gic, l khi nim con" l mt quan h.

1.2.3. Hm (function)Cc thao tc thc hin trn ontoIogy. V d: din tch ca tam gic c thc

tnh ton bng cc thuc tnh trong khi nim tam gic nh cc cnh ca tam gic


4/49

4

1.2.4 Tin (axiom)Tin c thphn tch thnh cc lut, cc lut thhin cc tri thc mang tnh

khi qut trn cc khi nim v cc loi skin khc nhau. Mi lut cho ta mt qui tc

suy lun i n mt skin mi tskin no , v vmt cu trc n gm 2 thnh

phn chnh phn githuyt v phn kt lun ca lut. Phn githuyt v phn kt lun

u l cc tp hp skin trn cc i tng nht nh. Nh vy, mt lut r c thc

m hnh di dng:

r: {skl, Skz, ..., sk,,} => {Skl, sk, ..., skm}

V dnu tam gic c 3 cnh bng nhau th tam gic ABC l tam gic u

1. 2.5 Th hin (instance)i din cho nhng phn tring bit ca khi nim hay quan h.

V d: tam gic c k hiu ABC l thhin ca khi nim tam gic.

1.3 Phn loiTheo cch phn loi ca Jom P. Sowa, c 2 loi :

Ontology hnh thc (formaI ontology): l ontology m tcc khi nim mt cch

chi tit n cc tin v nh ngha m khng quan tm n cc m tny c thc hin

ddng trong my tnh hay khng ontology hnh thc thng c xu hng nh, nhng

cc tin v nh ngha thng rt phc tp trong suy lun v tnh ton. Nhng

ontology ny thng do cc nh trit hc thit k.

Ontology thut ng(terminological ontology): l Ontology m tcc khi nim

theo hng tin v nh ngha c pht hiu dng logic hoc trong mt vi ngn ng

hng i tng cho my tnh thc hin vic chuyn i theo ang logic. Dng logicny khng c shn chvvic pht trin cc tin v nh ngha v cho my tnh

thc hin ddng. Cc tin v nh ngha chm tn cc vn m ng dung

quan tm Ontology thut ngln, nhng cc tin v nh ngha thng rt ddng

trong suy lun v tnh ton. Nhng ontology ny thng do cc nh tin hc thit k.


5/49

5

Theo cch phn loi ca D.PenSel, c 7 loi:

KnowIedge Representation ontology: da trn cc cch biu din tr thc truyn

thng.

V dPrame-Ontology.

General/Common ontology: tvng lin quan n mi th, skin, thi gian,

khng gian,

Td Ontology vbng trao i gia meter v inch.

Meta-ontology: nh ngha cc ontology.

Td Registry Ontology, dng qun l cc Ontology khc

Domain ontology: tvng ca cc khi nim trong trong mt phm vi.

Td ontology vl thuyt hoc cc nguyn l c bn ca mt min.

Task ontology: hthng cc tvng ca cc thut nggii quyt cc vn kt

hp lin quan n nhim vm c thcng hoc khng cng phm vi ng dng cth.

Td Ontology vkhoch phn cng nhim v.

Domain-task ontology: task Ontology c sdng li trong mt phm vi ng dng

cth.

Td Ontology vkhoch phn cng nhim vca cc chuyn bay.

Application ontology: cha cc kin thc cn thit ca mt ng dng trong phm vi

ng dng nht nh.

Td Ontology hnh hc.


6/49

6

CHNG 2: ONTOLOGY CHO C S TRI THC CC I TNG TNHTON

2.1 GII THIUHin nay c rt nhiu ontology nhng phn ln u tp trung vo biu din cc

ng dng web nh KAON, Protg, C rt t ontology biu din cc tr thc phc tp

V hin nay hu nh khng c cc ontology hiu din cc tri thc ca ng dng gii

ton da trn tri thc trm hnh COKB ca PTG.TS. Vn Nhn.

2.2 ONTOLOGY COKB-ONT

Mt ontology cho c str thc cc i tng tnh ton (vit tt l ontology COKB-

ONT) l mt hthng gm 6 thnh phn (C, H, R, Funcs, Ops, Rules) trong cc

thnh phn c m tnh sau:

2.2.1 Mt tp hp C cc khi nimMi khi nim c xc nh bng v danh sch cc loi khi nim

c sdng (nu c). c phn lm 3 loi:

Khi nim nn: l khi nim c mc nhin tha nhn. Trong m hnh ny ta chi

tha nhn mt skhi nim: stnhin (natural integer), snguyn (integer), shu ti

(rational), sthc (real), sphc (complex).

Khi nim c bn (cp 0): c cu trc rng hoc mt sthuc tnh c kiu khi nim

nn, cc khi nim ny lm hn cho cc khi nim cp cao hn.

Khi nim cp n (n > 0): c thc thit lp tmt danh sch cc khi nim nn

hoc c bn Trong cu trc m tchi c php xut hin khi nim, quan h, hm, ton

tcp nn hoc {0,.., n-1}. Trong cu trc phi xut hin t nht mt khi nim, quan h,

hm, ton tc cp l n-1.

V d Cc khi nim trong ontology hnh hc phng

Khi nim nn: stnhin, sthcKhi nim c bn: im, ng thng


7/49

7

Khi nim cp 1: on, gcKhi nim cp 2: tam gic, tgicMt khi nim cp n c thc m hnh ni b

(Df, Attrs, lR Facts, Rules)oDf l tp cc skin nh ngha khi nim.oAttrS l tp cc thuc tinh ca khi nim.oP l tp cc quan htnh ton c thc m hnh bi b(Mf, Expf)oExpf1 hiu thc tnh ton.oMf l tp cc thuc tnh c hiu din trong Expf.PactS l tp cc skin hay cc tnh cht vn c ca khi nim

Rules l tp cc lut suy din trn cc skin lin quan n cc thuc tnh cng nhlin quan n bn thn khi nim.

Cu trc bn trong ca mi khi nim cp n gm:

Kiu khi nim.Danh sch cc skin m tkhi nim.Danh sch cc thuc tinh.Quan htrn cu trc thit lp.Tp hp cc iu kin rng buc trn cc thuc tnh.

Tp hp cc tnh cht ni ti lin quan n cc thuc tnh ca khi nim.

Tp hp cc quan hsuy dintnh ton. Cc quan hny thhin cc lut suy din

v cho php ta c thtnh ton mt hay mt sthuc tnh tcc thuc tnh khc ca khi

nim.

Tp hp cc lut suy din trn cc loi skin khc nhau lin quan n cc thuctnh ca cc khi nim hay n bn thn cc khi nim. Mi lut suy din c dng: {cc

skin gi thit} => {cc skin kt lun }.

Cng vi cu trc trn, khi nim cn c trang bcc hnh vi c bn cho vic gii

quyt cc vn suy din v tinh ton trn cc thuc tnh ca khi nim, bn thn khi

nim hay cc khi nim lin quan c thit lp trn nn ca khi nim.


8/49

8

V du : Mt khi nim "tam gic" c hiu din theo m hnh trn sgm c cc

thnh phn nh sau

TAMGIAC[A:DIEM, B:DIEM, C:DIEM]

Df= {THANGHANG[A, B, C]}

- Attrs = {a, b, c, GocA, GocB, GocC, S, p, R, ha, hb, hc, ...}

P = {GOcA + GocB + GocC = Pi, a/Sin(GOcA) =

b/sin(GOcB),b/Sin(GOcB) = c/Sin(GOcC),

a/sin(GOcA) = 2*R, a2 = b +

2*b*c*cos(GocA), ...}

Facts = {}

Rules = {{a = b} =.> {GocA = GocB}, {GocA = GocB}=>{a = b},

{a"2 + N2 + c"2} => {GocA = Pi/2}, ...}

2.2.2 Mt tp hp H cc quan h phn cap trn cc loi khi nim H C x C l hthng phn cp cc khi nim, nu (C1,C2) H th C1 l khi nim

con ca C2 v c2 l khi nim cha ca c1. Cp ca khi nim con c quy c trng

vi cp khi nim cha

Vi d: Cc quan hphn cp trong ontology hnh hc phng.

[TAMGIACVUONGCAN, TAMGIACCAN]

[TAMGIACDEU, TAMGIACCAN]

TAMGIACVUONGCAN

TAMGIACDEU

TAMGIACVUONG TAMGIACCAN

TAMGIAC


9/49

9

[TAMGIACVUONG, TAMGIAC]

[TAMGIACCAN, TAM-GIAC]

2.2.3 Mt tp hp R cc quan h trn cc loi khi nim

Mi quan hc xc nh bi v danh sch cc loi khinim ca quan h. i vi cc quan h2 ngi th quan hc thc cc tnh cht

nh tnh phn x, tnh i xng, tnh phn xng, tnh bc cu

c phn lm 2 loi

Quan hnn l quan hc mc nhin tha nhn. Trong m hnh ny tachtha nhn mt squan htrn stnhin (natural integer), snguyn (integer), s

hu ti (rational), sthc (real), sphc (complex).

Quan hcp n (n>o): mtmi quen hcc khi nim cp {on}.oGm 2 loi:Loi khng m ti c cu trc rng, cc quan hny lm nn cho quan hcng

cp hoc cp cao hn.

Loi m l: c m ta bng tp cc skin v trong cu trc m tchc phpxut hin khi nim, quan h, hm, ton tcp nn hoc {0, .., n}.

Trong m tquan hphi xut hin t nht l mt khi nm, quan h, hm, ton t

cp n.

V d: Cc quan htrong ontology hnh hc phng

Quan hnn: cc quan htrn stnhin, sthcQuan hc bn: quan h3 im thng hng, quan him thuc ng thngQuan hcp 1: quan hsong song gia 2 tia, quan hgia im thuc tiaQuan hcp 2: quan hng dng ca 2 tam gc, quan hbng nhau ca 2 tam

gic

Mt quan hcp n, loi m tc thc m hnh bi b


10/49

10

(C, Df, Facts)

C l tp cc khi nim (quan h).

Df l tp cc skin nh ngha quan h.

PactS l tp cc skin hay cc tnh cht vn c ca quan h

V d: Trong Ontology hnh hc phng, quan hvung gc ca 2 ng thng.

VUONG[a:DUONGTHANG, b:DUONGTHANG]

C = {DUONGTHANG(a), DUONGTHANG(b)}Df= {DIEM(A), DIEM(B), THUOC[A, a],THUOC[A, b], THUOC[B, b],

THUOC[B, a]}

GOC[A, GIAODIEM[a, b], B] = Pi/2}Facts = {VUONG[b, a]}

2.2.4 Mt tp hp Funcs gm cc hmTp hp Funcs trong ontoIogy COKB-ONT thhin tr thc vcc hm hay cc qui

tc tnh ton trn cc loi khi nim. Mi hm c xc nh bi , tp bin,

kiu trvv cc qui tc nh ngha hm vphng din ton hc.

c phn lm 2 loi:

Hm nn: l hm c mc nhin tha nhn. Trong m hnh ta chtha nhn cc

hm trn stnhin (natural integer), snguyn (integer), shu ti (rational), sthc

(real), sphc (compleX).

Hm cp n: m tmi quan hcc khi nim cp {0, .., n}. uc m tbng tpcc skin v trong cu trc m tchc php xut hin khi nim, quan h, hm,

ton tcp nn hoc {0, .., n}. Kt quca hm l khi nim cp nn hoc {0, .., n}.

Trong cu trc m tphi xut hin t nht cc khi nim, quan h, hm, ton tc cp

n.


11/49

11

V d: Cc hm trong ontology hnh hc phng

Hm trn stnhin, sthc

Hm c bn hm xc nh giao im ca 2 ng thng

Hm cp 1 hm xc nh giao im ca 2 on thng, hm xc nh giao im ca 2

tia

Hm cp 2 hm xc nh trng tm ca tam gic, hm xc nh tm ng trn ni

tip tam gic

1 hm cp n c thc m hnh bi b

(C, Df, Facts)

C l tp cc khi nim (quan h, trv).Df l tp cc skin nh ngha hmFacts l tp cc skin hay cc tnh cht vn c ca hm.Vi dTrong ontology hnh hc phng, hm xc nh giao im ca 2 ng thng

GIAODIEM[a:DUONGTHANG, b:DUONGTHANG] :DIEM(X)

C = {DUONGTHANG(a), DUONGTHANG(b), DIEM(X)}Df = {THUOC[X, a], THUOC[X, b]}Facts = {}

2.2.5 Mt tp hp Ops cc ton tCc ton tthhin cc qui tc tnh ton nht nh trn cc hin thuc cc loi khi

nim. Chng hn nh cc php ton tnh ton vector, cc php ton tnh ton ma trn, v

trong trng hp cc php ton 2 ngi th php ton c thc tnh cht nh tnh giao

hon, tnh kt hp,


12/49

12

2.2.6 Mt tp Rules gm cc lut suy dinCc lut suy din c phn ip, chng thhin cc tri thc mang tnh phqut trn

cc khi nim v cc loi skin khc nhau. Mi lut cho ta mt qui tc suy lun i

n cc skin mi tnhng skin no . Mt lut suy din r c thc m hnh

ha di dng:

r:{Skl, sk, ..., sk,, } => {skl, sk, ..., skm}

2.2.6 Shng

t> x bin c kiu khi nim

| a hng

l Funcs[t1, t2, ..., tn] hm

V d

x, 5, cos(X), cos(ln2);

DOAN[A, B], TAMGIAC[A, B, C];

2.2.6.2 Biu thc tnh ton

compexp> Ops[t1, t2, ... tn]

| t1 Ops t2

l Ops[compexpl, compeXp, ..., compexp,,]

l compexp1 Ops compexpz

V d:

X + 3, y + KHOANGCACH[A, d];

X = 3, x = sin(Pi/2)


13/49

13

a^2 = b^2 + c^2, a/sin(GocA) = c/sin(GocC);

2.2. 6.3 Biu thc logic (logic expression)

logiceXp> R[tl, tz, ..., n]

C(t)

Funcs[tl, t, ..., t,,](t)

False

True

logicexp

logicexp1 logicexp2

logicexp1 logicexp2

logicexp1 logicexp2

logicexp1 logicexp2

logicexp1 logicexp2

x ,logicexp

x ,logicexp

V d:

THANGHANG[A, B, C], TUGIAC(tg), GIAODIEM[a, b](X)

((a < 5)V(a=1o))->(X = 9);

x. (TAMGIAC-CAN(X) TAMGIACVUONG(X));

2.2.6.4 Skin


14/49

14

Shng sau khi loi bshng hngBiu thc tnh ton sau khi loai bhiu thc hng v gi trca biu thc tnh ton

phi l kiu boolean.

Biu thc logic.CHNG 3: NGN NG C T ONTOLOGY CHO COKB -ONT

3.1 Gii thiuNgn ngontology thng c dng m tcc khi nim, thuc tnh, quan h

v cc rng buc ca cc khi nim. Ngn ng Ontology n gin (nh ngha cc khi

nim), da trn frame(nh ngha khi nim v thuc tnh), da trn logic

(DAML+OIL),

Cc ngn ngtrn u hn chkhi hiu din cc tri thc phc tp trong hgii ton

tng da trn tr thc v thng l biu din khng c ththc hin trn my

tnh. Qua vn nu trn ti xy dng mt ngn ngOntology c thhiu din

cc tri thc trong Ontology COKB-ONT.

3.2 ngn ng c t cho COKB-ONTL ngn ng dng m tcho ontology COKB-ONT. Cu trc c minh ho

di hnh

Ngn Ngc tCOCB-ONT

Cc thnh phn

ca m hnh

Tun ththeo

cc quy nh


15/49

15

3.2.1 Cc tokenCc k tkt hp vi nhau to thnh cc token bao gm :Tkha , s,ton t,

lng t,tn chui hm nn

3.2.1.1 Tkha

Tkha Mc ch

Concept Khai bo khi nim

Relation Khai bo quan h

Operator Khai bo ton t

Function Khai bo hm

Rule Khai bo lut

Define nh ngha cc thnh phn cha n

Property Khai bo thuc tnh

Constraint Khai bo rang buc trn cc thuc

tnh

Fact Khai bo skin

Computation_relation Khai bo quan htnh ton

Cc ngn ng

Maple ,description logic

Ngngha v suy

lun


16/49

16

Mf ,expf M tcc thuc tnh v biu thc tnh

ton ca quan htnh ton

Kind rule ,hypothesis, goal Kiu , githuyt, kt lun ca lut

Return Khi nim trvca hm

Collection Khai bo kiu khi nim mi thong

qua cc khi nim lit k

End Kt thc cu trc

Constant Khai bo hng

As i tn mt khi nim

Name Tn cu trc

Count m kt qutrvca mt cu truy

vn

3.2.2.2 S

Natural (stnhin)

Interger (sNguyn)

Rational (shu ti)

Real (sthc)

Boolean (logic)

Complex (sphc)


17/49

17

Cc kiu khi nim strn c xem nh l tp khi nim nn trong ontoylogy

COCB-ONT

3.2.2.3 Ton t

Ton t ngha

+ Cng

- Tr

* Nhn

/ Chia

^ M

, Tch biu thc

. Truy cp thnh phn

: Khai bo biu

:: Min

< Nhhn

Ln hn

>= Ln hn hoc bng

Khc

And Php ton and ca logic

Or Php ton or ca logic


18/49

18

Implies Php ko theo ca logic

Equivalent Php ton tng ng ca logic

Union Php ton hi

Minus Php ton tr

Interect Php ton giao

In Php ton thuc

Subset Tp con

3.2.2.4 Lng t

Lng t ngha

Exists Php ton tn tai ca logic

Forall Php ton vi mi ca logic

3.2.4 Khi nim (concept)y l kiu liu chnh ca ngn ngc tCOKB-ONT tun thcht ch

ontology COKB-ONT. Ngoi kiu khi nim nn (s) cn c thnh ngha cc khi

nim c bn v cp n thng qua tkho concept, collection

Kiu khi nim lit k (collection concept)

Kiu khi nim lit k l kiu khi nim c to thnh tnhiu khi nim. i

tng c khai bo kiu khi nim ny c kiu l mt trong cc khi nim thuc tp

khi nim c lit k.

Collection {dy kiu khi nim};


19/49

19

+ ;

+ {dy kiu khi nim} khng cn phi khai bo

V dTrong mt ontology hnh hc phng, tin xl cho cc i tng c cc

kiu khai nim tng tnhau. Ngi ta khai bo cc kiu khi nim lit k TIADOAN,

DTTIADOAN da trn cc kiu khi nim DUONGTHANG,TIA, DOAN

collection TIADOAN {TIA, DOAN};

collection DTTIADOAN {DUONGTHANG, TIA, DOAN};

xc nh bin thuc kiu khi nim

cp u ngoc n () dng xc nh mt i tng thuc kiu khi nim.

();

[,


20/49

20

3.2.5 biu thc (expression)Biu thc l thnh phn c bn v l kiu cu quan trng nht ca ngn ngc t

COKB-ONT.Biu thc c phn chia lm 3 loi shng (biu thc c bn), biu thc

tnh ton (computation expression), hiu thc logic (logic expression) c nh ngha

trong phn 2.2.6 trong hiu thc logic c biu din li thng qua cc tkho ca

ngn ngc tCOKB-ONT

V du:

THANGHANG[A, B, C], TUGIAC(tg), GIAODIEM[a, b](X);

(a < 5) of (a = 10))implies(x = 9);

exists (x) (TAMGIACCAN(x) and TAMGIACaVUONG(X));

forall (x) (TAMGIACVUONG(X)

equivalent (X.GocA = Pi/2));

Trong hiu thc c 2 khi nim c quan tm trong shng l hng sv bin

c nh ngha thng qua ngn ngc tCOKB-ONT nh sau

Hng s(constant)

Ngn ngc tCOKB-ONT cha 2 kiu s

S(numeric constant)

V d:1, -2, 0.l4

K hiu (symbolic constant): c khai bo bng tkho constant

C php khai bo bng k hiu

constant

cch sdng


21/49

21

V d: Khai bo mt hng sPi trong ontology hnh hc phng constant Pi 3.l4;

Mt ssymbolic constant mc nh:

True, falSe: mang gi trng sai ca logic

Null: gi trkhng xc nh

Bin (variable)

Khai bo mt bin c kiu khi nim

:;

Khai bo nhiu bin c kiu khi nim

:;

vi d:GocA : GOC[B, A, C];

S, p, r 1 real;

3.2.6 Mt skiu cu trc

3.2.6.1 Dy (Sequence)

Dy l nhm cc hiu thc c cch nhau bi u ,

expression1, expression2, expression3

Vd: 1,2,3

3.2.6.2 Tp hp (set)

Tp hp l dy ca cc hiu thc phn bit (khng phn bit tht) c t trong

{}


22/49

22

Vi d{a = b, SSONG[a, b]}

Tp hp lng tp hp l tp dy cc tp hp khng phn bit thtc t trong

{}

V d{{a, b}, {a,c}, {b, c}}

3.2.6.3 Danh sch (list)

Danh sch l dy ca cc hiu thc (c phn bit tht) c t trong []

V d[A,B,C] , [a,b,c]

3.2.7 Cu (statement)Cu l thnh phn quan trng trong ngn ng c tCOKB-ONT. C cc

kiu cu sau:

Khai bo bin

Cu lnh retum

Biu thc logic

Biu thc tnh ton

3.2.8 Mt s c php khai bo cc thnh phn ca ontology COKB-ONT3.2.8.1 khi nim ktha (C,H)

Kiu khi nim c bn (cp 0)

concept ;

Kiu khi nim cp n

Rng buc: trong cu trc m tchc php xut hin khi nim, quan h, hm

cp {0, n-1}.


23/49

23

concept [

:,

:,

:][:

[ , ..., ],

[, , ],

[, , ]]{

Define:

c php cc skin trn cc bin

Property:

cc thuc tnh c khai bo bi cc kiu khi nim nn, khi nim cbn, khinim cp n (nu c sdng bin th chi c php sdng cc bin ca khi nim khai

bo);

Constraint:

c php cc constraint lin quan n cc bin v thuc tnh ca khi nim;

Fact :

c php fact lin quan n cc bin v thuc tnh ca khi nim;

computationrelation:

c php cc computationrelation lin quan n cc bin v thuc tnh ca khi

nim


24/49

24

RuIe:

C php cc rule lin quan n cc bin v thuc tnh ca khi nim;

}

Quy c: tn cc property, conStraint, computation,rule trong mt khi nim khng

trng nhau

Sdng

[, , ]

v dkhai bo cc khi nim c bn im v ng thng ,khi nim cp 2 hnh

thang trong ontology hnh hc phng.

concept DIEM;

concept DUONG_THANG;

concept HINH_THANG[A:DIEM, B:DIEM, C:DIEM, D:DIEM]:

begin_object:TUGIAC[A, B, C, D]{

define:

SSONG[a, c];

property:

h : DOAN;

constraint:

fact:


25/49

25

GocA = PiGocD;

GocB = PiGocC;

TRUNG[h, DOAN[A, HINHCHIEU[A, DUONGTHANG[C, D]]]]

computationrelation:

CR1 {

mf = {S, a, c, h}

expf = "S = (a+c)*h/2";

}

rule:

end_object

3.2.8.2 Quan h(R)

Quan hkhng m t

relation [,

]

Quan hm t

Rng buc: trong cu trc m tchi c php xut hin khi nim, quan h, hm

cp {0, n}.

relation

[:,

:,


26/49

26

:]

{

define:

C php cc skin trn cc bin

Fact:

c php cc fact lin quan n cc bin ca quan h;

}

Qui c: cch khaI bo quan h"" th quan hc i xnh ton

t

S dng

[, , ];

V d: Khai bo quan hcp 1 loi khng m tvim thuc ng thng, quan

hc bn loi m tvssong song ca 2 ng thng trong ontology hnh hc phng.

relation THUOC[DIEM, DOAN]

begin_relation SSONG[a:DUONGTHANG, b:DUONGTHANG]

{

define:

not TRUNG[a, b];

GIAODIEM[a, b] = null;

fact:

SSONG[b, a]


27/49

27

}

relation =[a:DOAN, b:DOAN]

{

define:

a.dd = b.dd;

fact;

b = a;

end_relation

3.2.8.3 Hm (Funcs)

Hm cp n

Rng buc: trong cu trc m tchi c php xut hin khi nim, quan h, hm

cp {0n}. Kt quca mua l khi nim cp {0.., n}

Begin_function [

:,

:< kiu khi nim >,

...,

:< kiu khi nim >] :

{

return

define:


28/49

28

c php cc skin trn cc bin ca hm;

fact:

c php cc fact nn quan n cc bin ca hm;

end_function

Sdng

[, , ];

V d Khai bo hm giao im c bn gia 2 ng thng trong ontology hnh hc

phng.

Begin_function GIAODIEM[a, b]:DIEM

{

a,b : DUONG_THANG;

retum X;

defIne:

THUOC[X, a];

THUOC[X, b];

Fact:

GIAODIEM[b, a](X)

End_function

3.2.8.4 Ton t(ops)

Begin_operator [ :]:


29/49

29

{

return

define:

c php cc hiu thc tnh ton (ph cha 1 quan h) trn cc bin ca ton t\

fact:

c php cc fact lin quan n cc bin ca ton t;

end_operator

Quy c: nu sdng k tc bit tn ton tphi t trong cp u ".

V d: Khai bo ton t"+ sthc gia 2 on, ton tsin ca mt gc trong

ontology hnh hc phng.

operator +[op1 :DOAN, op2:DOAN]:real

{

retum x;

define:

X = op1.dd + op2.dd;

fact:

X = op2 + op1;

}

operator sin[op:GOC]:real

{


30/49

30

Return X;

Define:

X = sin(op.sd);

}

3.2. 8.5 Lut (rules)

rule

{

kind-rule = ";

variable:

khai bo cc bin c kiu khi nim;

Hypothesis:

{dy cc skin githuyt ca lut}goal:

{dy cc skin kt lun ca lut hoc "cOncept"}

}

Vi d: Khai bo lut hnh thnh nn khi nim tgic ABCD tmi quan hgia 5

im A, B, C, D, M trong ontolOgy hnh hc phng.

Rme Rl

{

kind-rule = "taokhainiem";


31/49

31

variale:

A, B, C, D, M : DIEM;

hypothesis:

{ THUOC[M, DOAN[A, C]], THUOC[M, DOAN[B, D]] }

goal:

{ TUGIAC[A, B, C, D] }

}

3.2.8.6 Quan htnh ton (computation relation)

Khai bo bn ngoi khi nim

computationreIation 0>::

{

mf = {dy cc thuc tnh ca cc khi nim};

expf = ;

}

Qui c nu khng chr thuc tnh thuc khi nim no th thuc tnh thuc tt

c cc khi nim.

Khai bo bn trong khi nim (sau tkho computatiOnrelation)

{

mf = {dy cc thuc tnh};

expf = ";


32/49

32

}

Vi d: Php ton tnh v hng ca 2 vector c khai bo di dng hiu thc tnh

ton trong Ontology hnh hc gii tch.

Computation_reIation VECTOR vl, VECTOR v2::GR1

{

mf = {v1.a, vl.b, v2.a, v2.b}

expf = v1 *v2 = v1 .a*v2.a + v1.b*v2.b;

}

3.2.8.7 Rng buc trn cc thuc tnh (constraint)

Khai bo bn ngoi khi nim

constraint 0>::

{

mf = {dy cc thuc tnh ca cc khi nim};

expf = "";

}

Qui c: nu khng chi rthuc tnh thuc khi nim no th thuc tnh thuc tt

ccc khi nim

Khai bo bn trong khi nim (Sau tkho constraint)

{

mf = {dy cc thuc tnh};


33/49

33

expf = ;

}

V d: Rng buc trn thuc tnh S ca khi nim tam gic v tgic trong ontology

hnh hc phng

constraint TAM_GIAC, TU_GIAC::GR1

{

mf = {S}

expf = S > 0";

}

3.2.8.8 Skin (fact)

Skin c nh ngha thng qua shng, biu thc tnh ton v hiu thc logic phn3.2.5.

CHNG IV: ng dng

4.1.Bi ton v t gic

4.1.1. T gic (li) tng qut

V mt tnh ton, chng ta c th xem t gic l mt mng tnh ton (hay mt itng tnh ton) bao gm cc bin ghi nhn gi tr ca cc yu t trong tam gic, v ccquan h l cc cng thc th hin mi lin h tnh ton gia cc yu t .


34/49

34

T gic ABCD.

Tp cc bin thng c xem xt trong t gic gm :

- a, b, c, d : 3 cnh ca tam gic.- A, B, C, D : 4 gc trong ca t gic .- AC, BD : 2 ng cho ca t gic. - S : din tch t gic.- p : chu vi ca t gic.- R : bn knh ngtrn ngoi tip t gic (nu c).- r : bn knh ng trn ni tip t gic (nu c).Cc h thc c bn gia cc yu t ca t gic :

f1: A + B + C + D = 2

f2: p = a+b+c+d

f3: 2.S = a.d.sinA + b.c.sinC

f4: 2.S = a.b.sinB + c.d.sinD

Ghi ch : c th gii t gic c hiu qu hn ta c th t t gic trong mtmng lin h vi 4 tam gic (ABD, CBD, BAC, DAC). K hiu t gic l O1, v k hiu4 tam gic ln lt l O2, O3, O4, O5. Khi mng tnh ton gm 5 i tng O 1, O2, O3,O4, O5c cc quan h sau y :

O2.a = O1.BD


35/49

35

O2.b = O1.d

O2.c = O1.a

O2.= O1.A

O3.a = O1.BD

O3.b = O1.c

O3.c = O1.b

O3.= O1.C

O4.a = O1.AC

O4.b = O1.b

O4.c = O1.a

O4.= O1.B

O5.a = O1.AC

O5.b = O1.c

O5.c = O1.d

O5.= O1.D

O1.A = O4.+ O5.

O1.B = O2.+ O3.

O1.C = O4.+ O5.

O1.D = O2.+ O3.


36/49

36

O1.S = O2.S + O3.S

O1.S = O4.S + O5.S

Ngoi ra ta cn mt cch th hai l t t gic trong mi lin h v 4 tam gicOAB, OBC, OCD, ODA (trong O l giao im ca 2 ng cho).

4.2. Hnh thang, thang cn, thang vung4.2.1. Hnh thang(vi 2 cnh y l AD v BC) l mt t gic c tnh cht sau :

g1: A + B =

g2: C + D =

(hai tnh cht ny thay th cho quan h f1trong t gic)

Hnh thang ABCD.

Ngoi ra trong hnh thang ta cn quan tm n ng cao h a(hnh 2.1). Tt nhinng cao hany trng vi ng cao hbca tam gic ABD, v cng trng vi ngcao hbca tam gic BAC. Do ta c :

g3: S = (b + d).ha/2

Trong mi lin h vi 4 tam gic nh ni nhn xt pha trn ta cn c:O1.ha= O2.hb

O1.ha= O4.hb

4.2.1. Hnh thang cn : l mt hnh thang c thm cc tnh cht :

g4: a = c


37/49

37

g5: B = C

g6: A = D

Hnh thang cn

Hnh thang cn cn c mt vng trn ngoi tip trng vi cc vng trn ngoi tip

ca 4 tam gic (ABD, CBD, BAC, DAC) c lin h vi t gic. T ta c :

O1.R = O2.R

O1.R = O3.R

O1.R = O4.R

O1.R = O5.R

4.2.2. Hnh thang vung : l mt hnh thang c thm cc tnh cht :

g4: A = /2

g5: B = /2

g6: a = ha

Hnh thang vung


38/49

38

Ghi ch :Trong trng hp ny (t gic l hnh thang cn) th trong 4 tam gic linh vi t gic c 2 tam gic vung : tam gic ABD v tam gic BAC.

4.2.3 Hnh bnh hnh

Hnh bnh hnh

Hnh bnh hnh l mt t gic c thm cc tnh cht sau :

g1: a = c

g2: b = d

T tt c cc quan h trong mt t gic bnh thng c th c thay th bi

g3: A = C

g4: B = D

g5: A + B =

g6: C + D =

g7: p = 2.(a+b)

g8: S = a.b.sinA

g9: S = a.b.sinB

Ghi ch: Trong lin kt t gic (k hiu O1) vi 4 tam gic tng ng (k hiu O2,O3, O4, O5), th i vi hnh bnh hnh ta cn c cc quan h sau y :

O2.ma = O1.AC / 2 // trung tuyn tam gic ABD = na ng cho ACO3.ma = O1.AC / 2 // trung tuyn tam gic CBD = na ng cho AC

O4.ma = O1.BD / 2 // trung tuyn tam gic BAC = na ng cho BD

O5.ma = O1.BD / 2 // trung tuyn tam gic DAC = na ng cho BD


39/49

39

4.2.4 Hnh thoi

Hnh thoi

Hnh thoi l mt t gic c 4 cnh bng nhau. T , Tt c cc quan h gia ccyu t trong mt t gic bnh thng s c thay th bi cc quan h sau y :

f1: a = b

f2: b = c

f3: c = d

f4: d = a

f5: A = C

f6: B = D

f7: A + B =

f8: C + D =

f9: S = a2.sinA

f10: S = a2.sinB

f11: S = a2.sinC


40/49

40

f12: S = a2.sinD

f13: S = AC.BD / 2

f14: p = 4.a

Ngoi ra, 4 tam gic lin kt vi hnh thoi u l tam gic cn v ta cng c ccquan h tng t nh i hnh bnh hnh :

O2.ma = O1.AC / 2 // trung tuyn tam gic ABD = na ng cho AC

O3.ma = O1.AC / 2 // trung tuyn tam gic CBD = na ng cho AC

O4.ma = O1.BD / 2 // trung tuyn tam gic BAC = na ng cho BD

O5.ma = O1.BD / 2 // trung tuyn tam gic DAC = na ng cho BD

Hnh thoi cn c mt vng trn ni tip v mt ng cao. Gi bn knh vng trnni tip l r, ng cao l h, ta c cc h thc :

f15: h = 2.r

f16: S = a.h

4.2.5 Hnh ch nht

Hnh ch nht

Hnh ch nht l mt t gic c 3 gc vung. T , Tt c cc quan h gia ccyu t trong mt t gic bnh thng s c thay th bi cc quan h sau y :

f1: A = / 2


41/49

41

f2: B = / 2

f3: C = / 2

f4: D = / 2

f5: a = c

f6: b = d

f7: AC = BD

f8: AC2= a2+ b2

f9: S = a.b

f10: p = 2.(a+b)

4.2.6 Hnh vungHnh vung l mt t gic c y cc tnh cht ca hnh thoi v hnh ch nht.

Nh vy, trong hnh vvung ta ch cn c cc quan h sau y:

f1: A = / 2

f2: B = / 2

f3: C = / 2

f4: D = / 2

f5: c = a

f6: b = a

f7: d = a

f8: AC = a 2

f9: BD = a 2

f10: S = a2

f11: p = 4.a

4.3 Cc lut bin i


42/49

42

Gia cc i tng hnh hc trnh by trn c mt s lut bin i m ta c th pdng trong qu trnh tnh ton.

4.4Mt s lut lin quan n t gicL1: Mt t gic c th c bin i thnh mt mng gm t gic v 4 tam

gic.

L2: Mt t gic c hai gc k mt cnh (hay gc lin tip) b nhau l mt hnh

thang.

L3: Mt hnh thang c hai cnh bn bng nhau l mt hnh thang cn.

L4: Mt hnh thang c hai gc k mt cnh y bng nhau l mt hnh thang

cn.

L5: Mt hnh thang c mt gc vung l mt hnh thang vung.

L6: Mt t gic c cc cnh i din bng nhau tng i mt l mt hnh bnh

hnh.

L7: Mt t gic c cc gc i din bng nhau tng i mt l mt hnh bnh

hnh.

L8: Mt t gic c 4 cnh bng nhau l mt hnh thoi.

L9: Mt hnh bnh hnh c hai cnh lin tip bng nhau l mt hnh thoi.L10: Mt hnh bnh hnh c mt gc vung l mt hnh ch nht.

L11: Mt hnh ch nht c hai cnh lin tip bng nhau l mt hnh vung.

L12: Mt hnh thoi c mt gc vung l mt hnh vung.

Mt sbi ton cth

Trong mt t gic ABCD, cho bit 4 cnh AB, BC, CD, DA, v gc A. Hy tnh

din tch S ca t gic.Ta dng O1 ch t gic ABCD (xem nh mt i tng tnh ton). Theo bi

ta c gi thit l : a, b, c, d, A, mc tiu cn tnh ton l : S .

t t gic O1(t gic ABCD) trong mng tnh ton lin h vi 4 i tng tamgic :


43/49

43

O2: tam gic ABD,

O3: tam gic CBD,

O4: tam gic BAC,

O5: tam gic DAC.

Ta c mng tnh ton gm 5 i tng O1, O2, O3, O4, O5. Trong O1ta c 4 quanh O1.f1, O1.f2, O1.f3, O1.f4. V mi lin h gia cc i tng trn ta c cc quan h sauy :

f1: O2.a = O1.BD

f2: O2.b = O1.d

f3: O2.c = O1.a

f4: O2.= O1.A

f5: O3.a = O1.BD

f6: O3.b = O1.c

f7: O3.c = O1.b

f8: O3.= O1.C

f9: O4.a = O1.AC

f10: O4.b = O1.b

f11: O4.c = O1.a

f12: O4.= O1.B

f13: O5.a = O1.AC

f14: O5.b = O1.c

f15: O5.c = O1.d

f16: O5.= O1.D


44/49

44

f17: O1.A = O4.+ O5.

f18: O1.B = O2.+ O3.

f19: O1.C = O4.+ O5.

f20: O1.D = O2.+ O3.

f21: O1.S = O2.S + O3.S

f22: O1.S = O4.S + O5.S

Nh th trong m hnh mng tnh ton cc i tng ca bi ton t ra ta c :

- Tp cc i tng :O = O1, O2, O3, O4, O5.

- Tp cc quan h (gia cc i tng) :F = f1, f2, . . . , f21, f22.- Tp cc bin c xem xt :

M = O1.a, O1.b, O1.c, O1.d, O1.A, O1.B, O1.C, O1.D, O1.S, O1.BD, O1.AC,

O2.a, O2.b, O2.c, O2., O2., O2., O2.S,

O3.a, O3.b, O3.c, O3., O3., O3., O3.S,

O4.a, O4.b, O4.c, O4., O4., O4., O4.S,

O5.a, O5.b, O5.c, O5., O5., O5., O5.S

- Gi thit (tp bin bit): A = O1.a, O1.b, O1.c, O1.d, O1.A - Mc tiu tnh ton (tp bin cn tnh) : B = O1.S Qu trnh xem xt cc quan h tm li gii nh sau :

Gi thit : O1.a, O1.b, O1.c, O1.d, O1.A

- Ln lt th p dng cc quan h gia cc i tng ta tnh c :O2.b, nh p dng f2

O2.c, nh p dng f3


45/49

45

O2., nh p dng f4

O3.b, nh p dng f6

O3.c, nh p dng f7

O4.b, nh p dng f10

O4.c, nh p dng f11

O5.b, nh p dng f14

O5. c, nh p dng f15

- Ln lt xt cc i tng theo th t O1, O2, O3, O4, O5 ta tnh c:O2.a, O2., O2., O2.S, nh p dng O2.

- Li xt cc quan h gia cc i tng ta tnh c :O1.BD, nh p dng f1

O3.a, nh p dng f5

- Li xt cc i tng theo th t O1, O2, O3, O4, O5 ta tnh c :O3., O3., O3., O3.S, nh p dng O3.

- Li xt cc quan h gia cc i tng ta tnh c :O1.C, nh p dng f8

O1.D, nh p dng f20

O1.S, nh p dng f21

- n y ta t c mc tiu cn tnh ton, v c mt li gii nh sau : f2,f3, f4, f6, f7, f10, f11, f14, f15, O2, f1, f5, O3, f8, f20, f21.

- p dng thut ton chng ta rt ra c mt li gii tt nh sau : f2, f3, f4, f6, f7, O2, f1, f5, O3, f21.

- Theo li gii ny, qu trnh tnh ton din tch S ca t gic nh sau : Tnh O2.b, (cnh AD) p dng f2

Tnh O2.c, (cnh AB) p dng f3


46/49

46

Tnh O2., (gc A) p dng f4

Tnh O3.b, (cnh CD) p dng f6

Tnh O3.c, (cnh CB) p dng f7

Tnh O2.a,O2.S, (cnh BD,din tch tam gic ABD) p dng O2

Tnh O1.BD, (ng cho BD ca t gic) p dng f1

Tnh O3.a, (cnh BD ca tam gic CBD) p dng f5

Tnh O3.S, (din tch tam gic CBD) p dng O3

Tnh O1.S, (din tch t gic ACBD) p dng f21.

CHNG V: KT LUNBi thu hoch mn nghin cu mt m hnh ontology cho biu din tri thc v

xy dng ngn ngny lm c scho vic thit kc stri thc v btng truy vn

tri thc .cc hthng ny hot ng da trn tri thc ca con ngi v cho ra kt qu

ging nh cch ngh v cch vit ca con ngi.Thng qua tri thc COKB-ONT ti xy dng tri thc hnh hc phng vtgic

trong hnh hc phng.


47/49

47

TI LIU THAM KHO1. Nhon Do,An ontology for Knowledge Representations and Applications,Proceeding of World Academy of Science, Engineering and Technology

Volum 32, Singaphore, 2008

2. Hong Kim, Phc, Vn Nhn, Gio trnh cc hc stri thc,Nh xut bn, HQG HCM (2011).

3. Vn Nhn,Xy dng htnh ton thng minhxy dng v pht trincc m hnh biu din tri thc cho cc hgii ton tng, Lun n tin s,

HQGHCM (2001 - 2002).


48/49

MC LC

MU ................................................................................................................................................ 1

CHNG 1 :TNG QUAN ONTOLOGY............................................................................................. 3

1.1 NH NGHA ............................................................................................................................... 3

1.2 CC THNH PHN CHNH CA ONTOLOGY........................................................................ 3

1.2.1. Cc khi nim ........................................................................................................................ 3

1.2.2 quan h(relation).................................................................................................................... 3

1.2.3. Hm (function)....................................................................................................................... 3

1.2.4 Tin (axiom)....................................................................................................................... 4

1. 2.5 Thhin (instance)................................................................................................................. 4

1.3 Phn loi.................................................................................................................................... 4

CHNG 2: ONTOLOGY CHO C STRI THC CC I TNG TNH TON.............. .......... 6

2.1 GII THIU ................................................................................................................................. 6

2.2 ONTOLOGY COKB-ONT............................................................................................................ 6

2.2.1 Mt tp hp C cc khi nim................................................................................................... 6

2.2.2 Mt tp hp H cc quan hphn cap trn cc loi khi nim.................................................... 8

2.2.3 Mt tp hp R cc quan htrn cc loi khi nim.................................................................. 9

2.2.4 Mt tp hp Funcs gm cc hm........................................................................................... 102.2.5 Mt tp hp Ops cc ton t.................................................................................................. 11

2.2.6 Mt tp Rules gm cc lut suy din..................................................................................... 12

CHNG 3: NGN NGC TONTOLOGY CHO COKB-ONT........................ ......................... 14

3.1 Gii thiu .................................................................................................................................... 14

3.2 ngn ngc tcho COKB-ONT................................................................................................ 14

3.2.1 Cc token.............................................................................................................................. 15

3.2.4 Khi nim (concept).............................................................................................................. 18

3.2.5 biu thc (expression)............................................................................................................... 20

3.2.7 Cu (statement)..................................................................................................................... 22

3.2.8 Mt sc php khai bo cc thnh phn ca ontology COKB-ONT............................... ....... 22

CHNG IV: ng dng....................................................................................................................... 33

4.1. Bi ton vtgic ...................................................................................................................... 33


49/49

4.1.1. Tgic (li) tng qut.......................................................................................................... 33

4.2. Hnh thang, thang cn, thang vung......................... ......................... .......................... ............ 36

4.2.1. Hnh thang cn : l mt hnh thang c thm cc tnh cht :....................... ......................... .... 36

4.2.2. Hnh thang vung : l mt hnh thang c thm cc tnh cht :................................................ 37

4.2.3 Hnh bnh hnh............................................................................................................... 38

4.2.4 Hnh thoi ........................................................................................................................ 39

4.2.5 Hnh chnht................................................................................................................. 40

4.2.6 Hnh vung..................................................................................................................... 41

4.3 Cc lut bin i .................................................................................................................... 41

4.4 Mt slut lin quan n tgic............................................................................................ 42

CHNG V: KT LUN .................................................................................................................... 46

TI LIU THAM KHO ..................................................................................................................... 47

Documents

Mo Hinh ONTOLOGY-COKB Va Ung Dung