Phn II. TRI THC V LP LUN1MC LCTrangLI NI U........................................................................................................6NHP MN............................................................................................................8PHN I GII QUYT VN BNG TM KIMChng 1. CC CHIN THUT TM KIM M..................................161.1. Biu din vn trong khng gian trng thi.......................161.2. Cc chin lc tm kim.......................................................191.3. Cc chin lc tm kim m.................................................221.3.1. Tm kim theo b rng...............................................221.3.2. Tm kim theo su.................................................241.3.3. Cc trng thi lp........................................................251.3.4. Tm kim su lp........................................................261.4. Quy vn v cc vn con. Tm kim trn th v/hoc..........................................................271.4.1. Quy vn v cc vn con....................................271.4.2. th v/hoc............................................................301.4.3. Tm kim trn th v/hoc.....................................34Chng 2. CC CHIN LC TM KIM KINH NGHIM................362.1. Hm nh gi v tm kim thiu kinh nghim.....................362.2. Tm kim tt nht - u tin.................................................372.3. Tm kim leo i..................................................................402.4. Tm kim BEAM..................................................................41Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN2Chng 3. CC CHIN LC TM KIM TI U.............................423.1. Tm ng i ngn nht.......................................................423.1.1. Thut ton A* ..........................................443.1.2. Thut ton tm kim nhnh v cn.......................463.2. Tm i tng tt nht..........................................................483.2.1. Tm kim leo i........................................................493.2.2. Tm kim gradient......................................................503.2.3. Tm kim m phng luyn kim..................................503.3. Tm kim m phng s tin ho. Thut ton di truyn........52Chng 4. TM KIM C I TH......................................................584.1. Cy tr chi v tm kim trn cy tr chi...........................584.2. Chin lc Minimax.............................................................604.3. Phng php ct ct alpha beta.........................................64PHN IITRI THC V LP LUNChng 5. LOGIC MNH .................................................................695.1. Biu din tri thc..................................................................695.2. C php v ng ngha ca logic mnh .............................715.2.1. C php......................................................................715.2.2. Ng ngha...................................................................725.3. Dng chun tc.....................................................................745.3.1. S tng ng ca cc cng thc............................745.3.2. Dng chun tc...........................................................755.3.3. Cc cu Horn..............................................................765.4. Lut suy din........................................................................775.5. Lut phn gii, chng minh bc b bng lut phn gii.......80Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN3Chng 6. LOGIC V T CP MT......................................................846.1. C php v ng ngha ca logic v t cp mt.....................856.1.1. C php......................................................................856.1.2. Ng ngha...................................................................876.2. Chun ho cc cng thc......................................................906.3. Cc lut suy din..................................................................926.4. Thut ton hp nht..............................................................956.5. Chng minh bng lut phn gii...........................................986.6. Cc chin lc phn gii...................................................... 1036.6.1. Chin lc phn gii theo b rng.............................1056.6.2. Chin lc phn gii s dng tp h tr....................1066.6.3. Chin lc tuyn tnh.................................................1076.7. S dng logic v t cp mt biu din tri thc................1076.7.1. V t bng...................................................................1086.7.2. Danh sch v cc php ton trn danh sch...............1086.8. Xy dng c s tri thc........................................................1136.9. Ci t c s tri thc.............................................................1156.9.1. Ci t cc hng thc v cc cu phn t...................1166.9.2. Ci t c s tri thc..................................................119Chng 7. BIU DIN TRI THC BI CC LUT 122V LP LUN........................................................................................1227.1. Biu din tri thc bi cc lut nu th................................1227.2. Lp lun tin v lp lun li trong cc h da trn lut........1247.2.1. Lp lun tin...............................................................1257.2.2. Lp lun li.................................................................1287.2.3. Lp lun li nh tm kim trn th v/hoc...........1307.3. Th tc lp lun tin.............................................................1327.3.1. Th tc For_chain......................................................1337.3.2. Th tc rete.................................................................136Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN47.3.3. H hnh ng da trn lut........................................1437.4. Th tc lp lun li............................................................... 1477.5. Biu din tri thc khng chc chn......................................1517.6. H lp trnh logic..................................................................1537.7. H chuyn gia.......................................................................157Chng 8. LOGIC KHNG N IU.................................................1598.1. Lp lun c th xem xt li v logic khng n iu...........1598.2. c im ca logic khng n iu.....................................1618.3. Logic mc nh.....................................................................1638.4. Gi thit th gii ng..........................................................1678.5. B sung v t.........................................................................1698.6. Hn ch phm vi...................................................................171Chng 9. LI NG NGHA V H KHUNG...................................1749.1. Ngn ng m t khi nim...................................................1749.2. Li ng ngha.....................................................................1769.3. Khung...................................................................................181Chng 10. TRI THC KHNG CHC CHN....................................18610.1. Khng chc chn v biu din..............................................18710.2. Mt s khi nim c bn ca l thuyt xc sut...................18910.3. Mng xc sut.......................................................................19710.3.1. nh ngha mng xc sut..........................................19810.3.2. Vn lp lun trong mng xc sut.........................20010.3.3. Kh nng biu din ca mng xc sut......................20110.3.4. S c lp ca cc bin trong mng xc sut.............20410.4. Suy din trong mng c cu trc cy....................................20510.5. Mng kt ni n..................................................................21210.6. Suy din trong mng a kt ni............................................22010.6.1. Suy din trong mng a kt ni..................................220Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN510.6.2. Bin i mng a kt ni thnh mng kt ni n.....22110.6.3. Phng php m phng ngu nhin...........................22310.7. L thuyt quyt nh.............................................................228Chng 11. LOGIC M V LP LUN XP X.................................23411.1. Tp m..................................................................................23511.1.1. Khi nim tp m.......................................................23511.1.2. Mt s khi nim c bn lin quan n tp m.........23911.1.3. Tnh m v tnh ngu nhin.......................................24211.1.4. Xc nh cc hm thuc.............................................24311.2. Cc php ton trn tp m....................................................24811.2.1. Cc php ton chun trn tp m...............................24811.2.2. Cc php ton khc trn tp m.................................25011.3. Quan h m v nguyn l m rng......................................25511.3.1. Quan h m................................................................25511.3.2. Hp thnh ca cc quan h m..................................25611.3.3. Nguyn l m rng.....................................................25811.4. Logic m...............................................................................25911.4.1. Bin ngn ng v mnh m..................................25911.4.2. Cc mnh hp thnh..............................................26211.4.3. Ko theo m - Lut if-then m...................................26411.4.4. Lut Modulus Ponens tng qut..............................26711.5. H m...................................................................................27011.5.1. Kin trc ca h m...................................................27111.5.2. C s lut m.............................................................27211.5.3. B suy din m...........................................................27311.5.4. M ho.......................................................................27511.5.5. Kh m.......................................................................27711.5.6. H m l h tnh xp x vn nng...............................278TI LIU THAM KHO..............................................................279Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN6LI NI UTr tunhnto(TTNT) lmt lnhvccakhoahcmytnh, nghincusthit kcacctcnhnthngminh( Computationalintelligence is the studi of the degn of intelligens). Cc p dng ca TTNT rt a dng v phong ph, hin nay c nhiu h thng minh ra i: cc h chuyn gia, cc h iu khin t ng, cc robot, cc h dch t ng cc ngn ng t nhin , cc h nhn dng, cc chng trnh chi c, K thut ca TTNT c s dng trong vic xy dng cc h mm, nhm to ra cc h mm mang yu t thng minh, linh hot v tin dng. nc ta, trong nhng nm gn y, TTNT c a vo chng trnh ging dy cho sinh vin cc nm cui ngnh Tin hc v Cng ngh thng tin. Cun sch ny c hnh thnh trn c s gio trnh TTNT m chng ti ging dy cho sinh vin v cc lp cao hc ngnh Tin hc v ngnh Cng ngh thng tin trong cc nm hc t 1997 ti nay, ti khoa Cng ngh thng tin, i hc Khoa hc t nhin, nay l khoa Cng ngh, i hc Quc gia H ni.Cunschnycvit nhmt cunnhpmnvTTNT, i tng phc v ch yu ca n l sinh vin cc ngnh Tin hc v Cng ngh thng tin. Ni dung cun sch gm hai phn: Phn 1: Gii quyt vn bng tm kim. Trong phn ny, chng ti trnh by cc phng php biu din cc vn v cc k thut tm kim. cc k thut tm kim, c bit l tm kim kinh nghim ( heuristic serch), c s dng thng xuyn trong nhiu lnh vc nghin cu ca TTNT. Phn 2:Biu din tri thc v lp lun. Phn ny cp n cc ngn ng biu din tri thc, c bit l cc logic v cc phng php lun trong mi ngn ng biu din tri thc. Cc k thut biu din tri thc v lp lun ng vai tr quan trng trong vic thit k cc h thng minh.Tuynhinvimongmuncunschnycthdnglmtiliu tham kho cho mt phm vi rng ri cc c gi, chng ti c gng trnh by mt cch h thng cc khi nim v cc k thut c bn ca TTNT, nhm gip cho c gi c c s i vonghin cu cc lnh vc chuyn su ca TTNT, chng hn nh lp k hoch (planning),hc my(machine learning), Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN7nhnmy(computer viison), hiungnngtnhin(natural language understanding).Haingnngthaotckhiucsdngnhiutronglptrnh TTNT l Lisp v Prolog. Trong cc sch vit v TTNT cc nm gn y, mt s tc gi, chng hn trong [5] v [7] , s dng common Lisp m t thut ton. Trong 20, cc tc gi li s dng Prolog biu din thut ton. nc ta, cc ngn ng Lisp v Prolog c t ngi bit n, v vy chng ti biu din cc thut ton trong sch ny theo cch truyn thng. Tc l chng ti s dng cc cu trc iu khin ( tun t, iu kin, lp) m mi ngi quen bit. c bit, chng ti s dng cu trc loop do biu din rng, c thc hin lp. Ton t exit thot khi vng lp, cn ton t stop dng s thc hin thut ton, cc bn c th la chn mt trong cc ngn ng sau s dng: Common Lisp, Scheme, Prolog, Smalltalk, C** hoc ML (xem [28]).Chngti xinchnthnhcmngiosNguynVnHiu, ch nhim khoa Cng ngh, i hc Quc gia H ni to iu kin thun li cho chng ti vit cun sch ny.Cunschchcchnkhngtrnhkhinhngthiust. Chngti mong nhn c s gp ca c gi. Th gp xin gi v B mn Khoa Hc My Tnh, Khoa Cng Ngh, i Hc Quc Gia H Ni.Tc giClick to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN8NHP MNTR TU NHN TO L G?Thut ngtr tu nhn to(artificial intelligence) c Jonh McCarthy a ra trong hi tho Dartmouth vo ma h 1956. Trong hi tho ny c mt cc tn tui ni ting nh Marvin Minsky, Claude Shannon, Nathaniel Rochester, Arthur Samuel, Allen Newell v Herbert Simon. Trc hi thony, tnm1952ArthurSamuel vit chngtrnhchi c. Samuel bc b t tng cho rng my tnh ch c th lm c ci m ngi ta bo n lm, v chng trnh ca Samuel c th hc chi tt hn ngi vit ra n. n hi tho ny, Allen Newell v Herbert Simon cng vit chng trnh lp lun vi tn gi the logic theorist. Chng trnh ca cc ng c kh nng chng minh hu ht cc nh l trong chng 2 cun Principia Mathematics ca Russell v Whitehead. Trong hi tho Dartmouth, cc nh nghin cu tho lun v vch ra cc phng hng nghincuca lnhvcTr tunhnto(TTNT). V vy, hi tho Dartmouth, ma h nm 1956 c xem l thi im ra i thc s ca lnh vc nghin cu TTNT.Trongccsch vitv TTNT cc nm gny, cc tc gia ra nhiu nh ngha v TTNT. Chng ti dn ra y mt s nh ngha: S nghin cu cc nng lc tr tu thng qua vic s dng cc m hnh tnh ton ( Thestudymental faculties throughthe use computational models Charniak and McDormott, 1985) Ngh thut to ra cc my thc hin cc chc nng i hi s thng minh khi c thc hinbi conngi (The art of creatingmachies that performfunctionsthat requireintelligencewhenperformedbypeople Kurzweil. 1990). Lnh vc nghin cu tm cch gii quyt v m phng cc hnh vi thng minh trong thut ng cc qu trnh tnh ton (A field of study that seeks to explain and emulate intelligent behavior in terms of computational processes Schalkoff, 1990). S nghin cu cc tnh ton c th nhn thc, lp lun v hnh ng (The study of computations that make it possible to perceive, reason, and act Winston, 1992).Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN9 Mt nhnh ca khoa hc my tnh lin quan ti s t ng ho cc hnh vi thng minh (The branch of computer science that is concerned with the automation of intelligent behavior Luger and Stubblefield, 1993)Sau y l mt s nh ngha gn y nht: TTNT l s thit k v nghin cu cc chng trnh my tnh ng x mt cch thng minh. Cc chng trnh ny c xy dng thc hin cc hnhvi m khi ngi hoc ngvt chngtaxeml thngminh (Artificial Intelligence is the design and study of computer programs that behave intelligently.These programs are constructed to perform as would a human or an animal whose behvior we consider intelligent Dean, Allen and Aloimonos, 1995). TTNT l s nghin cu cc tc nhn tn ti trong mi trng, nhn thcvhnhng(Artificial Intelligenceisthedesignofagentsthat exists in an environment and act Russell and Norvig, 1995). TTNTlsnghincucthit kcc tcnhnthngminh (Computational Intelligence is the study of the design of Intelligent agents Pulle, Mackworth and Goebel, 1998).Hin nay nhiu nh nghin cu quan nim rng, TTNT l lnh vc nghin cu s nghin cu cc tc nhn thng minh ( intelligent agent ). Tc nhn thng minh l bt c ci g tn ti trong mi trng v hnh ng mt cch thng minh ( Mt cu hi c t ra: hnh ng nh th no th c xem l thng minh?).Mc tiu khoa hc ca TTNT l hiu c bn cht ca cc hnh vi thng minh. mc tiu thc tin, cng ngh ca TTNT l xy dng nn cc h thngminh. Phngphplunnghincuycngtngtnhkhi chng ta nghin cu hiu c cc nguyn l bay, ri thit k nn cc my bit bay (my bay). My bay khng phi l s m phng con chim, song n c kh nng baybay tt hn chim.Mt s ngnh khoa hc khc, chng hn nh Trit hc, Tm l hc cng quan tm nghin cu cc nng lc c xem ca con ngi. Song khc vi Trit hc v Tm l hc, TTNT l mt ngnh ca khoa hc my tnh nghincuslthngtinbngmytnh, doTTNTt ramctiu nghin cu: lm th no th hin c cc hnh vi thng minh bng thut ton, ri nghin cu cc phng php ci t cc chng trnh c th thc hin c cc hnh vi thng minh. Nh vy chng ta cn xy dng cc m hnh tnh ton (Computational modeles phc v cho vic gii thch, m t Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN10cc hnh vi thng minh bng thut ton, tip theo chng ta cn ch ra tnh hiu qu, tnh kh thi ca thut tonthc hin mt nhim v, v a ra cc phng php ci t.TC NHN THNG MINHTc nhn (agent) l bt c ci g hnh ng trong mi trng. cc tc nhn c th l con ngi, con su, con con ch, robot infobot, Mc tiu ca TTNT l nhin cu v thit k cc tc nhn thng minh: cc tc nhn tn ti trong mi trng v hnh ng mt cch thng minh.Tn ti trong mi trng, nn tc nhn thng minh cn c kh nng nhn thc c mi trng. Chng hn, con ngi c th nhn thc c mi trngnhtai, mtvccgicquankhc. nhnthccmi trng cc robot s c trang b cc b cm nhn (sensors), l cc thit b vt l, chng hn camera, cc my o c,Cc tc nhn thng minh cn c cc b tc ng (effectors) a ra cc hnh ng p ng mi trng. Vi con ngi, l chn, tay v cc b phn khc ca thn th. Vi c robot, c th l cc cnh tay robot, Mi trngCc thng tin nTc nhn Cc hnh ng t mi trng thng minhChng ta c th xem tc nhn nh mt hp en, u vo l cc thng tinnhnthctmitrng, uralcchnhngthchngvimi trng, nh trong hnh trn. By gi chng ta xt xem cn phi ci t vo bn trong hp en ci g hnh ng u ra l hpl, thch ng vi cc thng tin u vo.Tc nhn cn c b nh lu gi cc tri thc chung v lnh vc, v mi trng m n c thit k hot ng trong lnh vc . Chng hn, i vi robot li taxi, tri thc v mi trng m robot cn c l cc tri thc v mng li giao thng trong thnh ph, v lut l giao thng, i vi cc h chuyn gia tr gip chn on bnh, cc tri thc cn lu l cc tri thc ca cc bc s v bnh l, v cc phng n iu tr,B nh ca tc nhn cn ghi li cc tri thc mi m tc nhn mi rt ra c trong qu trnh hot ng trong mi trng. Trong nhiu trng hp, n cng cn lu li vt ca cc trng thi ca mi trng , bi v hnh ng thch hp m n Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN11cn a ra khng ch ph thuc vo trng thi hin ti ca mi trng m cn ph thuc vo trng thi ca mi trng trong qu kh.Chng ta cn trang b cho tc nhn mt chng trnh: chng trnh tc nhn (agent program). Chng trnh ny l s m t thut ton kt hp vi cc thng tin v trng thi ca mi trng vi c tri thc c lu cho ra hnh ng thch ng.By gi, chng ta tr li cu hi: cc tc nhn nh th no th c xem l thng minh? bng nh ngha v thng minh ca Turing: th nghim Turing ( Turing test).TH NGHIM TURINGAlan Turing (1950) xc nh cc hnh vi thng minh nh l cc hnh vi trong cc nhim v nhn thc t ti mc c th nh la c con ngi.Sau y l dng tng qut ca th nghim Turing. Mt ngi hi l con ngi ngi mt phng. i tc ca ngi hi l mt my tnh c t mt phng khc, hai bn trao i thng tin vi nhau thng qua cc phngtintruyntinhini. Numytnhcthlmchongi hi tnglm lc ngikhcang nichuyn vimy mnhth mytnh c xem l thng minh.By gi chng ta xt xem, thc hin c c hnh vi c xem l thng minh, cc tc nhn thng minh (TNTM) cn c kh nng g? TNTM cn c kh nng ghi nh v lp lun. n s dng cc tri thc lu tr, v bng lp lun rt ra nhng kt lun p ng nhng cu hi m ngi t ra .Biudintri thcvlplunllnhvcnghincutrungtmca TTNT. Ngi hi c th hi bng ngn ng t nhin, chng hn ting Anh. V vy, TNTM cn c kh nng biu din ngn ng t nhin.Hiu ngn ng t nhin (natural language understanding) l mt lnh vc nghin cu quan trng ca TTNT. Ngi hi c th a ra mt s hon cnh v cc hnh ng cn tin hnh tng ng vi mi hon cnh , ri a ra mt hon cnh mi v hi tc nhn cn phi lm g trong hon cnh . tr li c cu hi ny, Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN12TNTM cn c kh nng hc c th a ra hnh ng thch ng vi hon cnh mi.Hc my (machine learning) l mt lnh vc nghin cu ca TTNT ang pht tin mnh m v c nhiu ng dng trong cc lnh vc khc nhau, chng hn trong khm ph tri thc v khai thc d liu. Ngi hi c th a ra mt s hnh nh v cc i tng v kim tra kh nng nhn bit ca cc i tng ca TNTM.Nhn my (computer vision) l lnh vc nghin cu my tnh c th hiu c cu trc v cc tnh cht ca cc i tng trong khng gian ba chiu t cc hnh nh hai chiu. Khi c cho cc nhim v cn thc hin, TNTM cn c kh nng a ra mt dy cc hnh ng m n cn thc hin t c mc ch . Qu trnh ny c gi l lp k hoch.Lp k hoch (planning) l mt lnh vc nghin cu quan trng ca TTNT.BIU DIN V LP LUNKhi gp mt vn cn gii quyt, mt nhim v cn thc hin, iu u tin chng ta phi lm l cn phi biu din vn , cn phi xc nh ci g to thnh li gii (nghim) ca vn , v sau mi i tm thut ton tnh nghim. Cn lu rng, biu din vn ng vai tr quan trng trong vic gii quyt mt vn . Trong nhiu trng hp, khi chng ta chn c cch biu din thch hp cho mt vn th vn hu nh c gii quyt. Chng ta c th biu din nhiu vn bng cch xc nh trng thi ch cn t ti v cc hnh ng lm bin i cc trng thi ca th gii. Khi vic tm nghim ca vn c quy v vic tm kim mt dy cc hnh ng dn ti trng thi ch. Ch rng, tm kim ng vai tr quan trng trong vic gii quyt vn v trong nhiu lnh vc nghin cu ca TTNT, chng hn nh trong hc my v lp k hoch. V vy, phn I ca sch ny dnh cho vic trnh by phng php biu din vn trong khng gian trng thi v nghin cu cc chin lc tm kim.Thc t cho thy rng, thc hin c cc nhim v kh khn v phc tp, con ngi cn s dng mt khi lng ln tri thc v lnh vc lin quan. Mt cu hi c t ra: tri thc l g? Mt cch khng hnh thc, chngtahiutri thclthngtinlinquantimtitng, mt hon cnh, mt lnh vc. my tnh c th lu tr c tri thc, s dng c tri thc, chng ta cn tm cc phng php biu din tri thc.Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN13Lp lun t ng c hiu l qu trnh tnh ton trn cc biu din tri thc, m khi cho u vo l cc biu din tri thc, chng ta nhn c cc u ra l cc biu din tri thc mi. Mc tiu trung tm ca TTNT l nghin cu thit k cc h thng minh, n lu tr tri thc v lnh vc v c kh nng a ra hnh ng thch ng bng lp lun da tren cc tri thc lu tr v cc thng tin thu nhn t mi trng. Do , vn trung tm m chng ta cp n trong sch ny l vn biu din tri thc v lp lun. Chng ta s nghin cu cc m hnh biu din tri thc khc nhau v cc phng php lp lun trong mi m hnh .CC P DNGCc p dng ca TTNT l rt a dng: cc h iu khin t ng cc qu trnh sn xut cng nghip; cc robot lm vic trong cc mi trng c bit, chng hn cc robot thm him cc hnh tinh; cc robot lm vic trong cc iu kin nguy him n tnh mng con ngi; cc h chuyn gia trong cc lnh vc; cc h dch t ng; cc h nhn dng; cc infobot lm vic trong mi trng thun tu thng tin; cc chng trnh chi c,Sau y chng ta s trnh by vi cch p dng. Qua cc v d ny, chng ta mun ch ra nhng vn cn gii quyt khi chng ta nh xy dng mt h thng minh. Robot a thGi s chng ta mun thit k mt robot phn pht th, cc gi nh v phc v c ph trong to nh lm vic ca mt cng ty. ng nhin l robot phi c trang bcc b cm nhn c th nhn v nghe, chng hn video camera, cc thit b thu thanh,N cn c cc b phnthc hin hnh ng, chng hn bnh xe chuyn ng, cnh tay nht ln, t xung cc vt,Cc thng tin n t mi trng y l cc hnh nh v m thanh, m robot thu c nh cc b cm nhn. Khi nhn c mnh lnh, chng hn mang c ph cho gim c, n phi a ra mt dy hnh ng p ng mi trng nhm t c mc ch: c c ph cho gim c.Cc tri thc m robot cn bit trc v c lu trong c s tri thc ca robot l cu trc ca to nh: Gm c my tng, cc phng trong mi tng v hnh lang c b tr ra sao, thang my u; cc i tng m robot c th gp trong to nh, ai lm vic u, c ph phng no, C s tri thc ca robot cn c th cha cc tri thc cho bit cc hon cnh m robot Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN14thng gp v cc hnh ng m robot cn thc hin cch thch hp sao cho thun tin cho vic lu tr, tm kim v suy din.T cc thng tin hnh nh, robot cn c kh nng hiu c cc i tng m n gp c th suy ra cc hnh ng thch hp cn thc hin.Robot cn c kh nng hiu c cc mnh lnh bng ngn ng t nhin, t suy ra cc mc ch m n cn t ti.Khi c nhiu mc ch cn t ti, robot cn c kh nng lp k hoch t c cc mc ch .Robot cn c kh nng tm ng i ( ti u nht ) gia cc v tr trong to nh, t cc thng tin v s b tr v chc nng ca cc phng v cc b phn trong to nh.Chng ta cng cn trang b cho robot c kh nng hc c th rt kinh nghim, khi qut ho t thc tin trong qu trnh phc v, v do , khi gp cc hon cnh mi n c th a ra cc hnh ng thch hp. H chuyn gia trong y hcCc h chuyn gia y hc c mc ch tr gip cc bc s trong chn on bnh v iu tr. Mi trng ca cc h chuyn gia ny l ngi bnh. Cc thng tin n t mi trng l cc triu chng ca ngi bnh, cc kt qu xt nghim t ngi bnh.C s tri thc ca cc h chuyn gia ny l cc tri thc ca cc bc s v bnh l, cc tri thc ny thng c biu din di dng cc lutif-then. Chng hn, Feigenbaur v Shortiffe pht trin h MYCIN chn on bnh nhim trng mu. C s lut ca h MYCIN cha khong 450 lut, mi lut gn vi mt mc chc chn ( iu ny ph hp vi tnh cht ca cc kt lun y hc ). H MYCIN c kh nng lm vic tt nh cc bc s gii trong lnh vc.Cc h chuyn gia ny c kh nng suy din t cc triu chng, cc kt qu xt nghim ngi bnh v s dng cc lut trong c s lut suy ra cc kt lun v bnh. N cng c kh nng gi cn kim tra ci g, cn xt nghim ci g ngi bnh. Cng nh cc bc s, cc h chuyn gia ny c kh nng gii thch cc kt lun m n a ra, n c th cho chng ta bit ti sao n i n kt lun nh th.Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN15PHN IGII QUYT VN BNG TM KIMVn tm kim, mt cch tng qut, c th hiu l tm mt i tng tha mn mt s i hi no , trong mt tp hp rng ln cc i tng. Chng ta c th k ra rt nhiu vn m vic gii quyt n c quy v vn tm kim.Cc tr chi, chng hn c vua, c car c th xem nh vn tm kim. Trong s rt nhiu nc i c php thc hin, ta phi tm ra cc nc i dn ti tnh th kt cuc m ta l ngi thng.Chng minh nh l cng c th xem nh vn tm kim. Cho mt tp cc tin v cc lut suy din, trong trng hp ny mc tiu ca ta l tm ra mt chng minh (mt dy cc lut suy din c p dng) a n cng thc m ta cn chng minh.TrongcclnhvcnghincucaTr TuNhnTo,chngta thng xuyn phi i u vi vn tm kim. c bit trong lp k hoch v hc my, tm kim ng vai tr quan trng.Trong phn ny chng ta s nghin cu cc k thut tm kim c bn c p dng gii quyt cc vn v c p dng rng ri trong cc lnh vc nghin cu khc ca Tr Tu Nhn To. Chng ta ln lt nghin cu cc k thut sau: Cc k thut tm kim m, trong chng ta khng c hiu bit g v cc i tng hng dn tm kim m ch n thun l xem xt theomt hthngnott ccci tngpht hinrai tng cn tm. Cckthut tmkimkinhnghim(tmkimheuristic) trong chng ta da vo kinh nghim v s hiu bit ca chng ta v vn cn gii quyt xy dng nn hm nh gi hng dn s tm kim. Cc k thut tm kim ti u. Cc phng php tm kim c i th, tc l cc chin lc tm kim nc i trong cc tr chi hai ngi, chng hn c vua, c tng, c car.Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN16CHNG 1CC CHIN LC TM KIM MTrong chng ny, chng ta s nghin cu cc chin lc tm kim m (blind search): tm kim theo b rng (breadth-first search) v tm kim theo su (depth-first search). Hiu qu ca cc phng php tm kim ny cng s c nh gi.1.1 . BIU DIN VN TRONG KHNG GIAN TRNG THIMt khi chng ta mun gii quyt mt vn no bng tm kim, u tin ta phi xc nh khng gian tm kim. Khng gian tm kim bao gm tt c cc i tng m ta cn quan tm tm kim. N c th l khng gian lin tc, chng hn khng gian cc vct thc n chiu; n cng c th l khng gian cc i tng ri rc.Trong mc ny ta s xt vic biu din mt vn trong khng gian trng thi sao cho vic gii quyt vn c quy v vic tm kim trong khng gian trng thi.Mt phm vi rng ln cc vn , c bit cc cu , cc tr chi, c th m t bng cch s dng khi nim trng thi v ton t (php bin i trng thi). Chng hn, mt khch du lch c trong tay bn mng li giao thng ni cc thnh ph trong mt vng lnh th (hnh 1.1), du khch ang thnh ph A v anh ta mun tm ng i ti thm thnh ph B. Trong bi ton ny, cc thnh ph c trong bn l cc trng thi, thnh ph A l trng thi ban u, B l trng thi kt thc. Khi ang mt thnh ph, chng hn thnh ph D anh ta c th i theo cc con ng ti cc thnh ph C, F v G. Cc con ng ni cc thnh ph s c biu din bi cc ton t. Mt ton t bin i mt trng thi thnh mt trng thi khc. Chng hn, trng thi D s c ba ton t dn trng thi D ti cc trng thi C, F v G. Vn ca du khch by gi s l tm mt dy ton t a trng thi ban u A ti trng thi kt thc B.Mt v d khc, trong tr chi c vua, mi cch b tr cc qun trn bn c l mt trng thi. Trng thi ban u l s sp xp cc qun lc bt u cuc chi. Mi nc i hp l l mt ton t, n bin i mt cnh hung trn bn c thnh mt cnh hung khc.Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN17Nh vy mun biu din mt vn trong khng gian trng thi, ta cn xc nh cc yu t sau: Trng thi ban u. Mt tp hp cc ton t. Trong mi ton t m t mt hnh ng hoc mt php bin i c th a mt trng thi ti mt trng thi khc.Tp hp tt c cc trng thi c th t ti t trng thi ban u bng cch p dng mt dy ton t, lp thnh khng gian trng thi ca vn .Taskhiukhnggiantrngthi lU, trngthi banulu0 (u0U). Mi ton t R c th xem nh mt nh x R: UU. Ni chung R l mt nh x khng xc nh khp ni trn U. Mt tp hp T cc trng thi kt thc (trng thi ch). T l tp con ca khng gian U. Trong vn ca du khch trn, ch c mt trng thi ch, l thnh ph B. Nhng trong nhiu vn (chng hn cc loi c) c th c nhiu trng thi ch v ta khng th xc nh trc c cc trng thi ch. Ni chung trong phn ln cc vn hay, ta ch c th m t cc trng thi ch l cc trng thi tha mn mt s iu kin no .Khi chng ta biu din mt vn thng qua cc trng thi v cc ton t, th vic tm nghim ca bi ton c quy v vic tm ng i t trng thi ban u ti trng thi ch. (Mt ng i trong khng gian trng thi l mt dy ton t dn mt trng thi ti mt trng thi khc).Chngtacthbiudinkhnggiantrngthi bngth nh hng, trong mi nh ca th tng ng vi mt trng thi. Nu c ton t R bin i trng thi u thnh trng thi v, th c cung gn nhn R i t nh u ti nh v. Khi mt ng i trong khng gian trng thi s l mt ng i trong th ny.Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN18Sau y chng ta s xt mt s v d v cc khng gian trng thi c xy dng cho mt s vn .V d 1: Bi ton 8 s. Chng ta c bng 3x3 v tm qun mang s hiu t 1 n 8 c xp vo tm , cn li mt trng, chng hn nh trong hnh 1.2 bn tri. Trong tr chi ny, bn c th chuyn dch cc qun cch trng ti trng . Vn ca bn l tm ra mt dy cc chuyn dchbinicnhhungbanu(hnh1.2bntri)thnhmtcnh hung xc nh no , chng hn cnh hung trong hnh 1.2 bn phi.Trong bi ton ny, trng thi ban u l cnh hung bn tri hnh 1.2, cn trng thi kt thc bn phi hnh 1.2. Tng ng vi cc quy tc chuyn dch cc qun, ta c bn ton t: up (y qun ln trn), down (y qun xung di), left (y qun sang tri), right (y qun sang phi). R rng l, cc ton t ny ch l cc ton t b phn; chng hn, t trng thi ban u (hnh 1.2 bn tri), ta ch c th p dng cc ton t down, left,right.Trong cc v d trn vic tm ra mt biu din thch hp m t cc trng thi ca vn l kh d dng v t nhin. Song trong nhiu vn Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN19vic tm c biu din thch hp cho cc trng thi ca vn l hon ton khng n gin. Vic tm ra dng biu din tt cho cc trng thi ng vai tr ht sc quan trng trong qu trnh gii quyt mt vn . C th ni rng, nu ta tm c dng biu din tt cho cc trng thi ca vn , th vn hu nh c gii quyt.V d 2: Vn triu ph v k cp. C ba nh triu ph v ba tn cp bn b t ngn mt con sng, cng mt chic thuyn ch c mt hoc hai ngi. Hy tm cch a mi ngi qua sng sao cho khng li bn b sng k cp nhiu hn triu ph. ng nhin trong bi ton ny, cctonttngngvi cchnhngch1hoc2ngi quasng. Nhng y ta cn lu rng, khi hnh ng xy ra (lc thuyn ang bi qua sng) th bn b sng thuyn va di ch, s k cp khng c nhiu hn s triu ph. Tip theo ta cn quyt nh ci g l trng thi ca vn . y ta khng cn phn bit cc nh triu ph v cc tn cp, m ch s lng ca h bn b sng l quan trng. biu din cc trng thi, ta s dng b ba (a, b, k), trong a l s triu ph, b l s k cp bn b t ngn vo cc thi im m thuyn b ny hoc b kia, k = 1 nu thuyn b t ngn v k = 0 nu thuyn b hu ngn. Nh vy, khng gian trng thi cho bi ton triu ph v k cp c xc nh nh sau: Trng thi ban u l (3, 3, 1). Cc ton t. C nm ton t tng ng vi hnh ng thuyn ch qua sng 1 triu ph, hoc 1 k cp, hoc 2 triu ph, hoc 2 k cp, hoc 1 triu ph v 1 k cp. Trng thi kt thc l (0, 0, 0).1.2. CC CHIN LC TM KIMNh ta thy trong mc 1.1, gii quyt mt vn bng tm kim trong khng gian trng thi, u tin ta cn tm dng thch hp m t cc trng thi ca vn . Sau cn xc nh: Trng thi ban u. Tp cc ton t. Tp T cc trng thi kt thc. (T c th khng c xc nh c th gm cc trng thi no m ch c ch nh bi mt s iu kin no ).Gi s u l mt trng thi no v R l mt ton t bin i u thnh v. Ta s gi v l trng thi k u, hoc v c sinh ra t trng thi u bi ton t Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN20R. Qu trnh p dng cc ton t sinh ra cc trng thi k u c gi l pht trin trng thi u. Chng hn, trong bi ton tm s, pht trin trng thi ban u (hnh 1.2 bn tri), ta nhn c ba trng thi k (hnh 1.3).Khi chng ta biu din mt vn cn gii quyt thng qua cc trng thi v cc ton t th vic tm li gii ca vn c quy v vic tm ng i t trng thi ban u ti mt trng thi kt thc no .C th phn cc chin lc tm kim thnh hai loi: Ccchinlctmkimm. Trongccchinlctmkimny, khng c mt s hng dn no cho s tm kim, m ta ch pht trin cc trng thi ban u cho ti khi gp mt trng thi ch no . C hai k thut tm kim m, l tm kim theo b rng v tm kim theo su.T tng ca tm kim theo b rng l cc trng thi c pht trin theo th t m chng c sinh ra, tc l trng thi no c sinh ra trc s c pht trin trc. Cn trong tm kim theo su, trng thI sinh ra sau cng s c pht trin trc.Trongnhiuvn, dchngtapht trincctrngthi theoh thng no (theo b rng hoc theo su) th s lng cc trng thi c sinh ra trc khi ta gp trng thi ch thng l cc k ln. Do cc thut ton tm kim m km hiu qu, i hi rt nhiu khng gian v thi gian. Trong thc t, nhiu vn khng th gii quyt c bng tm kim m.Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN21 Tm kim kinh nghim (tm kim heuristic). Trong rt nhiu vn , chng ta c th da vo s hiu bit ca chng ta v vn , da vo kinh nghim, trc gic, nh gi cc trng thi. S dng s nh gi cc trng thi hng dn s tm kim: trong qu trnh pht trin cc trng thi, ta s chn trong s cc trng thi ch pht trin, trng thi c nh gi l tt nht pht trin. Do tc tm kim s nhanh hn. Cc phng php tm kim da vo s nh gi cc trng thi hng dn s tm kim gi chung l cc phng php tm kim kinh nghim. Nh vy chin lc tm kim c xc nh bi chin lc chn trng thi pht trin mi bc. Trong tm kim m, ta chn trng thi pht trin theo th t m chng c sinh ra; cn trong tm kim kinh nghim ta chn trng thi da vo s nh gi cc trng thi.CY TM KIMChng ta c th ngh n qu trnh tm kim nh qu trnh xy dng cy tm kim. Cy tm kim l cy m cc nh c gn bi cc trng thi ca khng gian trng thi. Gc ca cy tm kim tng ng vi trng thi ban u. Nu mt nh ng vi trng thi u, th cc nh con ca n ng vi cc trng thi v k u. Hnh 1.4a l th biu din mt khng gian trng thi vi trng thi ban u l A, hnh 1.4b l cy tm kim tng ng vi khng gian trng thi .Mi chinlc tmkim trong khnggian trng thitng ngvi mt phng php xy dng cy tm kim. Qu trnh xy dng cy bt u t cy ch c mt nh l trng thi ban u. Gi s ti mt bc no trong chin lc tm kim, ta xy dng c mt cy no , cc l ca cy Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN22tng ng vi cc trng thi cha c pht trin. Bc tip theo ph thuc vo chin lc tm kim m mt nh no trong cc l c chn pht trin. Khi pht trin nh , cy tm kim c m rng bng cch thm vo cc nh con ca nh . K thut tm kim theo b rng (theo su) tng ng vi phng php xy dng cy tm kim theo b rng (theo su).1.3. CC CHIN LC TM KIM MTrong mc ny chng ta s trnh by hai chin lc tm kim m: tm kim theo b rng v tm kim theo su. Trong tm kim theo b rng, ti mi bc ta s chn trng thi pht trin l trng thi c sinh ra trc cc trng thi ch pht trin khc. Cn trong tm kim theo su, trng thi cchnphttrinltrngthicsinhrasaucngtrongscc trng thi ch pht trin.Chng ta s dng danh sch L lu cc trng thi c sinh ra v ch c pht trin. Mc tiu ca tm kim trong khng gian trng thi l tm ng i t trng thi ban u ti trng thi ch, do ta cn lu li vt ca ng i. Ta c th s dng hm father lu li cha ca mi nh trn ng i, father(v) = u nu cha ca nh v l u.1.3.1. Tm kim theo b rngTm kim theo b rngThut ton tm kim theo b rng c m t bi th tc sau:PROCEDURE BREADTH_FIRST_SEARCH;BEGIN1. KHI TO DANH SCH L CH CHA TRNG THI BAN U;2. LOOP DO2.1 IF L RNG THEN {THNG BO TM KIM THT BI; STOP};2.2 LOI TRNG THI U U DANH SCH L;2.3 IF U L TRNG THI KT THC THEN{THNG BO TM KIM THNH CNG; STOP};2.4 FOR MI TRNG THI V K U DO {T V VO CUI DANH SCH L;FATHER(V) U}END;Chng ta c mt s nhn xt sau y v thut ton tm kim theo b rng:Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN23 Trong tm kim theo b rng, trng thi no c sinh ra trc s c pht trin trc, do danh sch L c x l nh hng i. Trong bc 2.3, ta cn kim tra xem u c l trng thi kt thc hay khng. Ni chung cc trng thi kt thc c xc nh bi mt s iu kin no , khi ta cn kim tra xem u c tha mn cc iu kin hay khng. Nubitoncnghim(tntingittrngthibanuti trng thi ch), th thut ton tm kim theo b rng s tm ra nghim, ng thi ng i tm c s l ngn nht. Trong trng hp bi ton v nghim v khng gian trng thi hu hn, thut ton s dng v cho thng bo v nghim.NH GI TM KIM THEO B RNGBy gi ta nh gi thi gian v b nh m tm kim theo b rng i hi. Gi s rng, mi trng thi khi c pht trin s sinh ra b trng thi k. Ta s gi b l nhn t nhnh. Gi s rng, nghim ca bi ton l ng i c di d. Bi v nghim c th c tm ra ti mt nh bt k mc d ca cy tm kim, do s nh cn xem xt tm ra nghim l:1 + b + b2 +... + bd-1 + kTrong k c th l 1, 2,..., bd. Do s ln nht cc nh cn xem xt l:1 + b + b2 +... + bdNh vy, phc tp thi gian ca thut ton tm kim theo b rng l O(bd). phc tp khng gian cng l O(bd), bi v ta cn lu vo danh sch L tt c cc nh ca cy tm kim mc d, s cc nh ny l bd. thy r tm kim theo b rng i hi thi gian v khng gian ln ti mc no, ta xt trng hp nhn t nhnh b = 10 v su d thay i. Gi s pht hin v kim tra 1000 trng thi cn 1 giy, v lu gi 1 trng thi cn 100 bytes. Khi thi gian v khng gian m thut ton i hi c cho trong bng sau:Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN24 su d Thi gian Khng gian4 11 giy 1 megabyte6 18 giy 111 megabytes8 31 gi 11 gigabytes10 128 ngy 1 terabyte12 35 nm 111 terabytes14 3500 nm 11.111 terabytes1.3.2. Tm kim theo suNh ta bit, t tng ca chin lc tm kim theo su l, ti mi bc, trng thi c chn pht trin l trng thi c sinh ra sau cng trong s cc trng thi ch pht trin. Do thut ton tm kim theo su l hon ton tng t nh thut ton tm kim theo b rng, ch c mt iu khc l, ta x l danh sch L cc trng thi ch pht trin khng phi nh hng i m nh ngn xp. C th l trong bc 2.4 ca thut ton tm kim theo b rng, ta cn sa li l t v vo u danh sch L.Sau y chng ta s a ra cc nhn xt so snh hai chin lc tm kim m: Thut ton tm kim theo b rng lun lun tm ra nghim nu bi ton c nghim. Song khng phi vi bt k bi ton c nghim no thut ton tm kim theo su cng tm ra nghim! Nu bi ton c nghim v khng gian trng thi hu hn, th thut ton tm kim theo su s tm ra nghim. Tuy nhin, trong trng hp khng gian trng thi v hn, th c th n khng tm ra nghim, l do l ta lun lun i xung theo su, nu ta i theo mt nhnh v hn m nghim khng nmtrnnhnhth thut tonskhngdng. Dongi ta khuyn rng, khng nn p dng tm kim theo d su cho cc bi ton c cy tm kim cha cc nhnh v hn. phc tp ca thut ton tm kim theo su.Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN25Gi s rng, nghim ca bi ton l ng i c di d, cy tm kim c nhn t nhnh l b v c chiu cao l d. C th xy ra, nghim l nh ngoi cng bn phi trn mc d ca cy tm kim, do phc tp thi gian ca tm kim theo su trong trng hp xu nht l O(bd), tc l cng nh tm kim theo b rng. Tuy nhin, trn thc t i vi nhiu bi ton, tm kim theo su thc s nhanh hn tm kim theo b rng. L do l tm kim theo b rng phi xem xt ton b cy tm kim ti mc d-1, ri mi xem xt cc nh mc d. Cn trong tm kim theo su, c th ta ch cn xem xt mt b phn nh ca cy tm kim th tm ra nghim. nh gi phc tp khng gian ca tm kim theo su ta c nhn xt rng, khi ta pht trin mt nh u trn cy tm kim theo su, ta ch cn lu cc nh cha c pht trin m chng l cc nh con ca cc nh nm trn ng i t gc ti nh u. Nh vy i vi cy tm kim c nhn t nhnh b v su ln nht l d, ta ch cn lu t hn db nh. Do phc tp khng gian ca tm kim theo su l O(db), trong khi tm kim theo b rng i hi khng gian nh O(bd)!1.3.3. Cc trng thi lpNh ta thy trong mc 1.2, cy tm kim c th cha nhiu nh ng vi cng mt trng thi, cc trng thi ny c gi l trng thi lp. Chng hn, trong cy tm kim hnh 4b, cc trng thi C, E, F l cc trng thi lp. Trong th biu din khng gian trng thi, cc trng thi lp ng vi cc nh c nhiu ng i dn ti n t trng thi ban u. Nu th c chu trnh th cy tm kim s cha cc nhnh vi mt s nh lp li v hn ln. Trong cc thut ton tm kim s lng ph rt nhiu thi gian pht trin li cc trng thi m ta gp v pht trin. V vy trong qu trnh tm kim ta cn trnh pht sinh ra cc trng thi m ta pht trin. Chng ta c th p dng mt trong cc gii php sau y:1. Khi pht trin nh u, khng sinh ra cc nh trng vi cha ca u.2. Khi pht trin nh u, khng sinh ra cc nh trng vi mt nh no nm trn ng i dn ti u.3. Khng sinh ra cc nh m n c sinh ra, tc l ch sinh ra cc nh mi.Hai gii php u d ci t v khng tn nhiu khng gian nh, tuy nhin cc gii php ny khng trnh c ht cc trng thi lp. thc hin gii php th 3 ta cn lu cc trng thi pht trin vo tp Q, lu cc trng thi ch pht trin vo danh sch L. ng nhin, trng Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN26thi v ln u c sinh ra nu n khng c trong Q v L. Vic lu cc trng thi pht trin v kim tra xem mt trng thi c phi ln u c sinh ra khng i hi rt nhiu khng gian v thi gian. Chng ta c th ci t tp Q bi bng bm (xem [8]).1.3.4. Tm kim su lpNh chng ta nhn xt, nu cy tm kim cha nhnh v hn, khi s dng tm kim theo su, ta c th mc kt nhnh v khng tm ra nghim. khc phc hon cnh , ta tm kim theo su ch ti mc d no ; nu khng tm ra nghim, ta tng su ln d+1 v li tm kim theo su ti mc d+1. Qu trnh trn c lp li vi d ln lt l 1, 2,... dn mt sumaxno. Nhvy, thut tontmkimsulp(iterative deepening search) s s dng th tc tm kim su hn ch (depth_limited search) nh th tc con. l th tc tm kim theo su, nhng ch i ti su d no ri quay ln.Trong th tc tm kim su hn ch, d l tham s su, hm depth ghi li su ca mi nhprocedure Depth_Limited_Search(d);begin1. Khi to danh sch L ch cha trng thi ban u u0;depth(u0) 0;2. loop do2.1 if L rng then {thng bo tht bi; stop};2.2 Loi trng thi u u danh sch L;2.3 if u l trng thi kt thc then{thng bo thnh cng; stop};2.4 if depth(u) cost then Quay li 2.1;2.5 for mi trng thi v k u do{g(v) g(u) + k(u,v); f(v) g(v) + h(v); t v vo danh sch L1};2.6 Sp xp L1 theo th t tng ca hm f;2.7 Chuyn L1 vo u danh sch L sao cho trng thi u L1 tr thnh u L;end;Ngi tachngminhcrng, thut tonnhnh_v_cncngl thut ton y v ti u nu hm nh gi h(u) l nh gi thp v c di cc cung khng nh hn mt s dng no .3.2.TM I TNG TT NHTTrong mc ny chng ta s xt vn tm kim sau. Trn khng gian tm kim U c xc nh hm gi (hm mc tiu) cost, ng vi mi i tng x U vi mt gi tr s cost(x), s ny c gi l gi tr ca x. Chng ta cn tm mt i tng m ti hm gi t gi tr ln nht, ta gi i tng l i tng tt nht. Gi s khng gian tm kim c cu trc cho php ta xc nh c khi nim ln cn ca mi i tng. Chng hn, U l khng gian trng thi th ln cn ca trng thi u gm tt c cc trng thi v k u; nu U l khng gian cc vect thc n-chiu th ln cn ca vect x = (x1, x2,... xn) gm tt c cc vect gn x theo khong cch clit thng thng.Trong mc ny, ta s xt k thut tm kim leo i tm i tng tt nht. Sau ta s xt k thut tm kim gradient (gradient search). l k thut leo i p dng cho khng gian tm kim l khng gian cc vect thc n-chiu v hm gi l hm kh vi lin tc. Cui cng ta s nghin cu k thut tm kim m phng luyn kim(simulated annealing).Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN493.2.1.Tm kim leo iK thut tm kim leo i tm kim i tng tt nht hon ton ging nh k thut tm kim leo i tm trng thi kt thc xt trong mc 2.3. Ch khc l trong thut ton leo i mc 2.3, t mt trng thi ta "leo lntrng thi k tt nht (c xc nh bi hm gi), tip tc cho ti khi t ti trng thi ch; nu cha t ti trng thi ch m khng leo ln c na, th ta tip tc "tt xungtrng thi trc n, ri li leo ln trng thi tt nht cn li. Cn y, t mt nh u ta ch leo ln nh tt nht v (c xc nhbi hmgi cost) tronglncnununhny"cao hnnh u, tc l cost(v) > cost(u). Qu trnh tm kim s dng li ngay khi ta khng leo ln nh cao hn c na.Trong th tc leo i di y, bin u lu nh hin thi, bin v lu nh tt nht (cost(v) nh nht) trong cc nh ln cn u. Khi thut ton dng, bin u s lu i tng tm c.procedure Hill_Climbing;begin1. u mt i tng ban u no ;2.loop do2.1 v i tng tt nht (c xc nh bi hm gi)trong ln cn u;2.2if cost(u) < cost(v) then u v else stop;end;TI U A PHNG V TI U TON CCR rng l, khi thut ton leo i dng li ti i tng u*, th gi ca n cost(u*) ln hn gi ca tt c cc i tng nm trong ln cn ca tt c cc i tng trn ng i t i tng ban u ti trng thi u*. Do nghim u* m thut ton leo i tm c l ti u a phng. Cn nhn mnh rng khng c g m bo nghim l ti u ton cc theo ngha l cost(u*) l ln nht trn ton b khng gian tm kim. nhn c nghim tt hn bng thut ton leo i, ta c th p dng lp li nhiu ln th tc leo i xut pht t mt dy cc i tng ban u c chn ngu nhin v lu li nghim tt nht qua mi ln lp. Nu s ln lp ln th ta c th tm c nghim ti u.Kt qu ca thut ton leo i ph thuc rt nhiu vo hnh dng ca mt congca hm gi. Nu mt cong ch c mt s t cc i a phng, th k thut leo i s tm ra rt nhanh cc i ton cc. Song c nhng vn Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN50 m mt cong ca hm gi ta nh lng nhm vy, khi s dng k thut leo i i hi rt nhiu thi gian.3.2.2.Tm kim gradientTm kim gradient l k thut tm kim leo i tm gi tr ln nht (hoc nh nht) ca hm kh vi lin tc f(x) trong khng gian cc vect thc n-chiu. Nh ta bit, trong ln cn nh ca im x = (x1,...,xn), th hm f tng nhanh nht theo hng ca vect gradient:Do t tng ca tm kim gradient l t mt im ta i ti im ln cn n theo hng ca vect gradient.procedure Gradient_Search;beginx im xut pht no ;repeatx x + f(x);until |f| < ;end;Trong th tc trn, l hng s dng nh xc nh t l ca cc bc, cn l hng s dng nh xc nh tiu chun dng. Bng cch ly cc bc nh theo hng ca vect gradient chng ta s tm c im cc i a phng, l im m ti f = 0, hoc tm c im rt gn vi cc i a phng.3.2.3. Tm kim m phng luyn kim:Nh nhn mnh trn, tm kim leo i khng m bo cho ta tm c nghim ti u ton cc. cho nghim tm c gn vi ti u ton cc, ta p dng k thut leo i lp xut pht t cc im c la chn ngu nhin. By gi thay cho vic lun lun leo ln ixut pht t cc im khc nhau, ta thc hin mt s bc tt xungnhm thot ra khi cc im cc i a phng. chnh l t tng ca k thut tm kim m phng luyn kim.Trong tm kim leo i, khi mt trng thi u ta lun lun i ti trng thi tt nht trong ln cn n. Cn by gi, trong tm kim m phng luyn kim, ta chn ngu nhin mt trng thi v trong ln cn u. Nu trng thi v

,_

xn,...,2 x,x1f f ffClick to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN51c chn tt hn u (cost(v) > cost(u)) th ta i ti v, cn nu khng ta ch i tivvimtxcsutno. Xcsutnygimtheohmmca xuca trng thi v. Xc sut ny cn ph thuc vo tham s nhit T. Nhit T cng cao th bc i ti trng thi xu cng c kh nng c thc hin. Trong qu trnh tm kim, tham s nhit T gim dn ti khng. Khi T gn khng, thut ton hot ng gn ging nh leo i, hu nh n khng thc hin bc tt xung. C th ta xc nh xc sut i ti trng thi xu v t u l e/T, y = cost(v) - cost(u).Sau y l th tc m phng luyn kim.procedure Simulated_Anneaning;begint 0;u trng thi ban u no ;T nhit ban u;repeatv trng thi c chn nhu nhin trong ln cn u;if cost(v) > cost(u) then u velse u v vi xc sut e/T;T g(T, t);t t + 1;until T nhend;Trong th tc trn, hm g(T, t) tha mn iu kin g(T, t) < T vi mi t, n xc nh tc gim ca nhit T. Ngi ta chng minh c rng, nu nhit T gim chm, th thut ton s tm c nghim ti u ton cc. Thut ton m phng luyn kim c p dng thnh cng cho cc bi ton ti u c ln.Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN523.3. TMKIMMPHNGSTINHA. THUTTONDI TRUYNThut ton di truyn (TTDT) l thut ton bt chc s chn lc t nhin v di truyn. Trong t nhin, cc c th khe, c kh nng thch nghi tt vi mi trng s c ti sinh v nhn bn cc th h sau. Mi c th c cu trc gien c trng cho phm cht ca c th . Trong qu trnh sinh sn, cc c th con c th tha hng cc phm cht ca c cha v m, cu trc gien ca n mang mt phn cu trc gien ca cha v m. Ngoi ra, trong qu trnh tin ha, c th xy ra hin tng t bin, cu trc gien ca c th con c th cha cc gien m c cha v m u khng c.Trong TTDT, mi c th c m ha bi mt cu trc d liu m t cu trc gien ca c th , ta s gi n l nhim sc th (chroniosome).Mi nhim sc th c to thnh t cc n v c gi l gien. Chng hn, trong cc TTDT c in, cc nhim sc th l cc chui nh phn, tc l mi c th c biu din bi mt chui nh phn.TTDT s lm vic trn cc qun th gm nhiu c th. Mt qun th ng vi mt giai on pht trin s c gi l mtth h.T th h ban u c to ra, TTDT bt chc chn lc t nhin v di truyn bin i cc th h. TTDT s dng cc ton t c bn sau y bin i cc th h. Tont ti sinh (reproduction)(cn c gi lton tchnlc (selection)). Cc c th tt c chn lc a vo th h sau. S la chn ny c thc hin da vo thch nghi vi mi trng ca mi c th. Ta s gi hm ng mi c th vi thch nghi ca n l hm thch nghi (fitness function). Ton t lai ghp (crossover).Hai c th cha v m trao i cc gien to ra hai c th con. Ton t t bin (mutation).Mt c th thay i mt s gien to thnh c th mi.Tt c cc ton t trn khi thc hin u mang tnh ngu nhin. Cu trc c bn ca TTDT l nh sau:procedure Genetic_Algorithm;begint 0;Khi to th h ban u P(t);nh gi P(t) (theo hm thch nghi);repeatClick to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN53t t + 1;Sinh ra th h mi P(t) t P(t-1) biChn lcLai ghpt bin;nh gi P(t);until iu kin kt thc c tha mn;end;Trong th tc trn, iu kin kt thc vng lp c th l mt s th h ln no , hoc thch nghi ca cc c th tt nht trong cc th h k tip nhau khc nhau khng ng k. Khi thut ton dng, c th tt nht trong th h cui cng c chn lm nghim cn tm.By gi ta s xt chi tit hn ton t chn lc v cc ton t di truyn (lai ghp, t bin) trong cc TTDT c in.1. Chn lc:Vic chn lc cc c th t mt qun th da trn thch nghi ca mi c th. Cc c th c thch nghi cao c nhiu kh nng c chn. Cn nhn mnh rng, hm thch nghi ch cn l mt hm thc dng, n c th khng tuyn tnh, khng lin tc, khng kh vi. Qu trnh chn lc c thc hin theo k thut quay bnh xe.Gi s th h hin thi P(t) gm c n c th {x1,..,xn}. S n c gi l c ca qun th. Vi mi c th xi, ta tnh thch nghi ca n f(xi). Tnh tng cc thch nghi ca tt c cc c th trong qun th:Mi ln chn lc, ta thc hin hai bc sau:1) Sinh ra mt s thc ngu nhin q trong khong (0, F);2) xk l c th c chn, nu k l s nh nht sao choVic chn lc theo hai bc trn c th minh ha nh sau: Ta c mt bnh xe c chia thnh n phn, mi phn ng vi thch nghi ca mt c th(hnh3.5).Mtmi tnch vo bnhxe. Quay bnhxe, khibnhxe dng, mi tn ch vo phn no, c th ng vi phn c chn. n1 ii) x f( Fkiix f14 ) (Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN54R rng l vi cch chn ny, cc c th c thch nghi cng cao cng c kh nng c chn. Cc c th c thch nghi cao c th c mt hay nhiu bn sao, cc c th c thch nghi thp c th khng c mt th h sau (n b cht i).2. Lai ghp:Trn cc c th c chn lc, ta tn hnh ton t lai ghp. u tin ta cn a ra xc sut lai ghp pc. xc sut ny cho ta hy vng c pc.n c th c lai ghp (n l c ca qun th).Vi mi c th ta thc hin hai bc sau:1) Sinh ra s thc ngu nhin r trong on [0, 1];2) Nu r < pc th c th c chn lai ghpT cc c th c chn lai ghp, ngi ta cp i chng mt cch ngu nhin. Trong trng hp cc nhim sc th l cc chui nh phn c di c nh m, ta c th thc hin lai ghp nh sau: Vi mi cp, sinh ra mt s nguyn ngu nhin p trn on [0, m -1], p l v tr im ghp. Cp gm hai nhim sc tha = (a1,..., ap, ap+1,..., am)a = (b1,..., bp, bp+1,..., bm)c thay bi hai con l:a' = (a1,..., ap, bp+1,..., bm)b' = (b1,..., bp, ap+1,..., am)3. t bin: Ta thc hin ton t t bin trn cc c th c c sau qu trnh lai ghp. t bin l thay i trng thi mt s gien no trong nhim sc th. Mi gien chu t bin vi xc sut pm. Xc sut t bin pm do ta xc nh v l xc sut thp. Sau y l ton t t bin trn cc nhim sc th chui nh phn.Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN55Vi mi v tr i trong nhim sc th:a = (a1,..., ai,..., am)Ta sinh ra mt s thc ngu nhin pi trong [0,1]. Qua t bin a c bin thnh a nh sau:a' = (a'1,..., a'i,..., a'm)Trong :ainu pi pma'i =1 - ainu pi < pmSau qu trnh chn lc, lai ghp, t bin, mt th h mi c sinh ra. Cng vic cn li ca thut ton di truyn by gi ch l lp li cc bc trn.V d: Xt bi ton tm max ca hm f(x) = x2 vi x l s nguyn trn on[0,31]. sdngTTDT, tamhomi snguynxtrongon [0,31] bi mt s nh phn di 5, chng hn, chui 11000 l m ca s nguyn 24. Hm thch nghi c xc nh l chnh hm f(x) = x2. Qun th ban u gm 4 c th (c ca qun th l n = 4). Thc hin qu trnh chn lc, ta nhn c kt qu trong bng sau. Trong bng ny, ta thy c th 2 c thch nghi cao nht (576) nn n c chn 2 ln, c th 3 c thch nghi thp nht (64) khng c chn ln no. Mi c th 1 v 4 c chn 1 ln.Bng kt qu chn lcS liu c thQun th ban ux thch nghi f(x) = x2S ln c chn1 0 1 1 0 1 13 169 12 1 1 0 0 0 24 576 23 0 1 0 0 0 8 64 04 1 0 0 1 1 19 361 1Thc hin qa trnh lai ghp vi xc sut lai ghp pc = 1, c 4 c th sau chn lc u c lai ghp. Kt qu lai ghp c cho trong bng sau. Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN56Trong bng ny, chui th nht c lai ghp vi chui th hai vi im ghp l 4, hai chui cn li c lai ghp vi nhau vi im ghp l 2.Bng kt qu lai ghpQun th sau chn lcim ghpQun th sau lai ghpx thch nghi f(x) = x20 1 1 0 | 1 4 0 1 1 0 0 2 1441 1 0 0 | 0 4 1 1 0 0 1 5 6251 1 | 0 0 0 2 1 1 0 1 1 7 7291 0 | 0 1 1 2 1 0 0 0 0 6 256 thc hin qu trnh t bin, ta chn xc sut t bin pm= 0,001, tc l ta hy vng c 5.4.0,001 = 0,02 bit c t bin. Thc t s khng c bit no c t bin. Nh vy th h mi l qun th sau lai ghp. Trong th h ban u, thch nghi cao nht l 576, thch nghi trung bnh 292. Trong th h sau, thch nghi cao nht l 729, trung bnh l 438. Ch qua mt th h, cc c th tt lnrt nhiu.Thut ton di truyn khc vi cc thut ton ti u khc cc im sau: TTDT chsdng hmthch nghihngdnstmkim, hm thchnghi ch cnlhmthcdng. Ngoi ra, nkhngi hi khng gian tm kim phi c cu trc no c. TTDT lm vic trn cc nhim sc th l m ca cc c th cn tm. TTDT tm kim t mt qun th gm nhiu c th. Cc ton t trong TTDT u mang tnh ngu nhin. gii quyt mt vn bng TTDT, chng ta cn thc hin cc bc sau y: Trc ht ta cn m ha cc i tng cn tm bi mt cu trc d liu no . Chng hn, trong cc TTDT c in, nh trong v d trn, ta s dng m nh phn. Thit khmthch nghi. Trong cc biton tiu,hmthch nghi c xc nh da vo hm mc tiu. Trn c s cu trc ca nhim sc th, thit k cc ton t di truyn (lai ghp, t bin) cho ph hp vi cc vn cn gii quyt.Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN57 Xc nh c ca qun th v khi to qun th ban u. Xc nh xc sut lai ghp pc v xc sut t bin pm. Xc sut t bin cn l xc sut thp. Ngi ta (Goldberg, 1989) khuyn rng nn chn xc sut lai ghp l 0,6 v xc sut t bin l 0,03. Tuy nhin cn qua th nghim tm ra cc xc sut thch hp cho vn cn gii quyt.Ni chung thut ng TTDT l ch TTDT c in, khi m cu trc ca cc nhim sc th l cc chui nh phn vi cc ton t di truyn c m t trn. Song trong nhiu vn thc t, thun tin hn, ta c th biu din nhim sc th bi cc cu trc khc, chng hn vect thc, mng hai chiu, cy,... Tng ng vi cu trc ca nhim sc th, c th c nhiu cch xc nh cc ton t di truyn. Qu trnh sinh ra th h mi P(t) t th h c P(t - 1) cng c nhiu cch chn la. Ngi ta gi chung cc thut ton ny l thut ton tin ha (evolutionary algorithms) hoc chng trnh tin ha (evolution program).Thut ton tin ha c p dng trong cc vn ti u v hc my. hiu bit su sc hn v thut ton tin ho, bn c c th tm c [3], [9] v [16]. Nu nh [9] v 6] c xem l cc sch hay nht vit v TTDT,[3] li cho ta ci nhn tng qut v s pht trin gn y ca TTDT.Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN58CHNG 4TM KIM C I THNghin cu my tnh chi c xut hin rt sm. Khng lu sau khi mytnhlptrnhcrai, vonm1950, ClaudeShannonvit chng trnh chi c u tin. Cc nh nghin cu Tr Tu Nhn To nghin cu vic chi c, v rng my tnh chi c l mt bng chng r rng v kh nng my tnh c th lm c cc cng vic i hi tr thng minh ca con ngi. Trong chng ny chng ta s xt cc vn sau y: Chi c c th xem nh vn tm kim trong khng gian trng thi. Chin lc tm kim nc i Minimax. Phng php ct ct -, mt k thut tng hiu qu ca tm kim Minimax.4.1. CY TR CHI V TM KIM TRN CY TR CHI.Trong chng ny chng ta ch quan tm nghin cu cc tr chi c hai ngi tham gia, chng hn cc loi c (c vua, c tng, c ca r...). Mt ngi chi c gi l Trng, i th ca anh ta c gi l en. Mc tiu ca chng ta l nghin cu chin lc chn nc i cho Trng (My tnh cm qun Trng).Chngtasxt cctrchi hai ngi vi cccimsau. Hai ngi chi thay phin nhau a ra cc nc i tun theo cc lut i no , cc lut ny l nh nhau cho c hai ngi. in hnh l c vua, trong c vua hai ngi chi c th p dng cc lut i con tt, con xe,... a ra nc i. Lut i con tt Trng xe Trng,... cng nh lut i con tt en, xe en,... Mt c im na l hai ngi chi u c bit thng tin y v cc tnh th trong tr chi (khng nh trong chi bi, ngi chi khng th bit cc ngi chi khc cn nhng con bi g). Vn chi c c th xem nh vn tm kim nc i, ti mi ln n lt mnh, ngi chi phi tm trong s rt nhiu nc i hp l (tun theo ng lut i), mt nc i tt nht sao cho qua mt dy nc i thc hin, anh ta ginh phn thng. Tuy nhin vn tm kim y s phc tp hn vn tm kim m chng ta Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN59 xt trong cc chng trc, bi v y c i th, ngi chi khng bit c i th ca mnh s i nc no trong tng lai. Sau y chng ta s pht biu chnh xc hn vn tm kim ny.Vn chi c c th xem nh vn tm kim trong khng gian trng thi. Mi trng thi l mt tnh th (s b tr cc qun ca hai bn trn bn c). Trng thi ban u l s sp xp cc qun c ca hai bn lc bt u cuc chi. Cc ton t l cc nc i hp l. Cc trng thi kt thc l cc tnh th m cuc chi dng, thng c xc nh bi mt s iu kin dng no . Mt hm kt cuc (payoff function) ng mi trng thi kt thc vi mt gi tr no . Chng hn nh c vua, mi trng thi kt thc ch c th l thng, hoc thua (i vi Trng) hoc ha. Do , ta c th xc nh hm kt cuc l hm nhn gi tr 1 ti cc trng thi kt thc l thng (i vi Trng), -1 ti cc trng thi kt thc l thua (i vi Trng) v 0 ti cc trng thi kt thc ha. Trong mt s tr chi khc, chng hn tr chi tnh im, hm kt cuc c th nhn gi tr nguyn trong khong [-k, k] vi k l mt s nguyn dng no . Nh vy vn ca Trng l, tm mt dy nc i sao cho xen k vi cc nc i ca en to thnh mt ng i t trng thi ban u ti trng thi kt thc l thng cho Trng. thun li cho vic nghin cu cc chin lc chn nc i, ta biu din khng gian trng thi trn di dng cy tr chi.CY TR CHICy tr chi c xy dng nh sau. Gc ca cy ng vi trng thi ban u. Ta s gi nh ng vi trng thi m Trng (en) a ra nc i l nh Trng (en). Nu mt nh l Trng (en) ng vi trng thi u, th cc nh con ca n l tt c cc nh biu din trng thi v, v nhn c t u do Trng (en) thc hin nc i hp l no . Do , trn cng mt mc ca cy cc nh u l Trng hoc u l en, cc l ca cy ng vi cc trng thi kt thc.Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN60V d:XttrchiDodgen(ctorabiColinVout).Chai qun Trng v hai qun en, ban u c xp vo bn c 3*3 (Hnh v). Qun en c th i ti trng bn phi, trn hoc di. Qun Trng c th i ti trng bn tri, bn phi, trn. Qun en nu ct ngoi cng bn phi c th i ra khi bn c, qun Trng nu hng trn cng c th i ra khi bn c. Ai a hai qun ca mnh ra khi bn c trc s thng, hoc to ra tnh th m i phng khng i c cng s thng. Giseni trc, taccytrchi cbiudinnhtrong hnh4.2.4.2. CHIN LC MINIMAXQu trnh chi c l qu trnh Trng v en thay phin nhau a ra quyt nh, thc hin mt trong s cc nc i hp l. Trn cy tr chi, qu trnh s to ra ng i t gc ti l. Gi s ti mt thi im no , ng i dn ti nh u. Nu u l nh Trng (en) th Trng (en) cn chn i ti mt trong cc nh en (Trng) v l con ca u. Ti nh en (Trng) v m Trng (en) va chn, en (Trng) s phi chn i ti mt trong cc nh Trng (en) w l con ca v. Qu trnh trn s dng li khi t ti mt nh l l ca cy.Gi s Trng cn tm nc i ti nh u. Nc i ti u cho Trng l nc i dn ti nh con ca v l nh tt nht (cho Trng) trong s cc nh Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN61con ca u. Ta cn gi thit rng, n lt i th chn nc i t v, en cng s chn nc i tt nht cho anh ta. Nh vy, chn nc i ti u cho Trng ti nh u, ta cn phi xc nh gi tr cc nh ca cy tr chi gc u. Gi tr ca cc nh l (ng vi cc trng thi kt thc) l gi tr ca hm kt cuc. nh c gi tr cng ln cng tt cho Trng, nh c gi tr cng nh cng tt cho en. xc nh gi tr cc nh ca cy tr chi gc u, ta i t mc thp nht ln gc u. Gi s v l nh trong ca cy v gi tr cc nh con ca n c xc nh. Khi nu v l nh Trng th gi tr ca n c xc nh l gi tr ln nht trong cc gi tr ca cc nh con. Cn nu v l nh en th gi tr ca n l gi tr nh nht trong cc gi tr ca cc nh con.V d:Xt cy tr chi trong hnh 4.3, gc a l nh Trng. Gi tr ca cc nh l s ghi cnh mi nh. nh i l Trng, nn gi tr ca n l max(3,-2) = 3, nh d l nh en, nn gi tr ca n l min(2, 3, 4) = 2. Vicgngitr choccnhcthchinbi cchmqui MaxVal v MinVal. Hm MaxVal xc nh gi tr cho cc nh Trng, hm MinVal xc nh gi tr cho cc nh en.function MaxVal(u);beginif u l nh kt thc then MaxVal(u) f(u)else MaxVal(u) max{MinVal(v) | v l nh con ca u}end;function MinVal(u); beginif u l nh kt thc then MinVal(u) f(u)Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN62else MinVal(u) min{MaxVal(v) | v l nh con ca u}end;Trong cc hm quy trn, f(u) l gi tr ca hm kt cuc ti nh kt thc u. Sau y l th tc chn nc i cho trng ti nh u. Trong th tc Minimax(u,v), v l bin lu li trng thi m Trng s chn i ti t u. procedure Minimax(u, v);beginval -;for mi w l nh con ca u doif val eval(v), ta khng cn i xung nh gi nh a na m vn khng nh hng g dn nh gi nh c. Hay ni cch khc ta c th ct b cy con gc a. Lp lun tng t cho trng hp a l nh en, trong trng hp ny nu eval(u) < eval(v) ta cng c th ct b cy con gc a. ci t kthut ct ct alpha-beta, i vi ccnhnmtrn ng i t gc ti nh hin thi, ta s dng tham s ghi li gi tr ln nht trong cc gi tr ca cc nh con nh gi ca mt nh Trng, cn tham s ghi li gi tr nh nht trong cc nh con nh gi ca mt nh en. Gi tr ca v s c cp nht trong qu trnh tm kim. v c s dng nh cc bin a phng trong cc hm MaxVal(u,,) (hm xc nh gi tr ca nh Trng u) v Minval(u, , ) (hm xc nh gi tr ca nh en u). function MaxVal(u, , );beginif u l l ca cy hn ch hoc u l nh kt thcthen MaxVal eval(u)else for mi nh v l con ca u do{ max[, MinVal(v, , )]; // Ct b cc cy con t cc nh v cn li if then exit};Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN66MaxVal ;end;function MinVal(u, , );beginif u l l ca cy hn ch hoc u l nh kt thcthen MinVal eval(u)else for mi nh v l con ca u do{ min[, MaxVal(v, , )]; // Ct b cc cy con t cc nh v cn liif then exit};MinVal ;end;Thut ton tm nc i cho Trng s dng k thut ct ct alpha-beta, c ci t bi th tc Alpha_beta(u,v), trong v l tham bin ghi li nh m Trng cn i ti t u.procedure Alpha_beta(u,v);begin -; ;for mi nh w l con ca u doif MinVal(w, , ) then{ MinVal(w, , ); v w;}end; V d. Xt cy tr chi gc u (nh Trng) gii hn bi cao h = 3 (hnh 4.8). S ghi cnh cc l l gi tr ca hm nh gi. p dng chin lc Minimax v k thut ct ct, ta xc nh c nc i tt nht cho Trng ti u, l nc i dn ti nh v c gi tr 10. Cnh mi nh ta cng cho gi tr ca cp tham s (, ). Khi gi cc hm MaxVal v MinVal xc nh gi tr ca nh . Cc nhnh b ct b c ch ra trong hnh: Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN67Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN68PHN IITRI THC V LP LUNHai thnh phn c bn ca mt h da trn tri thc (khnowledge based system) l c s tri thc v b suy din. to ra cc phng php v k thut xy dng c s tri thc v b suy din cho mt h da trn tri thc, chng ta cn phi nghin cu cc m hnh biu din tri thc v lp lun. Biu din tri thc v lp lun l lnh vc nghin cu trung tm ca tr tu nhn to. Trong phn ny chng ta s xt cc ngn ng biu din tri thc v cc phng php lp lun trong tng ngn ng . Ngn ng biu din tri thc quan trng nht l logic v t cp mt (s c xt trong chng 6). Logic v t cp mt l c s xy dng nhiu ngn ng biu din khc. Cc ngn ng con ca logic v t cp mt (ngn ng cc lut, ngn ng m t khi nim) s c xt trong cc chng 7 v 9. Chng 8 dnh cho vic nghin cu cc lp lun khng n iu. Vn biu din tri thc khng chc chn s c trnh by trong chng 10. Chng 11 trnh by logic m v lp lun xp xClick to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN69CHNG 5LOGIC MNH Trong chng ny chng ta s trnh by cc c trng ca ngn ng biu din tri thc. Chng ta s nghin cu logic mnh , mt ngn ng biu din tri thc rt n gin, c kh nng biu din hp, nhng thun li cho ta lm quen vi nhiu khi nim quan trng trong logic, c bit trong logic v t cp mt s c nghin cu trong cc chng sau.5.1. BIU DIN TRI THCCon ngi sng trong mi trng c th nhn thc c th gii nh cc gic quan (tai, mt v cc gic quan khc), s dng cc tri thc tch lu c v nh kh nng lp lun, suy din, con ngi c th a ra cc hnh ng hp l cho cng vic m con ngi ang lm. Mt mc tiu ca Tr tu nhn to ng dng l thit k cc tc nhn thng minh(intelligent agent) cng c kh nng nh con ngi. Chng ta c th hiu tc nhn thng minh l bt c ci g c th nhn thc c mi trng thng qua cc b cmnhn(sensors)varahnhnghplpnglimitrng thng qua b phn hnh ng (effectors). Cc robots, cc softbot (software robot), cc h chuyn gia,... l cc v d v tc nhn thng minh. Cc tc nhn thng minh cn phi c tri thc v th gii hin thc mi c th a ra cc quyt nh ng n. Thnh phn trung tm ca cctc nhn da trn tri thc (knowledge-based agent), cn c gi l h da trn tri thc (knowledge-based system) hoc n gin l h tri thc, l c s tri thc. C s tri thc (CSTT) l mt tp hp cc tri thc c biu din di dng no . Mi khi nhn c cc thng tin a vo, tc nhn cn c kh nng suy din a ra cc cu tr li, cc hnh ng hp l, ng n. Nhim v ny c thc hin bi b suy din. B suy din l thnh phn c bn khc ca cc h tri thc. Nh vy h tri thc bo tr mt CSTT v c trang b mt th tc suy din. Mi khi tip nhn c cc s kin t mi trng, th tc suy din thc hin qu trnh lin kt cc s kin vi cc tri thc trong CSTT rt ra Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN70cc cu tr li, hoc cc hnh ng hp l m tc nhn cn thc hin. ng nhin l, khi ta thit k mt tc nhn gii quyt mt vn no th CSTT s cha cc tri thc v min i tng c th . my tnh c th s dng c tri thc, c th x l tri thc, chng ta cn biu din tri thc di dng thun tin cho my tnh. l mc tiu ca biu din tri thc.Tri thc c m t di dng cc cu trong ngn ng biu din trithc. Mi cu c th xem nh s m ha ca mt s hiu bit ca chng ta v th gii hin thc. Ngn ng biu din tri thc (cng nh mi ngn ng hnh thc khc) gm hai thnh phn c bn l c php v ng ngha. C php ca mt ngn ng bao gm cc k hiu v cc quy tc lin kt cc k hiu (cc lut c php) to thnh cc cu (cng thc) trong ngn ng. Cc cu y l biu din ngoi, cn phn bit vi biu din bn trong my tnh. Cc cu s c chuyn thnh cc cu trc d liu thch hp c ci t trong mt vng nh no ca my tnh, l biu din bn trong. Bn thn cc cuchachangmt ni dungnoc, chamangmt ngha no c. Ng ngha ca ngn ng cho php ta xc nh ngha ca cc cu trong mt min no ca th gii hin thc. Chng hn, trong ngn ng cc biu thc s hc, dy k hiu (x+y)*z l mt cu vit ng c php. Ng ngha ca ngn ng ny cho php ta hiu rng, nu x, y, z, ng vi cc s nguyn, k hiu + ng vi php ton cng, cn * ng vi php chia, th biu thc (x+y)*z biu din qu trnh tnh ton: ly s nguyn x cng vi s nguyn y, kt qu c nhn vi s nguyn z. Ngoi hai thnh phn c php v ng ngha, ngn ng biu din tri thc cn c cung cp c ch suy din. Mt lut suy din (rule of inference) cho php ta suy ra mt cng thc t mt tp nocccngthc. Chnghn, tronglogicmnh, lut modus ponens cho php t hai cng thc A v AB suy ra cng thc B. Chng ta s hiu lp lun hoc suy din l mt qu trnh p dng cc lut suy din t cc tri thc trong c s tri thc v cc s kin ta nhn c cc tri thc mi. Nh vy chng ta xc nh:Ngn ng biu din tri thc = C php + Ng ngha + C ch suy din.Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN71Mt ngn ng biu din tri thc tt cn phi c kh nng biu din rng, tc l c th m t c mi iu m chng ta mun ni. N cn phi hiu qu theo ngha l, i ti cc kt lun, th tc suy din i hi t thi gian tnh ton v t khng gian nh. Ngi ta cng mong mun ngn ng biu din tri thc gn vi ngn ng t nhin.Trong sch ny, chng ta s tp trung nghin cu logic v t cp mt (first-orderpredicatelogichocfirst-orderpredicatecalculus)-mtngn ngbiudintrithc, bivlogicvtcpmtckhnngbiudin tng i tt, v hn na n l c s cho nhiu ngn ng biu din tri thc khc, chnghntonhoncnh(situationcalculus)hoclogicthi gian khong cp mt (first-order interval tempral logic). Nhng trc ht chng ta s nghinculogic mnh (propositional logichoc propositional calculus). N l ngn ng rt n gin, c kh nng biu din hn ch, song thun tin cho ta a vo nhiu khi nim quan trng trong logic.5.2. C PHP V NGNGHA CA LOGIC MNH 5.2.1. C PhpC php ca logic mnh rt n gin, n cho php xy dng nn cc cng thc. C php ca logic mnh bao gm tp cc k hiu v tp cc lut xy dng cng thc.1. Cc k hiuHai hng logic True v False.Cc k hiu mnh (cn c gi l cc bin mnh ): P, Q,...Cc kt ni logic , , 1, , .Cc du m ngoc (v ng ngoc).2. Cc quy tc xy dng cc cng thc Cc bin mnh l cng thc.Nu A v B l cng thc th:(AB)(c A hi Bhoc A v B)(AB)(c A tuyn Bhoc A hoc B)(1A)(c ph nh A)(AB) (c A ko theo Bhoc nu A th B)Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN72(AB) (c A v B ko theo nhau)l cc cng thc.Sau ny cho ngn gn, ta s b i cc cp du ngoc khng cn thit. Chng hn, thay cho ((AB)C) ta s vit l (AB)C.Cc cng thc l cc k hiu mnh s c gi l cc cu n hoc cu phn t. Cc cng thc khng phi l cu n s c gi l cu phc hp. Nu P l k hiu mnh th P v 1 P c gi l literal,P l literaldng, cn 1 P l literal m. Cu phc hp c dng A1...Am trong Ai l cc literal s c gi l cu tuyn (clause).5.2.2. Ng nghaNg ngha ca logic mnh cho php ta xc nh ngha ca cc cng thc trong th gii hin thc no . iu c thc hin bng cch kt hp mi k hiu mnh vi s kin no trong th gii hin thc. Chng hn, k hiu mnh P c th ng vi s kin Paris l th nc Php hoc bt k mt s kin no khc. Bt k mt s kt hp cc k hiu mnhvi ccskintrongthgii thccgi lmtminhha (interpretation). Chng hn minh ha ca k hiu mnh P c th l mt s kin (mnh ) Paris l th nc Php . Mt s kin ch c th ng hoc sai. Chng hn, s kin Paris l th nc Php l ng, cn s kin S Pi l s hu t l sai.Mt cch chnh xc hn, ta hiu mt minh ha l mt cch gn cho mi k hiu mnh mt gi tr chn l True hoc False. Trong mt minh ha, nu k hiu mnh P c gn gi tr chn l True/False (P True/ PFalse) th ta ni mnh P ng/sai trong minh ha . Trong mt minh ha, ngha ca cc cu phc hp c xc nh bi ngha ca cc kt ni logic. Chng ta xc nh ngha ca cc kt ni logic trong cc bng chn l (xem hnh 5.1)P QlPPQ P Q PQ PQFalse False True False False True TrueFalse True True False True True FalseTrue False False False True False FalseTrue True False True True True TrueHnh 5.1 Bng chn l ca cc kt ni logicClick to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN73 ngha ca cc kt ni logic , v l c xc nh nh ngha ca cc t v,hoc lv ph nhtrong ngn ng t nhin. Chng ta cn phi gii thch thm v ngha ca php ko theo P Q (P ko theo Q), P l gi thit, cn Q l kt lun. Trc quan cho php ta xem rng, khi P l ng v Q l ng th cu P ko theo Q l ng, cn khi P l ng Q l sai th cu P ko theo Ql sai. Nhng nu P sai v Q ng, hoc P sai Q sai th P ko theo Ql ng hay sai ? Nu chng ta xut pht t gi thit sai, th chng ta khng th khng nh g v kt lun. Khng c l do g ni rng, nu P sai v Q ng hoc P sai v Q sai th P ko theo Ql sai. Do trong trng hp P sai th P ko theo Q l ng d Q l ng hay Q l sai. Bngchnlchophptaxcnhngnghacccuphchp. Chng hn ng ngha ca cc cu PQ trong minh ha {P True, Q False} l False. Vic xc nh ng ngha ca mt cu (P Q)lS trong mt minh ha c tin hnh nh sau: u tin ta xc nh gi tr chn l ca P Q v 1 S, sau ta s dng bng chn l ca xc nh gi tr (P Q) lS.Mt cng thc c gi l tho c (satisfiable) nu n ng trong mt minh ha no . Chng hn cng thc (P Q) lS l tho c, v n c gi tr True trong minh ha {P True, QFalse, S True}.Mt cng thc c gi l vng chc (valid hoc tautology) nu n ng trong mi minh ha chng hn cu P lP l vng chc.Mt cng thc c gi l khng tho c, nu n l sai trong mi minh ha. Chng hn cng thc P lP.Chng ta s gi mt m hnh (model) ca mt cng thc l mt minh ha sao cho cng thc l ng trong minh ha ny. Nh vy mt cng thc tho c l cng thc c mt m hnh. Chng hn, minh ha {P False, Q False, STrue } l mt m hnh ca cng thc (P =>Q) S.Bng cch lp bng chn l (phng php bng chn l)ta c th xc nh c mt cng thc c tho c hay khng. Trong bng ny, mi bin mnh ng u mt ct, cng thc cn kim tra ng u mt ct, mi dng tng ng vi mt minh ha. Chng hn hnh 5.2 l bng chn l cho cng thc (P=>Q) S. Trong bng chn l ny ta cn a vo cc ct ph ng vi cc cng thc con ca cc cng thc cn kim tra vic tnh gi tr ca cng thc ny c d dng. T bng chn l ta thy rng cng thc (P=>Q) S l tho c nhng khng vng chc.Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN74P Q SPQ (PQ) SFalse False False True FalseFalse False True True TrueFalse True False True FalseFalse True True True TrueTrue False False False FalseTrue False True False FalseTrue True False True FalseTrue True True True True Hnh 5.2 Bng chn l cho cng thc (PQ) SCn lu rng, mt cng thc cha n bin, th s cc minh ha ca n l 2n, tc l bng chn l c 2ndng. Nh vy vic kim tra mt cng thc c tho c hay khng bng phng php bng chn l, i hi thi gian m. Cook (1971) chng minh rng, vn kim tra mt cng thc trong logic mnh c tho c hay khng l vn NP-y .Chng ta s ni rng mt tp cng thc G = {G1,..,Gm } l vng chc (thoc, khngthoc)nuhi cachngG1.......Gmlvng chc(tho c, khng tho c). Mt m hnh ca tp cng thc G l m hnh ca cng thc G1.......Gm..5.3. DNG CHUN TC Trong mc ny chng ta s xt vic chun ha cc cng thc, a cc cng thc v dng thun li cho vic lp lun, suy din. Trc ht ta s xt cc php bin i tng ng. S dng cc php bin i ny, ta c th a mt cng thc bt k v dng chun tc.5.3.1. S tng ng ca cc cng thc Hai cng thc A v B c xem l tng ng nu chng c cng mt gi tr chn l trong mi minh ha. ch A tng ng vi B ta vit A B. Bng phng php bng chn l, d dng chng minh c s tng ng ca cc cng thc sau y:Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN75AB lA BA B (AB) (BA)l(lA)A1. Lut De Morganl(A B) lA lBl(A B) lA lB2. Lut giao hon A B B AA B B A 3. Lut kt hp (A B) C A (B C)(A B) C A (B C) 4. Lut phn phiA (B C) (A B) (A C)A (B C) (A B) (A C)5.3.2. Dng chun tcCc cng thc tng ng c th xem nh cc biu din khc nhau ca cng mt s kin. d dng vit cc chng trnh my tnh thao tc trn cc cng thc, chng ta s chun ha cc cng thc, a chng v dng biu din chun c gi l dng chun hi. Mt cng thc dng chun hi nu n l hi ca cc cu tuyn. Nh li rng, cu tuyn c dng A1 .... Am trong cc Ail literal. Chng ta c th bin i mt cng thc bt k v cng thc dng chun hi bng cch p dng th tc sau. B cc du ko theo () bng cch thay (AB) bi (lAvB). Chuyn cc du ph nh (l) vo st cc k hiu mnh bng cch p dng lut De Morgan v thay l(lA) bi A. p dng lut phn phi, thay cc cng thc c dng A(BC) bi (A B) (A B).V d: Ta chun ha cng thc (P Q) l(R lS): (P Q) l(R lS) (lP Q) (lR S) ((lP Q)vlR) ((lP Q) S) Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN76 (l P Q lR) (lP Q S). Nh vy cng thc (P Q) l(R lS) c a v dng chun hi (lP Q lR) (lP Q S).Khi biu din tri thc bi cc cng thc trong logic mnh , c s tri thc l mt tp no cc cng thc. Bng cch chun ho cc cng thc, c s tri thc l mt tp no cc cu tuyn. 5.3.3. Cc cu Horn trn ta ch ra, mi cng thc u c th a v dng chun hi, tc l hi ca cc tuyn, mi cu tuyn c dng:lP1 ........ lPm Q1 ..... Qn trong Pi, Qil cc k hiu mnh (literal dng) cu ny tng ng vi cu: P1 ^.......^ lPm => Q1 ..... Qn Dng cu ny c gi l cu Kowalski (do nh logic Kowalski a ra nm 1971).Khi n 0, n=1, cu Horn c dng:P1 ..... Pm => Q Trong Pi, Q l cc literal dng. Cc Pi c gi l cc iu kin (hoc gi thit), cn Q c gi l kt lun (hoc h qu). Cc cu Horn dngny cn c gi l cc lut if-then v c biu din nh sau: If P1 and....and Pm then Q.Khim=0, n=1cuHorntrthnhcunQ, hayskinQ. Nu m>0, n=0 cu Horn tr thnh dng lP1 v......v lPm hay tng ng l(P1^...^ Pm).Cn ch rng, khng phi mi cng thc u c th biu din di dng hi ca cc cu Horn. Tuy nhin trong cc ng dng, c s tri thc Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN77thng l mt tp no cc cu Horn (tc l mt tp no cc lut if-then).5.4. LUT SUY DINMt cng thc H c xem l h qa logic (logical consequence) ca mt tpcngthcG={G1,.....,Gm}nutrongbt kminhhanom {G1,.....,Gm} ng th H cng ng, hay ni cch khc bt k m hnh no ca G cng l m hnh ca H.Khi c mt c s tri thc, ta mun s dng cc tri thc trong c s ny suy ra tri thc mi m n l h qu logic ca cc cng thc trong c s tri thc. iu c thc hin bng cch s dng cc lut suy din (ruleofinference). Lutsuydingingnhmtthtcmchngtas dng sinh ra mt cng thc mi t cc cng thc c. Mt lut suy din gm hai phn: mt tp cc iu kin v mt kt lun. Chng ta s biu din cc lut suy din di dng phn s , trong t s l danh sch cc iu kin, cn mu s l kt lun ca lut, tc l mu s l cng thc mi c suy ra t cc cng thc t s.Sau y l mt s lut suy din quan trng trong logic mnh . Trong cc lut ny , i, , l cc cng thc: Lut Modus Ponens , T mt ko theo v gi thit ca ko theo, ta suy ra kt lun ca n. Lut Modus Tollens ,1 1 T mt ko theo v ph nh kt lun ca n, ta suy ra ph nh gi thit ca ko theo. Lut bc cu , Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN78T hai ko theo, m kt lun ca ko theo th nht trng vi gi thit ca ko theo th hai, ta suy ra ko theo mi m gi thit ca n l gi thit ca ko theo th nht, cn kt lun ca n l kt lun ca ko theo th hai. Lut loi b hi 1 ....... i ........miT mt hi ta suy ra mt nhn t bt k ca hi. Lut a vo hi 1,.......,i,........m1 .......i ....... mT mt danh sch cc cng thc, ta suy ra hi ca chng. Lut a vo tuyn i1....... i. ....... mT mt cng thc, ta suy ra mt tuyn m mt trong cc hng t ca tuyn l cng thc . Lut phn gii ,1 T hai tuyn, mt tuyn cha mt hng t i lp vi mt hng t trong tuyn kia, ta suy ra tuyn ca cc hng t cn li trong c hai tuyn. Mt lut suy din c xem ltin cy(sound) nu bt k mt m hnh no ca gi thit ca lut cng l m hnh ca kt lun ca lut. Chng ta ch quan tm n cc lut suy din tin cy.Bng phng php bng chn l, ta c th kim chng c cc lut suy din nu trn u l tin cy. Bng chn l ca lut phn gii c cho trong hnh 5.3. T bng ny ta thy rng, trong bt k mt minh ha no m Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN79c hai gi thit , 1 ng th kt lun cng ng. Do lut phn gii l lut suy in tin cy. l False False False False True FalseFalse False True False True TrueFalse True False True False FalseFalse True True True True TrueTrue False False True True TrueTrue False True True True TrueTrue True False True False TrueTrue True True True True TrueHnh 5.3 Bng chn l chng minh tnh tin cy ca lut phn gii.Ta c nhn xt rng, lut phn gii l mt lut suy din tng qut, n baogmlut ModusPonens, lut ModusTollens, lut bccunhcc trng hp ring. (Bn c d dng chng minh c iu ).Tin , nh l, chng minh. Gi s chng ta c mt tp no cc cng thc. Cc lut suy din cho php ta t cc cng thc c suy ra cng thc mi bng mt dy p dng cc lut suy din. Cc cng thc cho c gi l cc tin .Cc cng thc c suy ra c gi l cc nh l. Dy cc lut c p dng dn ti nh l c gi l mt chng minhca nh l. Nu cc lut suy din l tin cy, th cc nh l l h qu logic ca cc tin .V d: Gi s ta c cc cng thc sau: Q S G H (1) P Q(2)Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN80 R S (3) P (4) R (5)Gi s ta cn chng minh cng thc GH. T cng thc (2) v (4), ta suy ra Q (Lut Modus Ponens). Li p dng lut Modus Ponens, t (3) v (5) ta suy ra S. T Q, S ta suy ra QS (lut a vo hi). T (1) v QS ta suy ra GH. Cng thc GH c chng minh.Trongcchtri thc, chnghncchchuyngia, hlptrnh logic,..., s dng cc lut suy din ngi ta thit k ln cc th tc suy din (cn c gi l th tc chng minh) t cc tri thc trong c s tri thc ta suy ra cc tri thc mi p ng nhu cu ca ngi s dng.Mth hnh thc(formal system) bao gm mt tp cc tin v mt tp cc lut suy din no (trong ngn ng biu din tri thc no ).Mt tp lut suy din c xem l y , nu mi h qu logic ca mt tp cc tin u chng minh c bng cch ch s dng cc lut ca tp . PHNG PHP CHNG MINH BC BPhngphpchngminhbcb(refutationproof hocproof by contradiction) l mt phng php thng xuyn c s dng trong cc chng minh ton hc. T tng ca phng php ny l nh sau: chng minh P ng, ta gi s P sai (thm 1 P vo cc gi thit) v dn ti mt mu thun. Sau y ta s trnh by c s ca phng php chng minh ny.Gischngtacmt tpcccngthcG={G1,.....,Gm}tacn chng minh cng thc H l h qu logic ca G.iu tng ng vi chng minh cng thc G1^....^Gm H l vng chc. Thay cho chng minh G1^..... ^Gm H l vng chc, ta chng minh G1^....^Gm ^1 H l khng tha mn c. Tc l ta chng minh tp G= (G1,.......,Gm,1H) l khng tha c. G s khng tho c nu t Gta suy ra hai mnh i lp nhau. Vic chng minh cng thc H l h qu logic ca tp cc tiu G bng cch chng minh tnh khng tha c ca tp cc tiu c thm vo ph nh ca cng thc cn chng minh, c gi l chng minh bc b.Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN815.5. LUTPHNGII. CHNGMINHBCBBNGLUT PHN GII thun tin cho vic s dng lut phn gii, chng ta s c th ho lut phn gii trn cc dng cu c bit quan trng. Lut phn gii trn cc cu tuynA1 ............... Am C1 C B1 ............... Bn

A1 ........... Am B1 ... Bntrong Ai, Bj v C l cc literal. Lut phn gii trn cc cu Horn:Gi s Pi, Rj, Q v S l cc literal. Khi ta c cc lut sau:P1 ............... Pm S Q, R1 .............. Rn SP1 ........ Pm R1 ...... Rn QMt trng hp ring hay c s dng ca lut trn l:P1 ...... Pm S Q,SP1 .......Pm QKhi ta c th p dng lut phn gii cho hai cu, th hai cu ny c gi l hai cu phn gii c v kt qu nhn c khi p dng lut phn gii cho hai cu c gi l phn gii thc ca chng. Phn gii thc ca hai cu A v B c k hiu l res(A,B). Chng hn, hai cu tuyn phn gii c nu mt cu cha mt literal i lp vi mt literal trong cu kia. Phn gii thc ca hai literal i lp nhau (P v 1P) l cu rng, chng ta s k hiu cu rng l [], cu rng khng tho c.Gi s G l mt tp cc cu tuyn (bng cch chun ho ta c th a mt tp cc cng thc v mt tp cc cu tuyn). Ta s k hiu R(G) l tp Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN82cu bao gm cc cu thuc G v tt c cc cu nhn c t G bng mt dy p dng lut phn gii.Lut phn gii l lut y chng minh mt tp cu l khng tha c. iu ny c suy t nh l sau:NH L PHN GIIMt tp cu tuyn l khng tha c nu v ch nu cu rng [] R(G).nh l phn gii c ngha rng, nu t cc cu thuc G, bng cch p dng lut phn gii ta dn ti cu rng th G l khng tha c, cn nu khng th sinh ra cu rng bng lut phn gii th G tha c. Lu rng, vic dn ti cu rng c ngha l ta dn ti hai literal i lp nhau P v 1 P (tc l dn ti mu thun).T nh l phn gii, ta a ra th tc sau y xc nh mt tp cu tuyn G l tha c hay khng. Th tc ny c gi l th tc phn gii. procedure Resolution;Input: tp G cc cu tuyn ;begin1.Repeat1.1 Chn hai cu A v B thuc G;1.2 if A v B phn gii c then tnh Res(A,B);1.3 if Res(A,B)l cu mi then thm Res(A,B)vo G;until nhn c [] hoc khng c cu mi xut hin;2. if nhn c cu rng then thng bo G khng tho celse thng bo G tho c;endChng ta c nhn xt rng, nu G l tp hu hn cc cu th cc literal c mt trong cc cu ca G l hu hn. Do s cc cu tuyn thnh lp c t cc literal l hu hn. V vy ch c mt s hu hn cu c sinh ra bng lut phn gii. Th tc phn gii s dng li sau mt s hu hn bc. Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN83Ch s dng lut phn gii ta khng th suy ra mi cng thc l h qu logic ca mt tp cng thc cho. Tuy nhin, s dng lut phn gii ta c th chng minh c mt cng thc bt k c l h qu ca mt tp cng thc cho hay khng bng phng php chng minh bc b. V vy lut phn gii c xem l lut y cho bc b.Sau y l th tc chng minh bc b bng lut phn giiProcedureRefutation_Proof;input:Tp G cc cng thc;Cng thc cn chng minh H;Begin1.Thm 1 H vo G;2.Chuyn cc cng thc trong G v dng chun hi;3.T cc dng chun hi bc hai, thnh lp tp cc cu tuyn G;4. p dng th tc phn gii cho tp cu G;5. if G khng tho c then thng bo H l h qu logic else thng bo H khng l h qu logic ca G;end;V d: Gi gi G l tp hp cc cu tuyn sau1 A 1 B P (1)1 C 1 D P (2)1 E C (3)A(4)E(5)D(6)Gi s ta cn chng minh P. Thm vo G cu sau:1 P (7)p dng lut phn gii cho cu (2) v (7) ta c cu:Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN841 C 1 D(8)T cu (6) v (8) ta nhn c cu:1 C(9)T cu (3) v (9) ta nhn c cu:1 E(10)Ti y xut hin mu thun, v cu (5) v (10) i lp nhau. T cu (5) v (10) ta nhn c cu rng []. Vy P l h qu logic ca cc cu (1) --(6). Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN85CHNG 6LOGIC V T CP MTLogic mnh cho php ta biu din cc s kin, mi k hiu trong logic mnh c minh ha nh l mt s kin trong th gii hin thc, s dng cc kt ni logic ta c th to ra cc cu phc hp biu din cc s kinmangnghaphctphn. Nhvykhnngbiudincalogic mnh ch gii hn trong phm vi th gii cc s kin. Th gii hin thc bao gm cc i tng,mi i tng c nhng tnh cht ring phn bit n vi cc i tng khc. Cc i tng li c quan h vi nhau. Cc mi quan h rt a dng v phong ph. Chng ta c th lit k ra rt nhiu v d v i tng, tnh cht, quan h. i tng: mt ci bn, mt ci nh, mt ci cy, mt con ngi, mt con s.... Tnhcht:Cibncthctnhcht:cbnchn, lmbngg, khng c ngn ko. Con s c th c tnh cht l s nguyn, s hu t, l s chnh phng... Quan h: cha con, anh em, b bn (gia con ngi); ln hn, nh hn, bng nhau (gia cc con s); bn trong, bn ngoi nm trn nm di (gia cc vt)... Hm: Mt trng hp ring ca quan h l quan h hm. Chng hn, v mi ngi c mt m, do ta c quan h hm ng mi ngi vi m ca n. Logic v t cp mt l m rng ca logic mnh . N cho php ta m t th gii vi cc i tng, cc thuc tnh ca i tng v cc mi quan h gia cc i tng. N s dng cc bin (bin i tng) ch cc i tng trong mt min i tng no . m t cc thuc tnh ca i tng, cc quan h gia cc i tng, trong logic v t, ngi ta a vo cc v t (predicate). Ngoi cc kt ni logic nh trong logic mnh , logic v t cp mt cn s dng cc lng t.Chng hn, lng t (vi mi) cho php ta to ra cc cu ni ti mi i tng trong mt min i tng no .Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN86Chng ny dnh cho nghin cu logic v t cp mt vi t cch l mt ngn ng biu din tri thc. Logic v t cp mt ng vai tr cc k quan trng trong biu din tri thc, v kh nng biu din ca n (n cho php ta biu din tri thc v th gii vi cc i tng, cc thuc tnh ca i tng v cc quan h ca i tng), v hn na, n l c s cho nhiu ngn ng logic khc.6.1.C PHP V NGNGHA CA LGIC V T CP MT6.1.1. C php.CC K HIULogic v t cp mt s dng cc loi k hiu sau y. Cc k hiu hng: a, b, c, An, Ba, John,... Cc k hiu bin: x, y, z, u, v, w,... Cc k hiu v t: P, Q, R, S, Like, Havecolor, Prime,...Mi v t l v t ca n bin (n0). Chng hn Like l v t ca hai bin, Prime l v t mt bin. Cc k hiu v t khng bin l cc k hiu mnh .Cc k hiu hm: f, g, cos, sin, mother, husband, distance,...Mi hm l hm ca n bin (n1). Chng hn, cos, sin l hm mt bin, distance l hm ca ba bin.Cckhiuktnilogic:(hi),(tuyn),1(phnh),(ko theo), (ko theo nhau).Cc k hiu lng t: (vi mi), (tn ti).Cc k hiu ngn cch: du phy, du m ngoc v du ng ngoc.CC HNG THCCc hng thc (term) l cc biu thc m t cc i tng. Cc hng thc c xc nh quy nh sau. Cc k hiu hng v cc k hiu bin l hng thc.Click to buy NOW! PDF-XChange Viewerwww. docu-track. comClick to buy NOW! PDF-XChange Viewerwww. docu-track. comPhn II. TRI THC V LP LUN87 Nu t1, t2, t3,..., tn l n hng thc v f l mt k hiu hm n bin th f(t1, t2,..., tn) l hng thc. Mt hng thc khng cha bin c gi l mt hng thc c th (ground term). Chnghn, Anlkhiuhng, motherlkhiuhmmt bin, th mother(An) l mt hng thc c th.CC CNG THC PHN TChng ta s biu din cc tnh cht ca i tng, hoc cc quan h gia cc i tng bi cc cng thc phn t (cu n).Cc cng thc phn t (cu n) c xc nh quy nh sau.1. Cc k hiu v t khng bin (cc k hiu mnh ) l cng thc phn t.2. Nu t1, t2,...,tn l n hng thc v P l v t ca n bin th P(t1,t2,...,tn) l cng thc phn t. Chng hn, Hoa l mt k hiu hng, Love l mt v t ca hai bin, husbandlhmcamt bin, th Love(Hoa, husband(Hoa))lmt cng thc phn t.CC CNG THCT cng thc phn t, s dng cc kt ni logic v cc lng t, ta xy dng nn cc cng thc (cc cu).Cc cng thc c xc nh quy nh sau: Cc cng thc phn t l cng thc. Nu G v H l cc cng thc, th cc biu thc (G H), (G H), (1 G), (GH), (GH) l cng thc. Nu G l mt cng thc v x l bin th cc biu thc ( x G), ( x G) l cng thc.Cc cng thc khng phi l cng thc phn t s c gi l cc cu phc hp. Cc cng thc khng cha bin s c gi l cng thc c th. Khi vit cc cng thc ta s b i cc du ngoc khng cn thit, chng hn cc du ngoc ngoi