ONTT-V

Hmolytical Leasning.

Conceptual leaRO109 fOCuses 00 lea90ing bsgauzng poinUp

Induehve leasnirg 9s P povce of leasning and 8eosoO

30m detailedacb to qenesal poindples

Cestan ND Of tooinirg poDbleme

nduchue leoaoing eguse
to achieue a gven leue) of aCAUGa Cy

h i s melhnd, 4e genesalization is done y obsesUi9

dbeesVirg

toauni9 etamples ond identty Pels fatuses

ay +ve
clayified
on e bosis of eatuses they a3e

Ound Ve toani ng ecomples

and seaoO1g
Deducive legani- h e leoni 9
popces of
taom 9enesal pondples to detailed tact

Loduchive Reasoni
audt ( Speei-fic etademendt)
tcement 4 Mango is a

Sstalement 2 ha box is ful of ouu (specfie stolement)

Conclusio0The box is tul of mangoes ( Genesa) Conclubion

logically Toue
B u t saisholy may 0o moy not be TSue.

Deduciue Reosonin9
Srtaement i: AU mangoes ao tsuib (Grenesal stalement)
Stalement 9: AU touib raue Ceeds Ghenesal stadement)
Conclusio0: Mangoe) raue seeds (Speuific Concusion)
-5 Lcoly Tsue
14ol TIa
 nduchue Hnolyticod teo30n
Domain
/eps
D H

nducHve
Leason9 yticod leo9nirg

h Conislent
with D h ConbisBent
wt D&B
Arolurhco Leoeni9
Anoyticod leonning we paios Eroudedgp and deducthve 8eosonirg
to get an ument os inHoxnmation rabuvided by tsaiOig etample

Contoin) domain theDEy hich eeploins he tooinq example

S it is Called a erplonotoo bosed leo9Mni

By winq thee eeplanahons,analyticaJ leaning is mDse

accuhada than Oductie

leoaning Hoouthm- hypotReis

dokraset)

CnDledge

Lnd uchve larning

eDAning olopaitkm hypotPe,is

dodae (mwst be l0392
nduchuo- Aoolurhcol leoanirqt
ornd
Combioe hoth arolurticad lena ing
n hsleosoig melod ue

benefte of both oppapacChes

S0duchue leasoig io txden to goin

i s mefod, Re treoy Contaif) te erplonatio3 of

domain

induction mehod
toanim ecomples by
"hee explarations a10 Ued to petoam poedichons

Leaonnig padblem
Giuen A co otoooia ecomples D possibly Contanig an e80s

ADomon theooy BCortanig exODES

Space of Condidota hypothesis H

DelenmineA hy potReis 4Pot bet hb Pe tainig eomple

domaun Reoay
A bet t hypothesis is a ypotPesis uohidh contain zD

These ate a type) ot esDES

CooDss due to tsoinng ecamples
a) essDos due to domain theosy

T o t t eDsc Can be gvan a

039 mio ' pebo p (b) +eexo00 h)

neH

Hee pke 00e heighb tPot aso pesent tos tao nig

ecomple and domain thebs

r a y Con be calculaled by usirg Boupian melPod
Explanathon - based lea9nia (EbL

o t Use p 08 nDoledge
is arauica) leagpig
mepd
obseaved toaioifg etomnplo
bed tO analae, 08 explain houo much
t
saisHe e tasget Concept

hs
slea30n9 has been succeyfully applied to leamSeouch
tab
tabS
o u e s too VasieBy of plapnira and schedubg
a
19
EBL when the leagnea's plos knouoledge
Conbideas
Codsect and Complela

Defioto0:-
Giuen a hypo-tPesis Space H a seB df tsaoig etampiD
a a domaio theosy p Conistina of
oockoRpund Lnoudledge

tYot Con be ued to explain obcewed

tsoioirg eromples,t e
desised output ofaraluhical eaane iS a hupotResish
an

the taonirg ecompes D

taDm Hod is Consis-lent wrth bot
and domain theDsy B

EBL wods by genesabaiq Dt oDm-the taoni example

themselues, but tpm Pes expanation

s erplanation 1s ten sed tb distirquish the elesonk

featuge D tooning ample T2Dm P sselennt, so

e

tPot ecamples con be geneabaed cosed oo oica otPen

thon tatisticol sOLonirg9
1 Leazning with p0s fech Domolo heoaies g pabloq- e BG

A domain tPeoay is sald to bo Cosec),if eoach of its assesthons

s 0 ou-tul stalement obout tRe woald

A domain the08y Soaid to be Complela wit zespect toa gven

instance space, if he domain tReDay Cov@8s

tasget Concept Ond
eueRy
eUey positive example in the instance Space

algo-thnm
PRDLDG- EBG agosithm s seguentially Cov@ig
a

tRat Corbidoxs te toaining dato incsementally

not yet Covexed
F o o each neD postive tuniog example that is
tosn clailbe by
by a lea9hned +loan clause, itfoams a neuw

Explainirg tPe tsaining erample

mino LohelHen its on appbop
a) Hraysing -tis explanation tv delea
C not
Qenesai sation

ne tban clause
3) Refhioee Cusent hypothesis by addi r a
example,as well
as Othe
swe to Cove - s posHue
SimiUa1 intanceb.

e
PRoLo % ¬BG Compules
-
the most genexal gule by Computing
weacet poimaay(initia awestion) of e eplodation.

PROLDG- EBG Compules e oeakest paimoge ot tke tasqet

wrth epect to e explanation úsig a genesau
Concept
povcedune Caled segReion
 cBL a u t estabting whot e leasne nDuDs n t
one
Senbe, Re leonnes in ou Saleto Stack example begns w tR.
Aull
Lnbwledqe of e Safe tostack Concept 1hat is, if ib iniHal
initial domai
domoi

Thecbyis Sufhioient to eeplain any obseuwed töaning Tample

10
tRent i also Suffhdent to phedict theis clasiicai on
aduance

Chess b0 aad exanmple

loxget Concept: chevs boasd postion in which black wit ose i t
9ueen withio movey

inductiue Leasoing emboaayed, tS tob Comple.

Aralytical leaanin9
we can plain te stuation
Boand position: ha blac ng and queen age Simuaneo usly
atacked
Econpla -

Cole Tbetack
(1,y
Gyiven
ntance Space Cach intance de>cubes a pol 64
ojects epoeenled by poedi chtny type, Colb, U0Lime, O0na
Makia and 00

Hypothesis space H: Each upothesis s a cet of tos0

cdaue sule

TO3get Corcept SaleTb Stack (21y)

TaoOing etamples tpical positiue examp lo,

Saleypstach (Dhja, objp) o0
(clj Dbja), Duoneg (ohil, foos)
Type ( obt Box),Dwnea(olhj. Louise), THpe (oljo, éndtable).
 ( elue)
Donsity (Dlbjt, 0.2), Colos (obj1, Pe:d), Colox
obja ,

Cosdboasd)alesjal (b bjp, oood),Uourna (objh.o

malesial ( objl

-Domain epay B
ligbla(1.)
SafeTDStack (1,y)-7toogile ly) SaleTo Stack (1y)
Liales(a,y)weigt (, wn) U welght (y, uoy) ulewTan(u,og
w)voume (,u) U Density (7.d) U q ol(u,timesk
wel gt (,
tv,d)weight (a,5)
- TYpe (1, Cndtable)

fsagile () Mateiod (A, Gla)

-Deksmi0e
and
A hypothesis faom H obistent wi tsanig example

domainepy
Domaihenby)
PROLOG -EBG (asget Concept, T2ainirgExamples,

Leas(edRuley
Ccample.
pos positve ecomples fsom Tau0irg

each positiveExomple io poS rat not overed

fox
by LeasnedRules,do.

Cxplaun'
(paD0-f) 10 tee ms Of +he
explanation- Ao explanation r
Gadhi sHes te
Domain hecsy tod posrti uebxomple

Taaget GDUp
Hnolyae
he most gereal sat of
SufhientCondrtions
sufficent to satisfy to
featuses Df posithue Bcampla
taugetOoncept accoading to planation
 3Rehoe wea

lecunedRules + NeuD HosnCloLse, wheo

leas ned Rules
is of Potobm
WewHooncause
T a i g e lC o n c e p t SufficietCondrtrofy

Reusn LeaanedRules.

Cplonaion
Salebstat (obj1.0ojp

'ghden(toj dja)

weiyht (0bj1, D 6) weight (odbj2, 5)

olumu(bheja)
voluma(D Dentyob p)faod(o 6,240 3) Tpe (obj2, Endtabl)

le TPon (0 6,5)
Toaioi ecoumplo -

sa teTb Stack (,y)Voume (a, 2)n Density (x,0-3

tTHpe (y, éndtabl)
Wood

voume gei 0.3 molea

ob1
M a r e i o

Colg
ype
C o sd b o a s B d
yPe
Re d
foe Bue endiobly
DUse
weakext pde imogp ol Sofe'Tbstach (objl,bloja)

Safenbstoch(obj.ohj
SaleTbstack (1,

Gghlen (bj Dbja

iolea (7

tueight (obji,06) lemRan (o6,5) toaight(obj5)

weight (7, lo)
lewsnthon(D1,0)

Volume (objla) Dty (ojt,03) fal (0-6 D.HO.3)

Uotume,U) Danusity (nh) qual (w1,U1#d) lexs Than (Lwri,uy
Deig

Hnolly, we Con get tre m6st genexal ule

SofeTbstack (,y)voluma (a, u) A Denbity (a d) A

fqua (wi
times (vn a
lexsran(u1,5)ATHpe Cy, fndTabla)

The weoket poe imoap Df a Conclusion e uot epeet to a

enesa geB ot intod aeson A Such o
oDO+P is e mpst

A entaub e accobding to P

Poplog eB Compul most ceneaasule trot can be jubthed

by explanation by Compuhr9 tRe Lweaest of he

explanaion.
 paplog eB Compules e benkest pe imogp otasge
Concept wtR sespecd to explanauhon ubiq segebion Pca

Remaaks on planafio0- Based Leasoinge

) Thbduces jutiked genesal hupotResis y irg p108 enouoledoe
knouoledgp t
onalu2e iodividual ecample
BCxplanation delenmines elevant ataibudes
3 Ragkevieng allbuws dexivig mpse genesa Cobtsainb
1)
Leas 0ed ttoao clause Cotseponds to a Suttidet Cond iT
Satisfy toogeB Conept
aDlog- cBC mp city asumRS tra Complete ad Coxset dbmai
Pebsy
6) poepechves of eBL
eBL eoby-quded
Qenesaulzaion of exampla
CBL as
ecamplo quided sefosmoton of thepaie
-

eBL ubt
sestain9 wot tPe leounes aseady kndng"
7) Dis Coveing 02D
eadude>
fbonulato Deueotude) Not pudt i tsunig ecoumpla
Sa-feTbStack pabblem

SimilUas to Pe leotuges of hidden unu of peusa)

netuooac
D statistheca PoDceys derives hidden unut eotuye toom ma
txaioim eramples
eatuIe based on aallysis
eBl Arolyticod povces deives n

3ingle ecomple> using tro domain epsy

 Deduchue leoanirg
pobLD CBG oudpub a hupothesis h tot soieh es

( tO:)seD) Choa;)Efla)
DB-h
Beduce the efHechue siae of hypotesi s space

nducHve ogic poboRammirg

t21i, fta:)>eD) ( B Ahna) E#a

set of
Use) bockagpund
bnowledge b to enlasgp

hypothexe

EBL 0f Seaach Contab) rDoledgei

and Comple
domouns O t a Co deCt
Given eBl' xextaichon t
cdaYS Of appucation
is in speedir
domain-Rensy. an impoatant
leoaning how to Contoo)
hou Soac
Contso) saosc
podblem8 by leaa nirg
up Complec Seosch

CeL in Such a uwouy

t00 well-nown Suplemb employ
pRODICY and soAR

-Pe se of stadesin tohaich

PRDDIG4 leaans Concepts Such a
befobe subgool B"
Subgoal A should be solwed
CusenE
>SoAR eo by etplauning stuations fo which ib
stsadeoy leods to inehhicini es mobe geneaally, SOAR we

called Chunbg to ectact ganeaal

a uaiant of ee
Some eplaradion appley
Cond iti os undes ohich tne
 SOPR hos been oppied io a gRot pumbes of poDblem dom
and has abo been ppposed as a psyohological ploBibl
poUblL
model of human lepanirg CoDceeS

poDblema avsboaled o-th applyiro eeL to leaoninq eoach Co rtao)

h many Cases, the Dumbe 0f
ContaD)&ules tha mst be
leanned is vesy laago
Ppsthe syplem le0 mbbe ond mDoe ContadguWes to
impDve
S Seash, t must payo asqen and
las oRa Cost at eoch slep
to match this set of
tuwes aanist to Cusgent SeaaCh
9-tata
n n manyCose, H is itsactable to
Do desised tasgt Concept CoNstsuct tho erplarotionl
pmoi Deduchive melPod 1nduchue method

9ives neuo nooledg

neu
d o e s not 9ve any

cndwledge
i s a
metrnd Df distovay
method of vesticotioo
T t is a

method eochirg
of leochuro
tis a
i s method of inatsuchon
acgixes fiost hand
hond
child
schild 9ebs bendly made lofoom
and
intoorotion by
Enouoledge
matey we o-f it
ahon ond actualdbseauation

i s a
sloub paDee
T is guer pdees
ond
encousome dependence DO tsauns tho mind
e l f Conf dence
ond
giue
Otres ous ceb
rtotive
tull of activityy
is lexs stope of actiuty
tis
These

in t pODceY
upLOoRd poDCe
papces of 1 sic an
dounwosd
i s a and lads too
of thouat
leds to s e f
thoualt ond piocples
sesults