The Relevance of Computational Models of Knowledge Acquisition for the Design of Help in the Problem Solving Monitor ABSYNT

BEPBINTEO FROlv,l:

ADVANCED

COMPUTERS

IN

RESEARCH

ON

EDUCATION

Proceedings of the lFlP TC3 lnternational Conference 0n Advanced Research 0n

computeß in

Education

Tokyo, Japan,

1B

20 JulY, 1990

Edited by

ROBERT LEWIS

D epartne nl of Psychalory

University of Lanc aste

r

Lancaslet U.K.

SETSUKO

OTSUKI

DepatTment al AtTtficial lntelligence Kyushu lnstitute of Technology

tizul,,z, Japan

NH

II'I-C

tglLt

r'l

)t*l

v))

1S9l NORTH HOLLAND

AII/ISTERDAIVI NEW YORK . OXFORD . TOKYO

Elevio Scien@ Publishds 3.v, (Nonh üolland) t37

The

Relevance

of

Computational Models

of

Knowledge Acquisition

for the

Design

of

Helps

in the

Problem Solving

Monitor ABSYNT'

Claus Möbus

Department of ComptrndoMl Sciences Univeßity of Old€nburg

D 2900 Oldenbürg, F.R.

Gemey

Euner mcbus@uniol.uucp

Compubtiodar tuodels of krowlodge eqüisidon

e

indispensable

fü

rhe design of intelllgent tutoring systens. They give advice how ro design

iartrctioas,

helps and erylanations.We

want to show how two kinds of tuodeh (errernal and

irrerrrl

)

re

useful for rhe design

of

prcblen soh,rg

ronrcF

'PS\4s,. E.oecidl üequaliD orhe

o.

\ca\iallo,

rhed!(eplcnieof

a PSM. To püt

it

short:

Whcn are helps üsefül ahd ehen dre the! confusing ot pose new

probl%

to the

lear@?'

This paper

offeß

a contibution to

ICAI in

the franework of ihe

_lroblem

solving moniror ABSYNT. Our system - a special variani of an Inteuigent Tutoridg System

(lTS)

is designed with respectto a sequence of 37

proganüing

tasks which a& to be solved by stldenls in

üe

visual functional coftpute. laqguage ABSYNT (ABsd"ct SYNmx

T@9.

Besides providing the leamer with a frien.üy problem solving envjronnenr including a

äelp.onpor.rr.

u seres us as a tesbed for rcsemh in the donai,n ol intention-based diarrcstics, plan-parsinp and dßipn

of

l"lpr

for problems soLvers.

Research in these domains candol be done without stldyinE üe knotle.lge acquisnbn pro.ess

of the srudent.

tfaming

processes

e

modelled by .oftputatianal learaing mo.lels \e.E.l1l,

l2l'

lnr-edonc,nor

PSMS tre dj\r:ngui.h e\rem4

Mo,nrerl,orpula'

onä

mooe\

qn

;,?,nülmJdel i:

dn irre8raredpm of

,LePSMüdi.L.uall)

ered

\,"J/a/

eJl l,l l.

min

purpose _ß the useFtailored generation of i.structions. helps

dd

explanations. An

ar.rtul

model is nor a funcrional conponent of a PSM but is developed in pdallel using a broad dara

basis to gain a mole comllere insight into rhe leaming process of the subject.

41üe

present

sräre of ar't these modeh

wiil

rcpresent rhe knowledge acquisition process and rhe knowledge

sraß of the student at different gräin sizes and ranges. One of rhe reasoDs for üis discEpancl is the facl thar PSMS üe at üe present

üomnt

unable

t)

anälyse üe full .a!ge of _!rcblem solving behaviorwhich includes lerbal dara

_I4l.In€mal

nodels are based on data whicb fte PSM can gaüeronline. whercas our exiemar

ftode\

are based on videotaped _lroblem solving se$ions of dyades. which conmin verbal episodes.

l

_ABSI'I.IT

MS MAdC TCdNY b} K,D.FRANK. CJANKE. K KOHNERT, O.SCHRöDER Md H.J.THOL!

'*

This demh was sponsoEd by rhe Deußche Foßchun8s8cncinsch.ft {DFG) n the SPP Psychology of

138

We

üinl

rhat rhe development of PSMS or lTSs should

incllde

,or,

questions: Fi.st, how should the

leming

prcess be modetled with an extemal model to develop hrpotheses

_for

the

l.riga

or

optioal

helps and second how should the su.lenr

6odel

acquia ldowledge to Sereldre actual lser

rail@d

helps. Modelins

üe

knowledse acquisition

_lroces

of srudenls with extemal models

h6led

us to thecorclusion rhar

leming

prcceses in our domain

cd

be

adequarely described by a conbjnation of an

,upars?-drtrer

(rDL) _f5l änd

rM.e$

dri!"n

(SDL) _t6l-t?l

lemins

theory

(IDLSDL

Theory)

_t8l

_t101.

IDL

SDL hakes predictions

wrr,

the sbdent

will

a.cepr

infomtion

as help,

_-lr"'

sAe even acrively

will

r.dr.n

foi ne{ lnfomabon ard

,/dr

contenl of infomarion will

srt

üe srude.ß

needs. This has pracrical consequences for rhe construction ofPSMs. The

der€, o/t"rera.rile

and addptiee hzlps reqüifts üe successful solunon of a r)i n(hranization problen beveen the

knowledge snte ofthe

lemer

and the diagrosis of rhe PSM conceming rhis state:rhe student

üodel. So in our PSM the dpda,e of

üe

inteinal student

üodel

add

üe1/rr,r,o,

of help

infomdon

folows IDL SDL Thedy developed with extemal nodels.

2.

The

Problem-Solving

Monitor

ABSYNT

PSMS provi.le rhe leüner with a

problemiohing

environment including a diagnosis but no

curicular componenl. ABSYNT is used to communicate knopledge about a visual, purcly funcdonal, ree like visual

progmming

language based on ideas published in german school

I I 1l and univeßity text books [ 12]. Futher motivntion for the design of ABSYNT is given in

tl3l.

Basic resedch dealing

wnh

üe design of üe sysrem ftom apry.äologi.dl point of vlew

is descnbed jn _{11,11- f171.}

ABSYNT provides

^n

icohic enrirannent

and is äimed at suppdting rhe äcqüisition

of

functional programming concepts up to

/scmde

')stsfts. A program consists of a head and a

body dee. Also there is a stan tree

froft

which plogniDs can be called. The nodes of t\e lrees

ee consranrs, pdameteß,

pribitive

and self defined operators. The connecrions between the nodes ale

_{the lipelines}

for conEol and data flow. PDgrams üe edited by ßkjns nodes wirh

the mous ftom a menu bd md comecdng üem.

On demand rhere is also a visual räce which was implenented according 10

üe

runnable specificadon

of

the inrerpreter 1151. Additionally the user can test h)?orheses aboui rhe

corecfles

or her^is implemcntanons. Fig@s

I

and 2 depict snapshots of the interfäce when a srudent has prcgrammed a wrong solution of the

p.oblen

even

and

ries

!o p.opose some hypotheses about the _{usefulnes of larts of} his progrm. The mswers to her^is hypotheses

m

generated byrules defining a goals-mean$relation (GMRI morc deiails bolow). This leedback

can be vieved as helpr frcm th. sysFm ah the laiEMEe lerel.

3.

Rule-based

Help

for

tne Acquisition

of

Semantic

and

Planning

I

is standard theory in cognitive scien€ to assume that _!rcgranrming rcquires rhe a.rDarirn

dd

4ppli.@nb, of at least four knowledge soüces:

1.

nathenaticala.laleotii"n.al!rcloowledge

2.

knowledge about ihe

s]"tLt

of the ldguage

3.

knowledge abour üe scuartt r ofthe ldguage

4.

plazdr8

kdowledge about tbe pragtuatical use of the language

lr is qujre nalural to design helps accordingly.In our reseuch we confine ourselves ro rhe

No

ad 3: 2

D

d?s

describing the olerdrionor ffua4r'cr of tlte ABSYNT-lhCuage [ 16],[18]

{.),4: Planaing rules which

descnbeprS/ening

tMledge

n)ABSYNTLI9I

e

€

E

@

No:

Yoü

hypothesis cenor be conlleted ro a solurion known by the system.

Figu.e 1:

A

snatshoi of the ABSYNT-irErlace showing an incorect program with a user hypothesis (bold)

dd

rhe sysrems feedback.

Figu.e 2: The ABsYNT-interface showing

oother

user hypothesjs. The system retums rhe hypothesis (lower half on the

ldr)

to indicate its corechess. On denand (bold

line)

the system shows rhe nexr node of a conplele solution (lower hall on the /i8n4.

140

The behavior of

üe

ABsYNT-interpreter can be predicted by rhe knowledge

of

18 'srate centercd'

se@d.

r'der. They were reprEsented äs two-djmensional visual rules which seNe as

hel! material for ABSYNT Ds6.The complete set

cd

be found in t

l8l.

P

laaniq

kno||ledge fot 37 tasks is rcprcsented in 462 rules which define üe GMR. The GMR

cm

be looked at as a

rrk-rased

infe/ence

qsten.agtanna,

ot an ANDIOR-Gruph

qith

pdamerized nodes. The

nles

de

sinild

but nore powerfll than those found _{in f1l.l2l.[20].} The GMR is able ro

aebse

and s)rrnesize sevelal millions of soludors even

if

üe height

ol

ABSYNT

tres

is

fstricted

to five nodes. Because nodes

of

the AND/OR e.aph can be

odarem4d

ior subgoals. rhe relarion endble\ analysis and.ynrhe\is oteven pdrddl solu,ion\ which enables rhe testing ofüser hypotheses (Figu.es 1, 2). An exabple fo. the _Cnphicsl and natural language compilation of one

plming

nle

is give. in

FigG

3-Rule: "Planning

a

Recursion

on the

Goal

level"

IF

THEN

AND

IF

THEN

Fisure

3

üe bain

goar

is

to prcgraß

the

even

pre.licate which

can

be

applie.l

to

a

subgodl

rhe solurion of üis goal comprises üe folowing srep:

lede

qee

in the worksheet of üe ABSYI.IT enviionment for rhe _{)€t lo} be

programed ABSYNT tree

your next plaming ste! creares rhe moe dirercffiated AND goal üee

rhe solulion of this new goal is a ABSYNT tree which can be inserred in rhe solution of th€ main goäl

4.1

The GMR is delined by the

plan

q

rules and rcpftsents the corc of rhe help system ar the

/an8kge /evel, which is designed according to sode postulates. It should:

.

offer the e viroMent to che.k

wtioß

lEpotheses about the usefulness

of

several parts of the piogmm proposed by the student

.

ebbodl

avett

knawledee to genemte helps ol solution prcposals

.

ädCrrre _Coals, intentions

dd

the tnowledge stare of üe poblem solver

.

cohnahicate htu kharldd8e (belps) only in

rrrrttlt?

lrne periods, where the problen solver is wnling lo ecept such

infmüor

t5l

.

_{Sather data} ftom the hyothesis-testing process

,rl;a

to adapt the inEmal shrdlnt model continuously

.

deliver akl!

nikitul

i

_lomdria,

so thar the studeqt is able to leave tle

inpase

situation by his own ilus iüproving his problem solving skills

"lhß

_intertrbe

lEpothesß drtueh approach ß lathet d\ttercnt

fton

oüer sysEms known flom

literatu.e I1l, f21l -1251 and is a anred consequence of

IDLSDL

Theoly

_G6

betow).

4.

Extemal and

Int€rnal

ComDutational Models

of

Kno\tledge Acquisition

An

External Model

for

the Acquisition

of

Rule

Knowledge

on

the

Basis

of

Yisual

Helps

A

n€{e<6'yFeßq-i"

eorpogrmmingi\.omeknowledge"bour

the'yntll

a_d.etunbc.ot

.he language

\e

:r,d,ed

rhe d!qu,r uon

ol tenaa

, ln

alpd8c. The

\ena1ri.

or

lrogralnming languages can be defined

in

three ways: (a) the opelatiohal apprcach. (b) the denotationdl apprc

.h

Md(c)

rhe

dionat.

ap?rcach. We chose the oteradonal approach because

it

seemed 10 us more suitabte

for

nonces than the oiheß. The behavior

of

ihe ABsYNT-inrerpreteris representtdby

t

o tlitunsiohal (2 D) rßüdl /alss wbich pere süpplied

as help marerial in case of difficulries or impsses. We asked subjecß 10 predict the acdons

of

the ABsYNT'inlerpierer

[8] ilOl-

The resulrs dealing

wirh

knowledge acquisition

cm

be

described by an

trsratt€

twa4tage

sinuldtiot

nodelwhich is capable ofpredicting 607a

of

continuous _{ponions ofercoded prct@ols [10]:}

t . Knoa lctlgc a, qu^ idon

ot

trpase-dn ve4 lem, ng

Djfficulties 1261. t27l or inpasses L5l, t28l lead ro problem solvins by the applicarlon of weak heulisticr. With the help of the visual iules new knowledge about the s€mntics of ABSYNT is storcd in

nenory.

2. KtuwledSe

aprinizatio

by succes driven

leming:

Due lo _!racti@, the knowledg€ is reorganized so that it can be used

borc

efficiently. In tbe sibilation model this ß done by

_{üe.oflpositiat dtules}

to compound _{iules t29l,l30l} and mcro-operatos like rule nets _1311.

The daä show rhar the sDbjecß prcdicted tbe bohavior of the interpreter and tbe computadon

ol

prcsrams on the bäsis of nental tules

ü

nental nacro operaraff. They used help

idfomtion

ohly

in

hotuptinizarion stages of _{the lrocess. The questlon} is, wheüer to adapr rhe help

oaterial accordingly. That is to offer visual rules and visual

neio

rüles

st,.r/orted

ro

üe

112

4.2

An

lDternal Model

for

the Acquisition

of

Rüle

Knowledge

on

the

Bäsis

of

Checking Users

Hypothes€s

Ou

doDai. dakes it absolutely necessary

to.aarldtn

tho o\ewh.lni,nglaryEleedbdck spdce by an intemal nodel (sludent model) wbich is not implemenled yer It is not unusual that a

Ner

hypoftesis car be completEd by a hundred solulons- Even when only rhe ,exr node is shown üere are too

_{Mny losibilities}

ro ch@se Aom. IDL-SDL-Theory tels us to pspose only helps which the use.

co

assidilate according to his knowledge state. Gcnemtion of apFopnate bells

nüsr be done by rhe srudent model wbich

h6

to b€ leaned autoüatically.

A knowledge stare

ß

liewed as a set

ofnles,

malrules. and

üeir

comtosites. The student nodel consisrs of üar ser of

nles

which can gene*rle the implehentations

dd

which can be

de.ived from the student's proposals of hyporheses.

The

acq|ßitian o/

rules and their composites is easy. Those rüles which were used for sulce.sf.I Dar:rns nake

t

ch.rn

ol

ptuhslly instantialed planning

n

le:

The'e rulrs

ce

bF

.orpo,ed

iod

generdli^d arcord:4s ro

_{l2o. l0l1o}

htgh?t

_tLannhe

n tPucr.

Coroo.ine

n

successive rules results in an n rh order schem€- The highest schede is a tu1e which relates a

prcgralming task to a complete soluionr an

eMblle.

'the dcquisnion of

tulrules

is a bit trickier. Prografts ar€ ne€s. Selecting a subr@ for a

hyporhesis

is

equivalenr

lo

cür the

rce

(FiSure 4

left).

With our GMR

it

is

possible to reconstnct various goals depending on which üee is used fot rhe reconstuction af the _eodls.

we

can reconsdud the

rmr

goal of üe

,/,ole

F@. the root goal zA, of the s?k.red tree, rhc toor go?l Z ot the not selected tree and the conexr of ZA' in the nor selecled bur duronan.a/ly cowleted üee whi,.h ls <ZA,ZB,ZC>. These Z's arc eoals of the sübrees wnhin üe righl side

of the rdnc planning

nle. If

ZA' is not equivalent to

zA

then the selected lree implements a

rmng

goal. From

üis infolmtion

(goal _conflicts) we can generale malnles, rheir composites,

and

eior

expldations.

concrete

program

iree

studeni

₎

(=

proposal

of

lhe

selecled

lo

r

hypothesis

goal

tree

In the ned futurc we

will

convert the rules of üe GMR into visual planning helps

_Ge

Figw

3

as an

exdple)

.z

tle

Sddl ldr?/. But additional design features arc necessry. which arc

Momended

by our extemal and intemal modEl:

Oü

drerdl

model allowed rhe fuflber development of IDL-SDL-Theory. Tha! theory sives two main advices to PsM-buildeß:

.

The

.,,Fn,

of helps has to be syndo.i@d !o rhe knowledge state consistidg of tules and mac.ooPerätors.

.

Helps should only be offercd a! inpase

rue.

Besl is !o ler tne user äsk foi help.

Oü

t

l?/rrl

model (yet ro be

inll6m.teo

win

.

auromarica-lly

lemnles

ald malnles al impasw time (hlTothesis tes!tine)

.

consEain tne feedb'rck space

.

explaid erms on rhe basis of goal conflicß or goal colisionsr implemenBdons vs. task

Bonh models give valuable irfomalion for the design of PSMS: The

aterdl

_{eodel for Sereldl}

design dzcßiors, tle intettul t\odel

tü

caüete

help gendation.

REFERENCES

lll

ANDERSON. J.R.: Producrion Syslems. Ledning. and Tutonns. Ini

KIAHR,

D., et al. ,

hoduction system Models of r€amine and Developren! 437 458

t2l ANDERSON, J.R., A Theory of the Origins ofHuman Knowledge,

Anificial

Intetligence, 40. 1989.313 351

[3]

KASs,

R., Student Modeling

in

lntelligent Turoring

SysEms

Imtlications ror User Modeling. inrKOBSA, A. & WAHLSTER, W.

(edt:

User Models in Dialog Systems,Berlin Heidelbeig New York Springer, 1989

[4] VanLEHN. K.

&

CARLICK, S., Crmrsr An Autonated Protocot Analysis Tool, in: P.

LANGLEY (ed.), koceedings of the 4th Inlemational Workshop on Machine Ledning, Los Altos, CA:Kaufman. 1987.205 217

t5l

VanLEHN,

K.

Towards a Theory

of

Imlasse-D.iven

karning, jn:

H.MANDL

&

A.LESGOLD (eds), _{t eafring} hsues for Intelligent TDtoring Sysßms, Berlin Heidelberg'New

York

Springer. 1988, 19 41

t6l

NEVES,

D.M.,

ANDERSON, J.R.. Knowledge

CoDtjlation;

Mechanisüs

for

the Automatization of Cognitive SH1ls, in: ANDERSON, J.R. (ed): Coenitive Skills and their Acqüisirior, Hiusdale: Erlbaum, 1981. 5?-84

[7] WOLFFJ.G., Cognnive Developnenr as Optinizadon, in: L-BOLC (ed), CompulatioDal Models of

kaming.

Berlin-Heidelberg-New Yo.kr Springer,.1987, 161 205

[8] SCHRODER, O., FRANK, K.D., KOHNERT, K., MOBUS, C., RAUTERBERC, M., Instruction-Ba.sed Knowledge Acquisition and Modification: The Olerational Knowiedge for a

Functional, Visual Programming Languäge, Computeß

in

Human Behavior. Special Issuel

Ceman Experimental Resea.ch in Learning and Insnlcdon witn Coüpüteß, Vo1. 6, No. 1, 1990.3t 49

t9l

SCHRÖDER,

o.,

KOHNERT,

K., Towüd

a Model

of

Instrucrjon Based Knowledge

Acquisitior: The Operatonal Knowledge for a Furclional Visual Prograoming Länguage, Joumal of

Arificial

Inrelligence in Educaion,

vol.

I, No.2,1989,90. 105 128

[10] SCHRODER, O., A Model of the Acqüisition of RulE Knowledge pith Visual Helps: The Olerational Knopledge fo. a Functional. Visual Programding Language, P.oceedings ol

üe

3rd Intemational Conference on Conputer Assisled

llming

(ICCAI- '90),

Berlir

Heidelberg-New

York

Sprinsei (in pres)

[11]

SCHMITT,

H.

&

WOHLFARTH, P., Marhemarikbuch 5N, München: Bayeris.her

thulbuch,"iaB.

la78

[12] BAUER, F.L.

&

COOS, G., Infomätik: Eine einlühiende Ubersichi, Erster Teil, Be.lin: Sp.inger 1982

ll3l

DOSCH, W., New Prospecls of Teaching Programning Languages, in: F.B.

LOVN

&

E.D. TACC (ed9, Infomatics Educadon for

All

Studerts, Elsevier Science Publishers B.V. (Nonh-Holland), IFIP 1984, 153 169

ll4l

MOBUS, C., Die Entwickluns zutu Progmmieaxperten durch das Prcblemlösen mit

Automaten,

ini H.MANDL

&

P.M.FISCHER (6d), Le.nen itu Dialog

üit

deü

Compurer, München: Uibm

&

Schwdenbers, 1985, 1,lO- 154

l5l

MÖBUS

C

a

lHOLr.

H. J. TuroF. lnsr,acr'or\ dnd Helps ln:

CHRlslALLrR.

Th.

'ed'.

Kulsl,che

Inrelli8enz Krl-S 1o87.

lnfomatil'-fachberictF

202. HeidrlberS. SpnnEe,

tl6l

MÖBUS. C.

&

SCHRÖDER. O., Knowlealge Specification and lnsmclions for a Visual CoDputer Lansuase. In: KI-IX. F. et al-

(eö):

Man-Comluter ldter&tion

Rekmh

Macinter

II.

Proc@di.gs of the second Network

Senine

of Macinre! held in Bedin /CDR, 21. - 25.

L4;?

1088, Amqeroam

\oflh Holhrd,.o8o,5t5

565

ll'l

VÖBUS,

(..

Tow"rd Lhe Design

o

Adipuve l_(b--. hons and

Help.

lor

Kno$ edge Conmunicarion

with

the Problen Solving Monitor ABSYNT,

in:

STEPANKOVA, O.

&

MARIK, V.(eds), Proceedings of the CEPES UNESCO Workshop. "The Advent of

AI

ir

Higher Education", Piägue, Oc(ober,23'25, 1989. Heidelbeig Berlin New

Yoik

Springer (in

il

sl MÖBUS. c.

&

SCHRÖDER, o., Reprcsentirg semantic Knowle.lge wnh 2 Dimensioral Rules

in

the Domah

of

Funcdonal

Prcgranning, in:

TAUBER,

M.,

GORNY, P. (eds),

Visualizatioa

in

Huftan'Conputer

Inßraction. Heidelberg, Springei:

kcrure

Noles in Compurer Sciene, Berlin (in pre$)

llal

\4OBUS,

c.

&

rHOl

F, H 1., ln'emcri\e Süppon lor Plcnn,rÄ

v,.-al

Fogr.tr

rn

*e

Prcblems Solving Monnor ABSYNT: Giving Feedback to User Hypothesis on the Larguage

Le'el,

Proceedings

of

rhe 3rd Intornalional Conference on Computer

Asisred

Learning

Llc(

Al

o0/. Be' ,n-lre delbe,g-\etr

Yol.

Spdlger /in pre.n

lr0l \

rU

H\.

K..

Lf,ming

One S.

bpMed-ß

pe, Lf,$on.

An.t

InrelliSence.

lo8-.31.

-10 [21] HOUOHTON, R.C., Online Help Systeds: A Conspectus, Comdunlcations ofthe ACM, 27 _, 2, 1984, 1,26 133

l22l KEARSLEY. G., Online Help Sysrems, Design and Imple6entation. Noiwood: Ablex, lg88

f23l JOHNSON, w.L.,lnrendon Based Diagnosis ofNovice Programding Erors, Reseüch

Nores in Anificial htelligence, London: Pitnan, 1986

[24] MURRAY, W.R.. Autonated Program Debugging

for

lntelligent Tutoring Sysßns.

Research Noies in

Ar!ficial

InßUige.ce, Lndon: Piman. 1986

t25l

GREER, J.E.,

MARK, M.A.

&

MCCALLA,

G.l.:

Incorporating Grarulüiry-Based

Recognition

into

SCENT.

In:

BIERMANN,

D.,

BREUKXR. J., SANDBERG.

J.

(eds): Aniricial Inleiligence and Edücation. Amsttrdam: IOS. 1989. l07'1 15

126l LAIRD. J.E., ROSENBLOOM, P.S. &

NE\LELL,4.,

Chunking ln SOAR:The Anatofty

of a Gene.al

kming

Meachnism, Machine

lf,üning,

1986,

l,

1i'46

tz?l LAIRD.

J.E. NEWELL,

A.

&

ROSENBLOOM. P.S., SOAR:

An

Architecture

for

Cene.al Intelligence, Aitificial Imelligence, 33. 1987. 1-64

t28l

BROWN, J.S.

&

VanLEHN,

K.,

Repair Theory:

A

Generarive Theory

of

Bugs in Pr@edural Skills, Cognitive Science, 1980,4,379 426

[29]

vER!,

S., Relarional Producdon Systems. Artificial Intelligence, 1977. 8. 4? 68

f30l LEWIS, C., Composition of Productions,

in

KI-AHR. LANGLEY

&

NECHES

(edt,

Production Systen Models of Learning and Development, Catubridge,

Mas.: MIT

Pres,

1987, 329 358

t31l CHENG, P.

&

CARBONELL, J.G., The FERMI Sysrem: Inducing lteranve Macrc operarors

from

Experience, Proceedings

of

the 5th National Cotference

on A.tificial