6 simon ill defined problem

8/13/2019 6 Simon Ill Defined Problem

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ARTIFICIAL ,~qTELLIGENCE 181

T h e S tru c tu re o f I l l S tru c tu r ed P cob lemsH erb er t A S i m onC a r n e g i e - M e l l o n U n i v e r s i t y P i t t s b u r g h P a .

R e c o m m e n d e d b y S a ul A m a r e l

ABSTRACTThe boundary be tween we l l s t ruc tu red and i l l s t ruc tu red ~rob l ems i s vague , f l u id and no tsuscep t ib l e t o f o rma l i za t i on . A ny p rob l em so l v ing p roces s w 'i ii appear i l l s t ruc tu red i f t heprob l em so l ve r i s a s e r ia l mach ine t ha t has acces s t o a ~w:-y a r g e l o n g - t e r m m e m o r y o fpo t en t i a l l y r e l evan t i n fo rma t ion , and]or acces s to a v e ry la rge ex t e r lm me mo ry t ha t p rov ide sin fo rma t ion a bou t t he ac tua l r ea l -wor ld c~ ,seque nces o f problem-~olv ing ac t ions . There i s noreason t o suppose t ha t new a nd h i t he r to uakno wn concep t s o r t e ckn iques a re need ed t o enab lear t i f i c ia l in te l l igence sys tem s to op erate success fu l ly in dom ains tha t have these charac ter i s t ics .

1 . I n t r oduc t i onC e r t a i n c o n c e p t s a re d e f i n e d m a i n l y a s r e s i d u a l s - - i n t e rm s o f w h a t t h e y a r en o t . T h u s a U F O is a n a e r i a l p h e n o m e n o n n o t e x p la i n ab l e i n te r m s o f k n o w nl a w s a n d o b j e c t s; a n d E S P i s c o m m u n i c a t i o r : b e tw e e n p e r s o n s , w i t h o u te v i d e n c e o f t h e t r a n s m i s s i o n o f s i g n a ls o f a n y k i n d .

I n j u s t t h e s a m e w a y , " i l l st r u c tu r e d p r o b l e m " ( IS P ) is a r e s i d u a l c o n c e p t .A n I S P i s u s u a l l y d e f in e d a s a p r o b l e m w h o s e s t r u c tu r e l a c k s d e f i n i ti o n i ns o m e r e s p e c t. A p r o b l e m i s a n I S P i f i t is n o t a W S P ( w el l s t ru c t u r e d p r o b l e m ) .R es i d ua l ca t ego r i e s a r e t enac i ous : i t i s ex t r em e l y d if fi cu lt , o r even i m pos -s ib le , t o p r o v e t h a t t h e y a r e e m p t y . T h e s c o p e o f a r e s i d u a l c a t e g o r y c a n b en a r r o w e d p r o g re s si v e ly b y e x p l a i n i n g p r e v i o u s l y u n e x p l a i n e d p h e n o m e n a ; i tc a n n o t b e e x t in g u i sh e d a s l o n g a s a s in g le p h e n o m e n o n r e m a i n s u n e x p l a in e d .

I n t h i s p a p e r w i s h t o d is c u ss t h e r e l a t i o n b e tw e e n IS P s a n d W S P s w i t ht h e a i m o f a s k i n g w h e t h e r p r o b l e m s r e g a r d e d a s i ll s t ru c t u r e d a r e i n a c c e ss i b let o t h e p r o b l e m s o l v in g s y s t e m s o f a r ti fi c ia l i n te l li g e n c e i n w a y s t h a t t h o s e

* This research was supported in part by Research Grant MH-07722 from the NationalInstitute of Mental Health and in part by the Advanced Research Projects Agency of theOffice of the Secretary of Defense F44620-70-C-0107) which is monitored by the AirForce O ffice of Scientific Research. I am grateful to Dr. Aaron Slom an an d Prof. SaulAm arel for helpful comm ents on an earlier draft of th is paper.Ar tificial Intelligence 4 (1973), 181-201Copyright ~ 1973 by No rth-Holland Publishing Com pany


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182 HERBERT A. S IMONrega rded as well s truc tured a re no t . M y a im wi l l no t be to res t r i c t t he c lass ofp rob l em s w e rega rd a s ISP s - - i n f ac t I sha ll a rgue t ha t m any k i nds o f p rob l em sof ten t rea t ed as wel l s t ruc ture d a re be t t e r regar ded a s i ll s t ruc tured . Ins t ead ,I w i ll t ry t o show t ha t t he re i s no r ea l bo un da r y be tw een W SPs a nd ISPs , andno r e a son t o t h i nk tha t n ew and h i t he r t o un kno w n t ypes o f p rob l em so lv ingprocesses are need ed to ena ble ar t i f ic ia l intell igence system s to solve pro blem sthat are i l l s t ructured.Som e yea r s ago , W a l t e r R e i t m an p rov i ded t he f ir st ex tens ive d i scuss ion o fISP s (which he ca l led i l l def ined pr ob lem s ; see [10 , 11]) . M ore recently ,the top ic has been deve loped in a somewhat d i f fe ren t ve in by Al l en Newel l[6] , w ho em phas i zed t he r e l a ti on be t w een p rob l em s t ruc t u re an d p rob l em -so l v ing m e t hods . N ew e ll cha rac t e ri zed t he do m a i n o f ISPs a s t he do m a i n i nw h i ch on l y w eak p rob l em -so lv i ng m e t hods w ere ava il ab le . n t h i s accoun t , I con t i nue t he d i scuss ion begun by R e i t m an (an d on w h i chI ear l ie r m ade som e pre l imina ry rem ark s in [14, Sec tion 5 , pp . 274-76]).I sha ll t ry to g ive a pos i tive chara c te r i za t ion o f som e problem do m ains tha thave usua l ly been rega rded as il l s t ruc tured , rescuhag them f ro m the i r res idua ls t a t u s ; and t hen I sha l l a sk w he t he r t he m e t hod s u sed i n con t em pora ryar t i f i c i a l i n t e l l igence sys t ems are adequate for a t t ack ing problems in thesedomains . I sha l l no t pre judge whether the methods appl i cab le to thesep rob l em s a re w eak o r s t ro ng , bu t sha ll l e ave t ha t t o be dec i ded a f t e r thefact .

The f i rs t sec tion se ts for th a se t o f s t rong requi rem ent s th a t i t i s somet imesasse r t ed a t a sk m us t m ee t i n o rde r t o qua l ify a s a W SP. E ach o f t he se r equ i re -m ent s i s examined , in orde r to charac te r i ze the k inds of ISPs tha t fa il .osa t i s fy i t. The m eaning o f the requi rement s , an d the i r re l a t ion to the po we rof the ava i l ab le problem so lv ing sys t ems, i s t hen explored fur ther by con-s ider ing so m e spec if ic examples o f WSP s an d of ISPs . F ina l ly , t h i s explora t ionprovides the bas i s for a descr ip t ion o f pro blem so lv ing sys t ems tha t a readap t ed t o a t t ack i ng p rob l em s i n t he dom a i ns u sua l l y r ega rded a s i l l s t ruc -tured .

2 . Wel l S t ruc tured P roblemsFo r reaso ns tha t wi ll become c lear as we proceed , i t i s imposs ib le to cons t ruc ta fo rm a l de f in i ti on o f w e l l s t ruc t u red p rob l em . In s t ead , w e m u s t be con ten ts i m p ly t o se t fo r t h a l is t o f r equ i rem en t s t h a t have bee n p ro pos ed a t onet im e o r an o t he r a s c r it e ri a a p rob l em m us t s a t i sfy i n o rde r t o be r ega rded a swell s tructured . A fu rthe r e lement of indefini teness a nd re lat ivi ty ar i ses fro mthe fac t t ha t t he c r i t e r i a a re no t abso lu te , bu t genera l ly express a re l a t ionbe t w een charac te r is t ic s o f a p rob l em dom ai n , on t he one h and , and t hecharac te r i st i cs and pow er o f an impl ic i t o r expl ic it p rob lem so lv ingm echan i sm , on t he o t he r .

r t i f ic ia l ln te il ioence 4 ( 97 3), 18 -20 1


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T H E S T R U C T U R E O F I L L S T R U C T U R E D P R O B L E M S 183

W i t h t h e s e ca v e at s, w e w i ll sa y t h a t a p r o b l e m m a y b e r e g a r d e d a s w e l ls t r u c tu r e d t o t h e e x t e n t t h a t i t h a s s o m e o r a l l o f t h e f o l lo w i n g c h a r a c t e r is t i cs :

1. T h e r e i s a de f i n it e c r i t e r i o n f o r t e st i ng a ny p r o po s e d s o l u t i o n , a nd am e c h a n i z a b l e p r o c es s f o r a p p l y i n g t h e c r i t e ri o n .2 . T h e r e i s a t l e a s t o n e p r o b l e m s p a c e i n w h i c h c a n b e r e p r e s e n t e d t h ei n i t ia l p r o b l e m s t at e , the goa l s t a t e , a nd a l l o t h e r s t a t e s t ha t m a y be r e a c he d ,o r c o n s i d e r e d i n t h e c o u r s e o f a t t e m p t i n g a s o l u t i o n o f t h e p r o b l e m .

3 . A t t a i n a b l e s ta t e c ha nge s ( l ega l move s ) c a n be r e p r e s e n t ed i n a p r ob l e ms pa ce , a s t r a ns i t i ons f r om g i ve n s ta t e s t o t he s t a t e s d i r e c t ly a t t a i na b l e f r o mt h e m . B u t c o n s i d e r a b le m o v e s , w h e t h e r l e ga l o r n o t , c a n a l s o b e r e p r e s e n t e d - -t h a t i s, a ll t r a n s i ti o n s f r o m o n e c o n s i d e r a b le s ta t e t o a n o t h e r .

4 . A n y k n o w l e d g e t h a t t h e p r o b l e m s o lv e r c a n a c q u ir e a b o u t t h e p r o b l e mc a n b e r e p r es e n t e d in o n e o r m o r e p r o b l e m s p ac e s.

5 . I f t h e a c t u a l p r o b l e m i n v o l v es a c t in g u p o n t h e e x t e r n a l w o r l d , t h e n t h ed e f i n it io n o f s t a te c h a n g e s a n d o f t h e e f fe ct s u p o n t h e s t at e o f a p p l y i n g a n yo p e r a t o r r e f le c t w i t h c o m p l e t e ac c u r a c y i n o n e o r m o r e p r o b l e m s p a ce s t h el a w s ( la w s o f na t u r e ) t ha t gov e r n t he e x t e r na l w or l d .

6 . A l l o f t he s e c ond i t i on s ho l d i n t he s t r o ng s e nse t ha t t he ba s i c p r oc e s s e sp o s t u la t e d r e q u ir e o n l y p r a ct ic a b le a m o u n t s o f c o m p u t a t i o n , a n d t h ei n f o r m a t i o n pos t u l a t e d i s e f fe c ti ve ly a va i l a b l e t o t he p r oc e s s e s - - i . e ., a v a i l a b l ew i t h t h e h e l p o f o n l y p r a c t i c a b l e a m o u n t s o f s e ar c h.A s I ha v e w a r ne d , t he s e c r i t e r i a a r e n o t e n t i r e l y de f in i te . M or e ov e r ,p h r a se s l i k e ' p ra c ti c a b le a m o u n t s o f c o m p u t a t i o n a r e d e fi n ed o n l y re l at iv e l yt o t h e c o m p u t a t i o n a l p o w e r ( a n d p a t i e n c e ) o f a p r o b l e m s o lv i n g s y s te m . B u tt h i s va gue ne s s a n d r e l a t i v i t y s i mp l y r e fl ec t, a s i s ha l l t r y t o s how , t hec o n t i n uu m o f de g re e s o f de fi n i te ne s s be t w e e n t he w e l l s t r uc t u r e d a nd i lls t r u c tu r e d e n d s o f t h e p r o b l e m s p e c tr u m , a n d t h e d e p e n d e n c e o f d e fi n it e n es su p o n t h e p o w e r o f th e p r o b l e m s o lv i n g t e c h n i q u e s t h a t a re a v a i la b l e .2 1 The G eneral Problem S olver

I f a p r o b l e m h a s b e e n f o r m u l a t e d i n s u c h a w a y t h a t i t c a a b e g i v e n t o ap r o g r a m l i k e t h e G e n e r a l P r o b l e m S o l v e r ( G P ~ ) , c a n w e s a y t h a t i t i s aW S P ~ B e f o r e G P S c a n g o t o w o r k o n a p r o b l e m , i t r e q u i r e s :

( 1) a de s c r i p t i on o f t he s o l u t i on s t a te , o r a t e s t t o de t e r m i ne i f t ha t s t a t eh a s b e e n r e a c h e d ;( 2 ) a s e t o f t e r ms f o r de s c r i b i ng a nd c ha r a c t e r i z i ng t he i n i t i a l s t a t e , goa lstate an d intermediate states;

( 3) a s e t o f o p e r a to r s t o c h a n g e o n e s t a t e i n t o a n o t h e r , t o g e t h e r ~ i t h c o n -d i t i o n s f o r t h e a p p l i c a b il i ty o f t h e se o p e r a t o r s ;

(4) a se t o f d if f e rences , an d t e s t s to de tec t th e pre sence o f these d i f fe rencesbe t w e e n p a i r s o f s ta t e s ;

r t i f i c ia l In te l l igence 4 1 9 7 3 ) , 1 8 1 - 2 0 1


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184 HERBERT A. SIMON(5) a t ab le of connec t ions asso c ia t ing wi th each d i f fe rence one or m ore

opera tors tha t i s re l evant to reduc ing or removing tha t d i f fe rence .The f i r s t t h ree requi rement s for pu t t ing a problem in a form su i t ab le for

G PS correspond c lose ly to the f ir s t t h ree charac te r i s t ics of a W SP. Th efou r t h and f i f t h r equ i rem en t s fo r pu t t i ng a p rob l em i n a fo rm su i t ab l e fo rG PS co r re spond c lo sel y t o t he fou r t h cha rac t e r i s ti c o f a W SP. S ince G PSope ra t e s on t he fo rm a l l y p re sen t ed p rob l em , and no t o n a n ex t e rna l r ea lw or l d , t he f if th r equ i rem en t fo r a W SP a ppea r s i r r el evan t t o G P S .

In ou r descr ip t ion of the condi t ions for G PS ' s appl i cab i l it y , i t i s impl ic i ttha t t he s ix th requi rement for WSPs i s a l so sa t i s f i ed , for the opera tors andt e s t s m en t i oned above can a l l p re sum ab l y be execu t ed w i t h r ea sonab l eam oun t s o f com pu t a t ion . Th i s does o t i m p l y , o f cou r se , t ha t an y p rob l empresen t ed t o G PS w i t h in t he def ined dom a i n can be so lved w i t h on l y r ea son -ab l e am oun t s o f com p u t a t ion . M any p rob l em s m ay no t be so lvab le a t a ll .O f those t ha t a re so l vab le i n p ri nc ip le , m an y m ay requ ire i m m ense n um bersof appl i ca tions o f ope ra tors an d t es ts for the i r so lu t ion , so tha t t he to t a lam ou n t o f com pu t a t i on r equ i red m a y be i m prac ti ca l.

Thus , i t w ou l d appea r a t f i r s t b l u sh t ha t a l l p rob l em s t ha t can be pu t i np r o p e r f o r m f o r G P S c a n b e r eg a r d ed a s W P S s . B u t w h a t p r o b l e m d o m a i n ssa t i s fy these , o r s imi l a r , requi rem ent s? Le t us examine a co uple of poss ib leexamples .L2. Is theorem proving a W S P ?

Cons i de r w ha t w ou l d ap pe a r t o be an ex t r em e exam pl e o f a W SP : d i scove r-ing ~he pr oo f of a theorem in form al log ic . Co ndi t ion 1 fo r a W SP wi ll besa t is f i ed i f we have a m echanica l p r oo f checker . Con di t ion 2 might b eregarded as sa t i s f i ed by ident i fy ing the problem space wi th the space ofobjec t s tha t ca n be descr ibed in t e rms of wffs . How ever , we sh ould no tetha t l imi ting the problem so lver in th i s wa y exc ludes it f rom even con s ider ingexpress ions tha t a re no t wffs .The same reserva t ion m ust be mad e wi th respec t to Co ndi t ion 3 : def in it ionsof the ax ioms, the ru les of in fe rence , and the processes for app ly ing the l a t t e rde t e rm i ne t he l ega l m oves and a t t a i nab l e s t a t e changes ; bu t t he p rob l emsolver may wish to cons ider in ferences wi thout de te rmining in advancet ha t t hey m ee t a ll t he cond i t ions o f l eg a l i t y ' - - e . g . , w o rk i ng backw ardsf rom unpro ved wffs . He nce the se t o f cons iderab le m oves i s no t de te rminedunique ly by the se t o f lega l moves .

Sa t i s fy ing C ond i t ion 4 is even more problem at i c . T here i s no d i ff icu lty aslong as we res t r i c t ourse lves to the objec t l anguage of the log ic under con-s idera t ion . But we have no reason to exc lude meta l ingui s t i c knowledge ,knowledge expressed in a model space , o r even ana logica l o r metaphor i ca lknow l edge . A h um an t heo rem p rove r , u s ing a m e t a language , m ay p rove a

r t i f ic ia l In te l l igence 4 1973), 181-201


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TH E STRU CTU RE O F I LL STRU CTU RED PRO BLEMS 1.85theorem tha t i s no t p rovab le i n t he ob jec t l anguag e ; o r m ay use a t ru th t ab l eas a m ode l fo r so lv ing a p rob lem in t he p ropos i t i ona l ca l cu lus ; o r m ay uset h e p r o o f o f o n e t h e o r e m a s a n a n a lo g i ca l g u i de t o t h e p r o o f o f a n o t h e r t h a tseems, in so m e respec t, to be s im i la r to the f i rs t.O f cour se t he re i s no th ing m ag ica l he re i n t he p rob lem so lve r be ing hum an .M echan ica l syst ems can be , an d have bee n , g iven the same k in ds o f capa -b i li ti es . (Fo r an exam ple o f t he use o f m e ta l ingu i s t i c t echn iques i n theo remproving , see [9] ; for the use o f ana logies , see [3] ). Wh at some not io ns of wel l -s t ruc turedness requi re , however , i s tha t these capabi l i t i es be def ined inadvance , an d tha t w e do n o t a l l ow the p rob lem so lve r t o in t roduce newresources tha t oc cu r to h im in the course of h i s so lu t ion e f fort s . I f th i scond i t i on i s imposed , a p rob lem tha t admi t s r e s t ruc tu r ing th rough thein t roduc t ion o f such new re sources w ou ld be an i ll s t ruc tu red p rob lem.

A p r o b l e m t h a t i s n o t s o lv a b le w i t h r ea s o n a b le a m o u n t s o f c o m p u t a t i o nwh en a l l knowledge mus t be expres sed in te rms o f t he o r ig ina l p rob lem spacem ay be eas / ly so lvable i f the so lver i s a l lowed to (or has the w i t s to) useknow ledge in another space . I t fo l lows tha t , und er :. l i t e ra l in te rp re ta t ion ofCo nd i t i on 4 , p rob lems o f d i scove ring p roof s i n fo rma l log ic a r e no t , f o r a l lpro ble m solvers , wel l s t ruc ture d?C on di t io n 5 i s a lways sa ti s fied in th eorem prov ing s ince there i s no ex te rna l

rea l wo r ld to be conce rned about . C on di t io n 6 i s usua l ly sa t is f ied , asfa r as the bas ic processes a re concerned . Never the less , because of theenorm ous spaces to be sea rched , con tempo ra ry m echan ica l t heo rem p rover s ,confro nted wi th d i f ficu lt theorems, usua l ly fa i l to f ind proofs . I t i s somet ime ssa id t ha t t hey cou ld on ly succeed i f endowed wi th i ngenu i ty ; bu t i ngenu i ty ,whatever i t i s , genera l ly requi res v io la t ing Condi t ion 4- - -moving out in tothe b roa de r wor ld o f ISPs.2 3 I s chess p lay ing a W SP ?

Next t o t heo rem p rov ing , t he wor ld o f games wou ld appea r t o o f fe r t hebes t exam ples of wel l -s t ruc turedness . Al l of the reserva t ions , however , tha tapp l i ed to t he we l l -s t ruc tu redness o f t heo rem p rov ing app ly to gam e p l ay ingas wel l . In addi t ion , new reserva t ions a r i se wi th respec t to Condi t ion 1-the so lu t ion c r i t e r ion - - an d Con d i t i on 5 - - th e co r re spondence be tween theinne r wor ld o f t hough t a nd the ou te r w or ld o f ac t ion on r ea l ches s boa rds .Le t us con s ider these two m at te rs in m ore de ta i l .

I n bo th ca ses the d i f fi cu lty s t ems f rom the imm ense gap be tween com-pu tab i l i t y i n p r in ip le an d p rac t i ca l com putab i l i t y i n p rob lem spaces a s l a rgeN ot i ce t ha t w e a r e no t appea l i ng he r e t o f o r m a l undec i dab i l i t y o r i ncom pl e t enes s .O ur con ce r n t h r oug hou t i s w i t h e ff ec ti ve o r p r ac t i c ab l e so l vab i li t y u s i ng r ea sonab l e am o un t so f c o m p u t a t i o n . P r o b l e m s m a y b e a n d o f t e n a re ) u n s o l v a b l e in t h is p r a c ti c al s e n s e e v e n indom a i ns t ha t a r e l og ica ll y com pl e t e and dec i dab l e .

Art i f ic ia l In te l l igence 1973), 181-201


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86 HERBERT A. SIMONas t hose o f gam es l ike ches s. In p r inc ip le , t he concep t o f bes t mov e i swel l def ined; but in prac t ice , th i s concept has to be rep laced by , say , max-m iz ing some approx ima te eva lua t ion func t ion . W hen a ches s p l ay ing p rog ramhas foun d ( i f i t does) t he move tha t ma x imizes t h i s func t ion , i t c an s ti ll befa r f rom f ind ing the m ove tha t w i ll w in the gam e o f ches s - - a s t he m odes tab i l i ty of the bes t con tem pora ry prog ram s testi fies .In t e rms o f Co nd i t i on 5o i t is no t ha rd to de f ine t he W SP o f p l ay ing ana p p r o x i m a t e k i n d o f c h e s s , w h e r e w i n n i n g m e a n s m a x i m i z i n g t h epos tu l a t ed eva lua t ion func tion . B u t t he va lues o f moves a s ca l cu la t ed by theapprox ima te eva lua t ion func t ion a re s im ply a m eans fo r p red i c t i ng the ac tua lconsequences o f t he moves in t he r ea l gam e ou t s ide . Fee dbac k in t e rms o fthe expec t ed o r unexpec t ed moves o f t he opponen t and the expec t ed o runexpec ted boa rd s i tua t ions a r is ing f rom those m oves cal l s fo r new ca l cu l a-t i ons by the p rob lem so lve r t o mak e use o f t he new in fo rm a t ion tha t emerges.

Th e i ll - s truc turedness , by the usu a l c r i te r ia , o f chess p la y in g become s fu l lyev iden t when we cons ide r t he p l ay o f an en t i r e game , and do no t conf ine ou rv i ew to j u s t a s ing l e move . T he move in t he r ea l game i s d i s ti ngu i shed f rommoves in dynamic ana lys i s by i t s i r r evocab i l i t y - - i t ha s r ea l consequencestha t canno t be undone , and tha t a r e f r equen tly d i f fe r en t f rom the con-sequences t ha t we re an t i c ipa t ed . P l ay ing a gam e o f ch es s - -v i ew ing th isac t iv ity a s so lv ing a s ing l e p rob lem - - invo lv es con t inua l ly r ede f in ing wha t t hepro blem is. Even i f we regard chess p lay ing as a W SP in the sm al l ( i.e ., du r ingthe course of cons ider ing a s ingle move) , by m ost c r i te r ia i t mu s t be regarde das a n ISP in the la rge i. e. , over the course of the game) .2 4 S u m m a r y : T h e e lu s iv e n e ss o f s tr u c tu r e

As our two exam ples show, de f in i tenes s o f p rob lem s t ruc tu re i s l a rge ly ani l lu s ion tha t a r is e s wh en we sys tema t i cal ly confound the i dea li zed p rob lemtha t i s presented to an idea l ized (an d u nl im i ted ly pow erfu l ) proble m solverwi th t he ac tua l p rob lem tha t i s t o be a t t acked by a p rob lem so lve r wi thl imi ted (even i f l a rge) com puta t ion a l capac i t ies . I f form al com ple teness anddec idab i l it y a r e r a r e p rope rt ie s i n t he wor ld o f com plex fo rm a l sys tems ,ef fec tive def inabi l i ty i s equa l ly ra re in the rea l wor ld o f la rge problem s.

In gene ra l, t he p rob lems p re sen ted to p rob lem so lve r s by the wo r ld a r ebes t r ega rded a s ISPs . They become WSPs on ly in t he p roces s o f be ingprep ared for the pro ble m solvers. I t i s no t exaggera t ing m uch to say tha t therea re no WSPs . on ly ISPs tha t have been fo rma l i zed fo r p rob lem so lve rs .

A s tanda rd pos ture in a r t if ic ia l in te ll igence work , a nd in theo r iz ing in th i sf ield , has been to con s ider on ly the idea l ized problem s, an d to leave thequa l i t y o f the approx ima t ion , an d the p roces ses fo r fo rm ula t ing tha t app rox i -m a t ion to i n fo rma l d i scussion ou t side the scopes bo th o f t he t heo ry an d o fthe p ro b lem so lv ing p rograms . T h i s i s a de fens ib le s tr a tegy , cow m en to m an y

r t i f ic ia l In te l l igence 4 1973 ), 181-201


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THE STRUCTURE OF ILL STRUCTURED PROBLEMS 187f ie lds o f in te l lec tua l inq ui r y ; but i t encou rages a l lega t ions tha t the rea l 'p rob lem so lv ing ac t iv i ty occu r s w h i le p rov id ing a p rob lem wi th s t ruc tu re ,a n d n o t a f te r th e p r o b l e m h a s b e e n f o r m u l a t e d a s a W S P . A s N e w e l l a n d Iha ve obs erve d else~,vhere[7, p . 850, footno te 20] these al legat ions are refuteds imply by observ ing tha t ' i f [ they] were cor rec t, an d tasks f ro m th e sam eenv i ronm ent were presented sequent i' ,d ly to a subjec t , on ly the f ir s t o f themwould p re sen t h im wi th a p rob lem, s ince he w ea ld no t need to d e t e rmine anew p rob lem space and p rogram fo r t he subsequen t t a sks . Neve r the l e s s ,t he re i s me r i t t o t he c l a im tha t m uch p rob lem so lv ing e f fo r t i s d ir ec ted a ts t ruc tu r ing p rob lems , and on ly a f r ac tion o f i t a t so lv ing p rob lem s once theyare s t ructured.

3 I l l Structured P r o b l e m sPerhaps som e th ing i s t o be l ea rned by tu rn ing the q ues t ion a round . W e havegene ra lly a sked how p rob lem s can be p rov ided wi th su ff ic ien t s t ruc tu re sotha t p rob lem so lve rs l ike G PS can go to wo rk on them. W e m ay a sk in s t eadhow p rob lem so lve rs o f f ami l i a r k inds can go to wo rk even on p rob lem s tha ta rc , in impor tan t respec ts , i l l s t ruc tured . S ince the problem domains tha thave been mo s t exp lo red wi th mechan ica l t e chn iques f a il i n s eve ral ways tosa ti s fy t he r equ i remen t s fo r W SPs , pe rha ps we have exagge ra t ed theessent ia li ty of def in ite s t ruc ture for the app l icabi l i ty an d e f ficacy o f thesetechniques . Perhaps the t r icks tha t h ave wo rked in re la tive ly wel l s t ruc tureddom ains can be ex t ended to o the r d om a ins tha t l ie f a r ove r t owa rd the ISPend o f t he spec trum.To explore th i s poss ib i l i ty , we wi l l aga in e xam ine severa l exam ples . E achexam ple wi l l i llus t ra te som e spec if ic face t (or severa l fa ce ts )o f i l l- s t ruc tured-hess. A naly s i s of these face ts wi l l p rovide us w i th a pos i tive chara c te r iza t ionof ISP% re scu ing them f rom the s t a tus o f a r e s idua l ca tegory . W i th t h i spos i t ive charac te r iza t ion in ham i , we wi l l be in a be t te r pos i t ion to se t for ththe capab i l i t ie s a p rob lem so lv ing syst em mu s t have in o rde r t o be ab l e t oa t tack pro blem s tha t a re in i t ia l ly i l l s t ruc tured i:~ one or m ore w ays .3 1 D e s i g n i n g a h o u s e

I t w i ll gene ra lly be ag reed tha t t he wo rk o f an a r ch i t ec t - - i n des ign ing ahouse, s ay - -p re sen t s t a sks t ha t l i e we l l t oward the i l l s t ruc tu red end o f t hep rob lem con t inuum . O f course t h i s i s on ly t rue i f t he a r ch i tec t i s try ing to bec re a t iv e - - i f he does no t beg in the t a sk by t ak ing o f f h i s she l f one o f a s e to f s tan dar d house des igns tha t he keeps there .Th e d es ign task (w i th th i s proviso) i s i ll s t ruc tured in a nu m be r o f respects.The re i s in i t i a l ly no def in i te c r i te r ion to test a pro pose d so lu t ion , m uc h lessa m echan izeab le p roces s t o app ly the c r i t er ion . The p rob lem space i s no tde f ined in an y m ean ingfu l way , fo r a de f in i ti on wo u ld have to encom pass

r t i f i c ia l In te l l igence 4 1973), 181-201


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18 8 HERn~.R1 A. s ~ o N

a l l k inds of s t ruc tures the a rchi tec t might a t some poin t cons ider (e .g . , ageodes ic dome, a t russ roof , a rches , an A-f rame, cant i levers , and so on andon) , a l l cons iderable mater ia l s (wood, meta l , p lex ig lass , i ce - -before youob ject , I m us t r em ind yo u i t s been don em re in fo rce d conc re t e , c am e l s h ides,f ie ld s tone , Ve rm on t marb le , New H am psh i r e g ran i te , syn the t i c rubbe r , . . . ) ,a l l des ign processes and organiza t ions of des ign processes ( s ta r t wi th f loorp l ans , s t a rt w i th l is t o f func t iona l needs, s t a rt w i th f ac ad e , . . . ) .The hope les sness o f even t ry ing to ske t ch the conge ri e s o f e l emen t s t ha tm igh t have to be i nc lude d in t he spec i fi ca tion o f a p rob lem space p roves t heg rea te r hope le s sness o f de f in ing in r ea sonab le com pass a p rob lem space tha tcou ld no t , a t any t ime d u r ing the p ro b lem so lv ing p roces s, f i nd i ts boun da r i e sb reached by the i n t rus ion o f new a l t e rna t ives . The second , t h i rd , an d tbu r thcha ract e ri s ti c s o f a W SP appea r , t he re fo re , t o be absen t f rom the housedes ign problem.Th e f i f th charac te r i s t ic i s al so lacking . O ne th ing an a rchi tec t of ten does i sto m ake r ende r ings o r mo de l s o f the p ro j ec t ed s truc tu re . H e d oes t h i s pa r t l ybecause these p roduc t ions p red ic t , more accu ra t e ly t han o the r means ,proper t ies tha t the rea l -w or ld s t ruc ture wi l l possess i f i t i s ac tua l ly bui l t.V iewing a mode l , the a r ch it ec t can de t ec t r e la t ions am on g co m pone n t s o f t hedes ign tha t w ere no t ava i l ab l e t o h im d i r ec tly from h i s p l ans . O f cour se , eventhe render ings an d m od els fa ll fa r s hor t o f predic t ing the ac t~ al charac te r i s t icso f t he r ea l bu i ld ing , o r t he w ay in wh ich the l aws o f na tu re w i ll ope ra te upo ni t and a ff ec t i t. H ence , wh i l e F ran k L loy d W r igh t was no t g rea t ly d i s tu rbedby a leaking roof , i t can ha rd l y be supposed tha t he des igned h is roofs to leak ,wh ich they o f ten d id . No r was the ac tion o f New Y ork s a tm osphe re on thesu r f ace o f t he Seagram Bu i ld ing , and i t s consequen t change o f co lo r ,predic ted . Doors s t ick , foundat ions se t t le , par t i t ions t ransmi t noise , andsome t imes even ha pp y acc iden ts ( examples o f t he se a r e ha rde r t o come by)consp i r e to m ake the bu i ld ing a s i t a c tua l ly ex is ts and i s u sed som e th ingd i f fe r en t f rom the bu i ld ing o f the p l ans .F ina l ly , even i f we were t o a rgue th a t t he p rob lem space can r ea lly bede f ined - - s ince any th ing the a rch i tec t t h inks o f mus t som ehow be gene rat edf rom, o r d redged f rom, h i s r e sources o f memory o r h i s r e f e rence l i b ra ry - -som e o f t h i s i n fo rma t ion on ly shows up in l a t e s tages o f t he des ign p rocessa f t e r la rge am oun t s o f s ea rch ; and som e o f i t shows up , w hen i t does , a lmos tacc identa l ly . Hence , the problem is even less wel l def ined when cons ideredf r o m t h e s t an d p o i n t o f w h e t i s a c t u a ll y k n o w n a t a n y p o i n t i n t i m e t h a n w h e ncons ide red f rom the s t andpo in t o f wha t i s knowab le , even tua l ly and inpr inc ip le .

Al l o f th i s wou ld seem to m ake des ign ing a house a ve ry d i ff e r en t m a t t e rf rom us ing GP S to so lve the mi s s iona r ie s and cann iba l s puzz le , o r f romdiscover ing the proof of a theorem in the predica te ca lcu lus . I t sure ly i s

r t i f ic ia l In te l l igeRce 4 1973), 181-201


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THE STRUCTURE OF ILL STRUCTURED PRO LEMS 89

d i f f e r e n t , b u t I s h a l l t r y i n t h e n e x t p a r a g r a p h s t o s h o w t h a t u n d e r s t a n d i n gw h a t t h e a r c h i t e c t d o e s g o e s f a r t o w a r d b r i d g i n g t h e g u l f b e t w e e n t h e s ep r o b l e m d o m a i n s . I n t h i s I s h a l l b e f o l l o w i n g q u it e c lo s e ly t h e p a t h f ir stb l a z e d b y W a l t e r R e i t m a n [1 1, oh . 8 ] i n h i s a n a l y s is o f t h e t h i n k i n g - a l o u dp r o t o c o l o f a c o m p o s e r w r i ti n g a f u g u e. I t s h o u l d n o t , o f c o u rs e , a p p e a rs u r p r is i n g t h a t a h o u s e - d e s i g n i n g p r o c es s w o u l d h a v e m u c h in c o m m o n w i t ha p r o ce s s o f m u s ic al c o m p o s i t i o n . S h o w i n g t h a t t h e y d o h a v e m u c h i nc o m m o n is cr it ic a l t o t h e a t t e m p t h e r e to p r o v i d e a p o s i ti v e e h a r a c t e r i ~ t i o no f t he p r oc e s se s f o r s o l v i ng I SPs.3.2 . T he architect s processes

R e i t m a n u s es th e t e r m " c o n s t r a i n t s " q u i t e b r o a d l y to r ef er t o a n y o r a ll o ft he e l e me n t s t ha t e n t e r i n t o a de f i n i t ion o f a p r ob l e m. H e o bs e r ve s [11,p. 169]:

"'One of the interesting features of many o f the problem in sta nc es. . , is that eventhough th ey generally w ou ld be considered com plex, they include ver y few constraintsas given. Com posing a fugue is a good exam ple. H ere the m ain initial constraint, andit is an open constraint at th at [i.e.. on e that is incom pletelyspecified], is th at the endproduct be a fugue. All oth er constraints are in a sense supplementary,generated fromone transformation of the problem to the nex t."S i m i l a r ly , t he a r c h i t e c t be g i ns w i t h t he s o le p r o b l e m o f de s i gn i ng a hous e .T h e c l i en t h a s p r e s u m a b l y t o l d h i m s o m e t h i n g o f h is n ee d s, in t e r m s o f f a m i ly

s iz e o r n u m b e r o f r o o m s , a n d h i s b u d g e t ( w h i c h t h e a r c h i te c t w i l l m u l t ip l yby 1 .5 o r 2 be t b r e a c c e p t i ng i t a s a c ons t r a i n t ) . A dd i t i ona l spe c i f ic a t ion w il lb e o b t a i n e d f r o m t h e d i a l o g u e b e tw e e n a r c h i t e c t a n d c li e n t, b u t t h e t o t a l i t y o ft ha t d i a l og ue w i ll s ti ll l e a ve t he de s i gn goa l s qu i t e i n c om pl e t e l y s pec if ie d .T h e m or e d i s t i ngu i s he d t he a r c h i t e c t , t he l e ss e xpe c t a t i on tre at the c l i e n t s ho u l dp r o v i d e t h e c o n s t r a in t s .3.2.1. E v a l ~ a t i n o d t e s p e c i f i c a t io n s

W e c a n i m a g i n e a d e s i g n p r o c e s s t h a t p r o c e e d s a c c o r d i n g t o t h e f ol lO w i n ggenera l sch em e . Tak ing the in i t ia l goa l s and co nstra int s , the archit ec t beg inst o d e r i v e s o m e g l o b a l sp e c if ic a t io n s f r o m t h e m - - p e r h a p s t h e s q u a r e f o o t a g eo r c u b i c f o o t a g e o f t h e h o u s e a m o n g t h e m . B u t t h e t a s k i ts e lf , " d e s i g n i n g ah o u s e " , e v o k e s f r o m h i s l o n g - t e r m m e m o r y a l is t o f o t h e r a t tr i b u t e s t h a t w i lha ve t o be s pe c if ie d a t a n e a r l y s t a ge o f t he de s i g n : c ha r a c t e r i s ti c s o f t he l o ton w h i c h t he hous e i s t o be bu i l t , i t s ge ne r a l s t y l e , w he t he r i t i s t o be on as i ng le le ve l o r m u l t i - s to r i e d , type o f fr a me , t yp e s o f s t ruc t u r a l m a t e r i a l s a n do f s h e a t h i n g m a t e r ia l s, a n d s o o n . T h e t a s k w i ll a l s o e v o k e f r o m m e m o r ys o m e o v e r - a l l o r g a n i z a t i o n , o r e x e c u t i v e p r o g r a m , f o r t h e d e s i g n p r o c e s sitself. Ar tificial lntelh gence 4 (I973), 181-201

15


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190 HERBERT A. S I MONNei ther the gu id ing organ iza t ion nor the a t t r ibu tes evoked f rom m em oryneed a t a ny t ime during the process :;: 3vide a complete proc edure no r com -ple te information for designing a house . As a matter of fac t , the entire

procedure could conceivably be organized as a system of productions, inwhich the e lements a l ready evoked f rom memory and the aspec ts o f thedesign a lready arr ived a t up to any given poin t , w ould serve as the st imu li toevoke the next set of elements.W hether o rgan ized as a system of p roduc t ions o r as a sys tem of sub ,rou t ine ca l l s , the evoca t ion o f re levan t in format ion and subgoa is f romlong-term m em ory can be sequentia l. A s R eitm an says of the fugue [11,p. 169]:' J u s t a s 's en tence t r ans f o r m s t o ' s ub j ec t p l u s p r ed i ca t e ' , and ' s ub j ec t ' m ay t r ans f o r m

t o ' a r ti c le p l u s n o u n p h r a s e ' . . . , s o 'f u g u e ' m a y b e t h o u g h t o f a s t r a n s fo r m i n g t oexpos i t i on p l us deve l opm en t p l u s conc l us i on ' , ' expos i t i on ' t o ' t hem a t i c m a t e r i a l p l u sc o u n t e r m a t e r i a r , a n d ' t h e m a t i c m a t er ia l ' t o ' m o t i v e p lu s d e v e lo p m e n t o f m o t i v e ' .Ap ply ing the same l ingu ist ic m etaphor to house des ign , ho use migh tt ransform to genera l f loor p lan p lus s t ruc tu re , s t ruc tu re to sup por tp lus roof ing p lus shea th ing p lus u t i li t ie s , u t i l i tie s to p lum bing p lusheating system plus electrical system , and so on.Th e requirements tha t any of these com pon ents sh ould mee t can a lso beevoked a t appropria te t imes in the design process, and need not be specif iedin advance . Considera t ion o f the hea ting sys tem can evoke f rom the a rch i-tec t ' s long- te rm memory (o r the appropr ia te re fe rence handbooks) tha t thesys tem should be des igned to m ain ta in a tem pera tu re o f 70 , tha t the m in imumouts ide tempera tu re to be expec ted i s - 5 tha t the hea t t ransmiss ioncoeff ic ient o f the p roposed shea th ing i s kB TU per ho ur pe r square foo t pe rdegree o f tem pera ture differential, an d so on.Design a l ternat ives can a lso be evoked in component-by-componentfashion. The subgoal o f designing the heat ing system m ay lead the architec t

to consider various fuels and various distr ibution systems. Again, the sourceof these genera to rs o f a l te rna t ives i s to be found in h is long- te rm memoryand reference facilities (including his access to specialists for helping designsome of the component systems).The whole design, then, begins to acquire structure by being decomposedinto various problems of component design, and by evoking, as the designprogresses, a l l k inds of requirements to be applied in test ing the design ofi ts com ponents. D uring an y given short period o f t ime, th e architec t w il l f indhimself working on a problem which, perhaps beginning in an i l l s t ructuredsta te , soon conver ts i t se l f th rough evoca t ion f rom m em ory in to a we l ls t ruc tu red p rob lem. We can make here the same comment we made abou~playing a che~,g gam e: the problem i~ well s trv~tured ia the sm all , ba t i l lstructured in the large.

rfbeWial Intelligence 4 (1973) , 181-201


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THE STRUCTURE OF ILL STRUCTURED PROBLEMS 1913.2.2. Coordination o f the design

Now som e obv ious d if f icu l ti e s can a r i s e f rom so lv ing p rob lem s in t h i smanne r . In t e r r e l a t i ons among the va r ious we l l s t ruc tu red subprob lems a rel ike ly to be neglec ted or underem phas ized . Solu t ions to par t icu la r sub -p rob lem s a re ap t t o be d i s tu rbe d o r un don e a t a I a te r s tage when new aspec t sa re a t t ended to , and the cons ide ra t ions l ead ing to t he o r ig ina l so lu t ionsforgot ten or not not iced . In fac t , such unwanted s ide e f fec ts accompany a l ldes ign processes tha t a re as complex as the a rchi tec tura l one we are con-s idering . A s a resu lt , whi le the f ina l prod uct m ay sa t i s fy a l l the req ui rem entstha t a r e evoked w hen tha t f i na l p roduc t i s t e s ted , i t m ay v io la t e som e o f t herequ i r emen t s t ha t we re imposed ( and t empora r i l y s a t i s f i ed ) a t an ea r l i e rs tage of the des ign . The a rch i tec t m ay or m ay not be aware o f the v io le .tion .Some o the r appropr i a t e des ign c r i te r i a m ay s im ply r ema in do rm an t , neve rhav ing been evoked du r ing the des ign p rocess .The dange r o f i ncons is t enci e s and l acunae o f t he se k inds i s mi t iga t ed tosome ex ten t by tha t p a r t o f t he a r ch i tec t 's sk i l l t ha t i s imbedded in t he ove r -a l lo rgan iza t ion o f h i s p rog ram fo r design . Pa r t o f h i s p ro fe s siona l t r a in ing an dsubsequen t l ea rn ing i s d i r ec t ed to o rgan iz ing the p roces s i n such a way tha tthe ma jo r in t e r ac tions am on g com ponen t s wi l l be t aken ca re o f. Ce r t a in waysof d iv id ing the who le t a sk in to pa r t s w i l l do l e ss v io l ence to t hose i n t e r ac tionsthan o the r ways o f d iv id ing i~ - -~ , good p rocedure wi l l d iv ide the t a sk in tocom ponen t s tha t a r e a s nea r ly s e l f - con ta ine~ a s poss ib le [1 ]. .Ea r ly s tageso f t he des ign ca~ a l so e s t ab l i sh g loba l pa ram e te r s w h ich then becom e con-s t r a in t s ope ra t ing on each o f t he componen t s t o wh ich they a re r e l evan t .Thus gene ra l dec i sions abo u t s ty l e can impose cons t ra in t s on the s ty li st icdec i sions abo u t pa r t i cu l a r po r t i ons o f t he house .M uch o f t he coord ina t ion o f t he va r ious we l l s t ruc tu red des ign sub ta sks i sim p l i c i tm bu i l t i n to t he o rgan iza t ion o f t he who le p roces s. T o the ex t en t t ha tth i s is so , the loca l des ign ac t iv i ties a re gu aranteed to m esh in to a reasona bleove r-a ll st ruc tu re . T h i s m eans tha t t he f i na l p roduc t m ay be ve ry muchinf luenced by the order in w hich the des ign s teps a re tak en up . A s a resu lt ,d i f fe rences in s ty le be tween d i f fe rent des igns can resu l t as read i ly f rom theorgan iza t ion o f the des ign proce ss as f rom expl ic i t dec is ions of the a rchi tec tto spec i fy one s ty le or ano ther . I f the process ca l l s for des igning the facadebefore the f loor p lan , d i f fe rent k inds o f des igns wi l l emerge than i f the processca l l s for spec i fy ing the ro om ar ran gem em s before the facade [13] .3,2.3. The over all design process

The des ign p roces s ske t ched above ca r be com posed f rom a com bina t ionof a G PS , wh ich a t any g iven m orne r : f i nds i t s e l f work ing on som e we l ls t ruc tured subproblem, wi th a re t r ieva~ sys tem, which cont inua l ly modi f ies

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1 9 2 ~ A S I M O N

t he p rob lem space by evok ing f rom long- t e rm memory , new cons t r a in t s ,new subgoals , and new genera tors for des ign a l te rna t ives . We can a l so v iewthis re t r ieva l sys tem as a recogni t ion sys tem tha t a t tends to fea tures in thecu r ren t p rob lem space and in ex t e rnal me m ory ( e.g ., m ode l s an d d rawings ) ,ano , r ecogn izing f ea tu re s a s f ami l i a r , evokes r e levan t i n fo rm a t ion f romm em ory wh ich i t adds t o t he p rob lem space (o r subs ti tu t e s fo r o the r i n fo rma -t ion cur ren t ly in the pr ob lem space). Th e re t r ieva l sys tem, then , i s capa ble ofin t e r rup t ing the ongo ing p roces ses o f t he p rob lem so lv ing sys t em. Aschemat ic f low diagram for a sys tem wi th these charac ter i s t ics i s shown inFig. 1.

P R O B L E MC L V E R

E X T E R N A LE N V I R O N M E N T

L O N G - T E R MM E M O R Y

I M M E D I A T EP R O B L E M S P A C E

(Goa ls ; cons t ra in ts ; s pec i f i ca -t i o n s ; & a l t e r n a t i v e g e n e r a t o r s l

I_ _ [ N O T I C I N G_ T [ E V O K I N G- - ~ _ ] f I E C H A N I S M)

FIG . I . Schem a t i c d i ag r am o f a sys t em f o r ill s t r uc t u r ed p r ob l em s . I t sho w s t he a l t e r na t i onb e t w e e n a p r o b l e m s o l v e r w o r k i n g o n a w e ll s t r u c tu r e d p r o b l e m , a n d a r e c o g n i t io n s y s t e mc o n t i n u a ll y m o d i f y in g t h e p r o b l e m s p a ce .One migh t a sk wh y the sys tem is o rgan ized in t h i s f a sh ion - -w i th a l te rna -t i on be tween p rob lem so lv ing in a ( loca lly ) we l l s t ruc tu red p rob lem space and

m o d i f ic a ti o n o f t he p r o b l e m s p ac e t h r o u g h r e tr ie v a l o f n e w i n f o r m a t i o n f r o mlong- t e rm mem ory . The answer r evo lves a rou nd the bas i ca lly s e r ia l cha rac t e ro f t he p rob lem so lv ing sys tem. The p rob lem so lv ing p roces ses a r e capab le ,t yp ica l ly , o f t ak ing a few a rgum en t s a s i npu t s an d p roduc ing a sm a l l num bero f sym bol s truc tu re s a s ou tpu t s . T he re i s no way in wh ich a l a rge am ou n t o fin fo rma t ion can be b rough t t o bea r upon these p roces ses l oca l ly - - tha t i s ,over a shor t per iod of process ing . I f a la rge long- te rm m em ory i s assoc ia tedwi th a s e ri al p roces sor c f t h i s k ind , t hen m os t o f t he con ten t s o f l ong- t e rmm em ory wi ll be i rr e l evan t du r ing an y b r i e f i n t e rva l o f p roces s ing .

Cons ide r t he a l te rna tive , o f b r ing ing a l l o f t he po ten t i a l ly r e l evan t i n fo rm a-t ion in l ong- te rm m em ory toge the r once and fo r a l l a t t he ou t se t, t o p rov ide awe l l s t ruc tu red p rob lem space tha t does no t change du r ing the cour se o fthe p rob lem so lv ing e ffo rt . On e mus t a sk b r ing ing i t t oge the r whe re?Presum ab ly i t cou ld a l l be a s sem bled in som e des igna ted pa r t o f l ong- te rm

r t i f ic ia l In te l l igence 4 1973) , 181-201


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THE STRUC IURE OF ILL STRUCTURED PROBLEMS 193m e m o r y . B u t t o w h a t p u r p o s e ? R e t r i e v a l p r o c e s se s w o u l d s ti ll b e n e c e s s a r yf o r t h e s e r ia l p r o b l e m s o l v in g p r o c es s e s t o d is c o v e r t h e i n p u t s t h e y n e e d e d a tt h e t i m e t h e y n e e d e d t h e m . T o t h e o u t s i d e o b s e r v e r , th e c o n t i n u i n g s h if t i na t t e n t i o n f r o m o n e p a r t o f t h e a ss e m b l e d t a s k in f o r m a t i o n t o a n o t h e r w o u l ds ti ll l o o k l i k e a s e r ie s o f t r a n s f o r m a t i o n s o f t h e p r o b l e m s p a c e.

I n t h e o r g a n i z a t i o n d e s c r i b e d i n F i g . 1, t h e r e i s n o n e e d f o r t h i s i n i ti a ld e f i n i t i o n o f t h e p r o b l e m s p a c e a n d t a s k s t r u c t u r e . A l l o f th e n e c e s s a r yd e f i n i t o r y i n f o r m a t i o n i s p o t e n t i a l ly a v a i la b l e , b u t d i s t r ib u t e d t h r o u g hl o n g - t e r m m e m o r y . I t i s r e t r i e v e d t h r o u g h t w o m e c h a n i s m s : f ir st , t h e n o r m a ls u b r o u t i n e s t r u c t u r e , w h i c h e n a b l e s p r o c e s s e s t o c a l l s u b p r o c e s s e s a n d t op a ss i n p u t a n d o u t p u t i n f o r m a t i o n f r o m o n e t o a n o t h e r ; s e c on d , t h e e v o k i n gm e c h a n i s m , w h i c h r e co g n iz e s w h e n c e r ta i n i n f o r m a t i o n h a s b e c o m e r e le v a n t,a n d p r o c e e d s t o r e tr ie v e t h a t i n f o r m a t i o n f r o m l o n g - te r m m e m o r y .3 3 D e s i g n a s a n o r g a n i z a t i o n a l p r o c e s s

I f t h is d e s c r i p t i o n o f h o w a n i l l s t r u c t u r e d p r o b l e m o f d e si g n c a n b eh a n d l e d s e e m s a t a ll f a n c i fu l , i ts r e a l is m c a n b e s u p p o r t e d b y c o m p a r i n g i tw i t h t h e d e s c r i p t i o n o f c o m p l e x d e s i g n p ro c e s s e s t h a t t a k e p l a c e i n o r g a n i z a -t io n s . L e t m e q u o t e a t l e n g t h t h e p ro c e s s, d e s c r i b e d b y S i r O s w y n M u r r a ys o m e f if ty y e a rs a g o , o f d e s i g n i n g a n d p r o d u c i n g a n e w b a t t le s h i p [5 ,p p . 2 1 6 - 2 1 7 ) :"W e s ta r t wi th the F i rs t Sea Lord and h i s Ass is tan t Ch ief o f Naval S ta ff l ay ing downin gene la t e rms the fea tu res tha t they desi re to see embo died in the new des ign--the speed, the rad ius of ac t ion, the offensive quali ties , the arm our p rotect ion. Th ere-upo n the D i rec to ry o f Naval Cons t ruc tion , ac ting under an d in consu l ta t ion wi th theCon trol ler , formulates provis ional schemes out l in ing the k ind o f ship desired togetherwith forecasts of the s ize and cost involved by the d ifferent arrangem ents . T o do th ishe : rod his officers m ust have a good genera~ kn ow ledg e--in i tself only at ta inable byclose relat ions with those in charge of these m at te rs- -of the lates t developmen ts andideas in rega rd to a g reat ran ge of subjects--gunnel 'y, torpe do, engineering, arm our ,f ire-control, navigat ion, s ignall ing, acc om mo dat ion, and so o n- -in orde r to be reason-ably su re tha t th e prov ision inc|~d ed in his schemes is likely to satisfy the experts in allthese subjects wh en the t ime for act ive coope rat ion arr ives .W i th these a l t erna t ive schemes befo re them, the Sea Lords ag ree on the genera ll ines of the new ship , which done , the actual pr epara t ion of the actual des igns begins.Th e dime nsions and shape o f the ship are d raw n ot~t approximately by the navalcons t ruc to rs. Th en the E ng ineer- in -Chief and h i s Depar tme n t a re ca l l ed in to ag reeup on the a rrangem ent of the propel l ing mac hinery , the posit ions of shafts, propel iers,bunkers , fumnels, e tc . , and a t the sam e t ime the coop era t ion o f the D i rec to r o f NavalO rdnan ce is required to set t le the posit ions o f the guns w ith their barbet tes , an d maga-zines and shell rooms an d th e m eans of supplying am mu nit ion to the gun s in act ion.

An unders tanding between these three main departments enables further progressto be m ade , The coopera t ion o f the Di rec to r o f Torpedoes and the D i rec to r o f Elec tr ica lEngineering is now cal led for to set t le the arrangements for torpedo armament ,electric generating machinery, electric l ighting, etc. So the design progresses and iselabora ted from th e Iowe ~ port ions upwards, a nd present ly the D irector o f Na valr t i f i c ia l In te l l igence 4 (1973), 181-201


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194 HERBERT A. SIMONConstruction is able to consu|t the Director o f Naval Equipment as to the proposedarrangements in regard to the sizes and towage of the motor boats, steamboats, rowingand sailing boats to be carried, as we l as of the anehors and cables; the Director ofthe Signal Department as to the wireless telegraphy arrangements; the Director ofNavigation as to the arrangements for navigating the ship, and so on. In this way thescheme goes on growing in a tentative manner, its progress always being dependent onthe efficiency of different parts, until ultimately a more or less complete whole isarrived at in the shape o f drawings and specifications provisionally embodying all theagreements. This really is the most difficult and interesting stage, for generally it be-comes apparent at this point that requirements overlap, and that the best possiblecannot be achieved in regard to numbers of points within the limit set to the con-tractors. These difficulties are cleared up by discussion at round-table conferences,where the compromises which will least impair the value of the ship are agreed upon,and the completed design is then finally submitted for the Board's approval. Somefourteen departments are concerned in the ~ ettlement of the final detai led arrange-ments."

The main part icular in which th is account d iffers from our descript ion ofthe architec tura l process is in the more e laborate provision, in the shipdesign process, for coordinat ing the numerous cri ter ia of design that areevoked during the process, and preventing cri ter ia , once evoked, from beingoverlook ed in the la t ter s tages of the process. In the ship design process toothe evok ing takes on an o rgan iza t iona l fo rm -- i t invo lves consu l t ing therelevant specialists. The long=term memory here is li terally a distributedm emo ry , d iv ided am ong the va r ious g roup s o f experts wh o a re invo lved a tone or a noth er stage of the design process.What i s s t r ik ing about S i r Oswyn 's account i s how wel l s t ruc tu red eachpa rt of the design process appears. W e car~ visual ize each gro up of experts ,prov ided with the overal l specif ica tions, s i~t ing dow n w ith their specif icsubproblem of designing a part icular system, and f inding that s t~bproblemto be a re la t ively well s tructured task. Of course the more complex sub-prob lems may themse lves be in numerous ways i l l s t ruc tu red un t i l fu r the rsubdivided in to co m pone nts (cL the ' descript ions o f the role o f the Engineer=in-Chie f and of the D irec to r o f Nava l Ordnance) .Wherever complex designs are produced by organizat ions, and where , asa consequence, the d esi gn process m ust h part ia l ly external ized andformalized, we f ind descript ions o f tha t p rocess n ot unlike ).h is descript ion o fship design. A n ini t ia l s tage o f laying dow n general (and tenta t iv e) specif ica-t ions is fo l lowed by stages in which experts are ca l led up ( evoked ) toin t rod uc e new des ign c r i te r ia and com ponent des igns to sa t is fy them. A t ala ter s tage , there is a t ten t ion to inconsistencies of the com pon ent designs, an da search for m odifica tions that w ill continu e to ineet m:~st o f the cri teria , o rdecisions to sacrifice certa in cri ter ia in fa vo r of o thers. E ach sm all phase o fthe act iv i ty appears to be quite w ell s tructured, but th~ ~verail process meetsnone of the c r i te r ia we set down for WSPs.

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THE STRUCTURE OF ILL STRUCTURED PROBLEMS 1953 4 A n i n te l li g e n t r o b o t

A d i f fe r e n t a s p e c t o f s tr u c t u r e c o m e s t o t h e f o r e f r o n t w h e n w e c o n s i d e rt h e d e si g n o f a n i n te l li g e n t r o b o t c a p a b le o f l o c o m o t i n g a n d s o l v in g p r o b l e m si n a r e a l e x te r n al e n v i r o n m e n t . T h e r o b o t ' s p l a n n i n g a n d p r o b l e m s o lv i n gm u s t b e c a r r ie d o u t i n t e r m s o f s o m e i n t e r n a l r e p r e s e n ta t i o n o f th e e x t e r n a le n v i r o n m e n t . B u t t h i s i n t e r n a l r e p r e s e n t a t io n w i l l b e i n ex a c t f o r a t l e a s t t w or e a s o n s : F i r st , i t m u s t a b s t r a c t f r o m m u c h ( o r m o s t ) o f t h e d e t a i l o f t h e a c t u a lp h y s i c a l e n v i r o n m e n t . ( I t s u r e l y c a n n o t r e p r e s en t t h e i n d i v i d u a l m o l e c u le sa n d t h e i r i n t e ra c t io n s , a n d i t m u s t a l m o s t a l w a y s i g n o r e d e ta i ls t h a t a r e m u c hg r o s se r a n d m o r e i m p o r t a n t t h a n t h o s e a t t h e m o l e c u l a r l ev e l. ) S e c o n d , t h ei n t e r n a l r e p r e s e n t a t io n i n c l u d e s a r e p r e s e n t a t i o n o f t h e c h a n g e s t h a t w i ll b ep r o d u c e d i n t h e e x t e r n a l e n v i r o n m e n t b y v a r i o u s a c t i o n s u p o n i t . B u t f o rt h i s p r e d i c t i o n o f th e e ff ec ts o f o p e r a t o r s t o b e e x a c t w o u l d r e q u i r e a n e x a c tk n o w l e d g e o f t h e l aw s o f n a t u r e t h a t g o v e r n t h e e ff ec ts o f r e a l a c ti o n s u p o n ar e al e n v i r o n m e n t .

T h e r ob o t , t he r e f o r e , w i l l c on t i nu a l l y be c on f r ,. ,a t e d ~ a,ith ne w i n f o r m a t i o nf r om t he e nv i r on m e n t : f e a t u r e s o f t he e nv i r on m e n t w i f ic l~ ha v e bec,:,~ ner e l e v a n t t o i t s b e h a v i o r b u t a r e o m i t t e d f r o m , o r d i s t o r t e d i n , i t s i n t e r n a l

~ p r e s e n t a t i o n o f t h a t e n v i r o ~ a a e n t ; a n d c h a n g e s i n t h e e n v i r o n m e n t a s ac o n s e q u e n c e o f i t s b e h a v i o r t h a t a r e d i f fe r e n t f r o m t h e c h a n g e s t h a t w e r ep r e d i c te d b y t h e p l a m f i n g a n d p r o b l e m s o l v i n g pr oc ee se s.B u t t h i s e x t er n a l i n f o r m a t i o n c a n b e u s e d b y t h e r o b o t i n e x a c tl y th e w a yt h a t i n f o r m a t i o n e v o k e d f r o m l o n g - te r m m e m o r y w a s u s e d b y t h e a r c h it ec t .T h e p r o b l e m r e p r e s e n t a t i o n c a n b e r ev i se d o o n ti n u a U y t o t a k e a c c o u n ) o f th ei n f o r m a t i o n - - o f t h e r e a l s i t u a t i o n - - s o t h a t t h e p r eb l e m s o lv e r is f a ~ d a te a c h m o m e n t w i t h a w e l l s t r u c t u r e d p r o b l e m , b u t o n e t h a t c h a n g e s f r o mm o m e n t t o m o m e n t. 2

I f t h e c o n t i n u i n g a l t e r a t i o n o f th e p r o b l e m r e p r e s e n t a ti o n i s s h o r t - t e r m a n dr e v er s ib l e, w e g e n e r a ll y c a ll i t a d a p t a t i o n o r f e e d b a c k , i f t h e a l t e r a t i o n i sm or e o r le s s pe r m a ne n t (e .g . , r e v is i ng t he l a w s o f na t u r e ) , w e re f e r t o i t a s

l e a r n i n g . T hu s t h e r o bo t mo d i f ie s i t s p r o b l e m , ,' ep r e se n t at ion t e mpo~ 'a r il yb y a t t e n d i n g i n t u r n t o s e le c te d f e at u r es o f t h e e n v i r o n m e n t ; i t m o d i f ie s i tm o r e p e r m a n e n t l y b y c h a n g i n g i t s c o n c e p t i o n s o f t h e s t r u c t u r e o f t h ee x t e r na l e nv ir o r~ me n t o r t he l a w s t ha t gov e r n i t .

2 Robo'+s that opera te on synthesized worlds represented inside the comI:-uter, likethe well-knownsystem of T . W inograd, are not robots in the sense in w hich I am using theterm here; for they do not f ace the issue tha t ~s critical to a robot when dealing with a realexternal cnviro nm em ~th e isst: o f continually revising its internal r~presentation of theproblem situation +o conform to the facts of the wo rld. T hu s the information givenPLAN NER , ~.he problem solving component of W inograd's system, is a complete andaccurate characterization of the loy wo rld of blocks that the system manipulates. Theaccuracy of the information guarantees in turn that any theorem proved by PL ANN ERwill be true o f the block wo rld.

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96 H E R B E R T A . S IM O N

3 .5 . Chess p l ay ing a s an I S PW e can now re t u rn t o t he t a sk env i ronm en t o f chess , and r e i n te rp re t ou r

ea r l i e r com m ent s - - t ha t i n som e re spec t s chess appea r s t o r e sem bl e an ISPra t he r t han a W SP. To m ake t he po i n t s t i l l sha rpe r , w e cons i de r a (ove r -s impl i f i ed) chess program tha t has th ree pr inc ipa l component s :

(1) a se t o f prod uct ions ,(2) an eva lua tor ,(3) an updat ing process .The se t o f p roduc t i ons se rves a s a m ov e gene ra to r . Each p roduc t i on

cons is ts o f a cond i ti on p a r t a nd an ac t i on pa r t ; t he cond it ion pa r t t e s ts fo r t hepresence of some conf igura t ion of pi eces or o ther fea tures in a chess pos i t ion ;t he ac t i on pa r t evokes a m ove t ha t shou l d be cons i dered w hen t he cond i ti onwi th wh ich it is assoc ia t ed i s p resent . Such a se t o f 9roduc t ions can a l so bev i ew ed a s an i ndexed m em ory , o r d isc r im i na t ion and r ecogn i ti on ne t . W henthe presence of a condi t ion i s recognized by the ne t , t he correspo nding ac t ioni s accessed i n long - t e rm m em ory . By t he ope ra t i on o f th i s sys tem o f p roduc -t ions , each chess pos i t ion evokes a set o f mov es tha t should be cons idered inthat posi t ion.

The second com ponen t o f t he chess p rog ram i s an eva l ua t o r t ha t t akes am o ve a nd a pos it ion a s i npu t and ( recu rs ive ly ) m akes a dyna m i c eva l ua t ion o ft ha t m ove . W e w ill a s su m e- -w i t hou t speci fy ing exac t m ech an i sm s- - t ha t t hedynamic eva lua t ion converges . The eva lua tor produces a search t ree tha tcons t i tu tes i ts p red ic t ion of the consequences th a t m ight fo l low on any g ivenm ove .

The t h i rd com ponen t o f t he chess p ro g ra m is t he upda t i ng rou t i ne . A f t e ra m ove has been m a de and t he opponen t ha s r ep li ed , t he upda t e r b r ings thepos i t ion on t he boa rd up t o da t e by reco rd i ng t he m oves , p runes t he ana l ysi s ree , and turns co nt ro l over aga in to the d i scr imina t ion ne t .

Co ns ider n ow a pro blem space cons is t ing o f the se t o f fea tures recognizableby the product ions , t oge ther wi th the moves assoc ia t ed wi th those fea tures .Co ns ider the subspac e cons i s ting of the fea tures ac tua l ly evoke d by ag iven pos i t ion , t oge ther wi th the moves assoc ia t ed wi th th i s smal l e r se tof fea tures. I f we re gard the l a t te r , a nd smal l e r, space a s the e ffec tiveproblem space for the program (s ince i t s p rocess ing dur ing a l imi t ed per iodof t im e w ill be gov e rned on l y by t he p roduc t i ons ac t ua ll y evok ed du r i ng t ha tt ime) , t hen the e f fec t ive problem space wi l l undergo cont inu ing changet h roughou t t he cou r se o f t he gam e , m ov i ng f rom one subspace t o ano t he rof the l a rge space def ined by the en t i re con tep t s of long- t e rm mem ory .The p roblem faced by the chess pro gra m will ap pe ar jus t a s ill s t ruc turedas t he a rch i tec t s p rob l em o r t he ro bo t s p ro b l e m --a nd fo r exac tl y thesam e rea sons .Art i f ic ia l In te l l igence 1973) , 181 -201


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T H E S T R U C T U R E O F I L L S T R U C T U R E D P RO B LE M S 1973.6. Ser ial processors and I S P s

Ou r ana lys i s has l ed us t o s ee t ha t a ny p rob lem so lv ing p roces s w i ll appe a ri l l s t ruc tu red i f t he p rob le m so lve r i s a m ac h i ne tha t h as acces s t o a ve ryl a rge long-t e rm m em ory ( an e ff ec tive ly i n f in it e mem ory) o f po t en t i a l l yre l evan t i n fo rma t ion , and /o r acces s t o a ve ry l a rge ex t e rna l memory tha tp rov ides i n fo rma t ion abou t t he ac tua l r ea l-wor ld consequences o f p rob lem-so lv ing ac t ions . La rg e i s de f ined r e la t ive t o t he amou n t o f i n fo rm a t ion tha tcan d i r ec t o r a ff ec t t he behav io r o f t he p rocesso r ove r any sho r t pe r iod o ft ime ; wh i l e po ten ti a .l ly r e l evan t me ans tha t any sma l l pa r t o f th i s i n fo rma -t ion m ay b e evoked a t som e t ime du r ing the p rob lem so lv ing p rocess byrecogn i t i on o f some f ea tu re i n t he cu r r en t p rob lem s t a t e ( t he i n fo rma t ionava i l ab l e direct ly to the processor) .

I f we r e fe r back to t he o r ig ina l de f in i t ion o f WSP, we see t ha t t he p re sen tv i ew o f t he boun da ry be tween W SPs and ISPs de r ives f rom o ur i n s i st ence tha tno t ions o f com putab i l i t y i n p r inc ip l e be r ep l aced by no t ions o f p rac t i cab lecom putab i l i t y i n t he de f in it i on o f W SP. Bu t t h i s sh i f t i n b oun da ry has h igh lyim po r t an t consequences . It imp l i e s t ha t, f ro m the s t andpo in t o f t he p rob lemso lve r , any p rob lem wi th a l a rge base o f po t en t i a l ly re l evan t knowledge m ayapp ea r t o be an i l l s t ruc tu red p rob lem ; and th a t t he p rob lem so lve r can b eef fec tive in d ea l ing wi th i t on ly i f i t h as capab i l i t ies for d ea l ing w i th ISPs.Converse ly , i t sugges ts tha t there may be noth ing o ther than the s ize of theknowledge base to d i s t i ngu i sh ISPs from W SPs , and tha t gene ra l p rob lemso lv ing mechan i sms tha t have show n the r~selves to be e ff icacious fo r han d l inglarge , a lb e i t pp ren t ly wcl l s t ruc tu red do m a ins shou ld be ex t endab le t o i lls t ruc tu red d om a ins w i thou t a ny need fo r i n t roduc ing qua l i t a ti ve ly newcomponen t s .However we l l s t ruc tu red the p rob lem space in wh ich a p rob lem so lve rope rat e s, i f it is to be capab le o f mo d i fy ing tha t space a s p rob lem so lv ingprogresses , i t mu s t possess me ans for ass im i la t ing the in form at ion i t acqui resf rom long- t e rm memory , f rom p rob lem ins t ruc t ions , and f rom the ex t e rna lenvi ronmer i t . The next sec t ion d iscusses br ie f ly the na ture of the capab i l i ti esof these k in ds tha t a re requi red .

4 Assimilating New InformationW h e n t h e p r o b l e m s p a c e r e m a i n s u n c h a n g e d th r o u g h o u t t h e p r o b l e m s o l v in gprocess , t he a s s imi l a t ion o f n ew in fo rm a t ion by the p rob lem so lv ing syst emoffers no par t icu la r d if f icu l ties . A ny info rm at ion th a t can be used be longs toone o f t he fo rms o f i n fo rm a t ion tha t a r e spec if ied in t he de f in it i on o f t hep rob lem space . In f ac t , t he on ly new in fo rma t ion tha t can be acqu i r e4 i sinformat~ ,n descr ip t ive of new s ta tes tha t a re reached in the course o i thepro blem solv ing search .When the p rob lem space i s sub jec t t o mod i f i ca t ion du r ing p rob lem

r t i f i c ia l Im e l ligence 4 1 9 7 3 ) , 1 8 1 - 2 0 1


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198 HERBERT A. SIMONsolving, provis ion mu st be made for accept ing an d assimilat ing inform at ionf rom one or more of three sources : informat ion evoked f rom long- te rmmemory, informat ion conta ined in problem ins t ruc t ions or addi t ions andmodif icat ions to inst ruct ions, and informat ion obtained through sensorychannels f rom the e xternal world.4.1. Information from long-term memory

Informat ion evoked by the product ion- recogni t ion sys tem f rom long- te rmm em ory should no t create par t icular dif ficult ies o f ass imilat ion. The form s inwhich such inform at ion is stored, the processes for re t rieving i t an d inco rporat -ing i t in the redef ined problem space are a l l par t of the problem solvingsystem, broa dly construed.Th is does not m ean tha t we have had m uch a ctual experience in construct ingand using such semant ic informat ion s tores . Perhaps, when we come to havesuch experience, difficult ies will emerge that cannot now be anticipated.Nevertheless , the designer of the problem solving system contro ls the form atin which informat ion is to be s tored in long-term memory. The s toragescheme can p ut tha t inform at ion into a re latively s imple, gen eral , and hom o-geneous form at (e .g., a n etwork o f descr ipt ion l is t s t ructure s--com m onlyreferred to as a colored directed graph); an d the system can be provided with

relatively simple, general , and hom ogen eou s processes for searching for infor-m at ion and retr ieving i t f rom the s tore . Interfacing with an en vironm ent whosedesign is under our con trol (m emo ry search) is a lways several orders o f mag-nitud e easier than in terfac ing with a given extern al environ m ent (perception).4.2. Information from instructions

Task s presented to a problem solver thro ug h natural language inst ructionspose the difficult ini t ial problem of understanding the instructions, that is ,o f generat ing from them a wel l s t ructured (o r i l l s t ructured) s ta temen t o f theFroblem. A general discussion of und erstanding n atural languag e wouldtake us fa r a f ie ld f rom our main concerns here , and must be omi t ted f romthe present paper . The reader is referred to Simon [14] , Sikl6ssy and Simon[12], chapters by B obrow and Rap hael in [4] , an d W inograd [15].Ha yes an d Simon [2] have cecent ly constructed a system tha t rea ds probleminstruct ions in natural language, and constructs f rom them a problemrepresenta tion in the form o f input appropr ia te for a p roblem solv ing sys temlike GP S. T heir pro gram carr ies out the m ajor s teps in t ranslat ing relativelysimple ISPs into WSPs.4 3 In format i on ab ou t th e ex tern a l wor ld

An abi l i ty to ass imilate informat ion about the external world--ei therinform at ion ab out the effects of the problem solver s actions, or inform at ionr t i f i c ia l ln t e l l igo~ce 4 1973), 181-201


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T H E S T R U C T U R E O F I L L S T R U C T U R E D P RO B LE M S 199a b o u t a u t o n o m o u s c h a n g e s i n t h a t w o r ld , o r b o t h - - i s t h e e a r m a r k o f t h os ep rob lem so lve r s we have ca ll ed robo t s . He re we a re conce rned wi th t hep rob lem so lve r ' s pe rcep tua l o r pa t t e rn r ecogn izmg capab i l i t i e s - - ano the rtop ic t ha t f a l ls ou t s ide t he scope o f t he p re sen t pape r . T he ou te r l imi t s onacqu i s i t ion o f such in fo rm a t ion a re de f ined by the p r imi t ive senso ry d i s-c r im ina t ions o f wh ich the p rob lem so lve r i s capab le , bu t i n the sho r t run , t heh ighe r l eve l concep ts a l r eady deve loped and s to red m ay pose the m os t s eve rep rob lem s o f a s s imi l a t i ng new in fo rma t ion .

I n t h e c a se s b o t h o f i n f o r m a t i o n f r o m i n s tr u c ti o n s a n d i n f o r m a t i o n a b o u tthe ex terna l wor ld , the acq uis i t ion process involves a cont inu a l in te rac t ionb e tw e e n th e i n c o m i n ~ r a w d a t a a n d p r o g r a m s a n d d a t a a l r e a d y st o re d i n t h ep rob lem so lve r. Th i s i n t e rac t ion i s bo th a v i t a l a id t o , an d a l im i t a t i on upon ,the u nde r s t and ing p rocess . I t i s an a id because i t fi ts t he new in fo r m a t io n tofo rm a t s and s truc tu res t ha t a r e a l r eady ava i l ab l e , and adap t s i t t o p roces sesfor m anip ula t in g those s t ruc tures . I t i s a l im i ta t ion , because i t t ends to m olda l l new in fo rm a t ion to t he p a rad igm s tha t a r e a l r eady ava il ab le . The p rob lemsolver never perce ives the D i n g a n ~ i ch , bu t on ly the ex t e rna l s t imu lusf i l t e red through i t s own preconcept ions . Hence the acquis i t ion processexercises a s t rong inf luence in the d i rec t ion of conserv ing exis ting proble mformu la t ions . The w or ld a s pe rce ived is be t te r s t ruc tu red than th e r aw wor ldoutside.

5. Im plicat ions for A rt i f ic ial Intel ligenceM ol i t r e ' s he ro d i scove red tha t he had been speak ing p rose a l l h i s l i fe wi thou tknow ing i t. O ur ana lys i s he re imp l i es t ha t t h rough ou t t he h i s to ry o f a rt if ic i a li n te l li gence , com pute r p rob lem so lv ing p rogram s have , a l so unkno wing ly ,been hand f ing man y a spec ts o f p rob lem so lv ing tha t a r e u sua l ly r ega rded a si l l s t ruc tured . Several exam ples of prog ram s n ow f i fteen years o ld can be c i ted .

The e a r ly NSS chess p rog ram [8] con ta ined a n um ber o f independ en t mo vegenera tors , each assoc ia ted wi th a par t icu lar subgoal (development , centercon t ro l ; Ki ng safe ty , e tc .). A mo ve genera tor w as ac t iva ted by the presencein the chess pos i t ion of fea tures re levant to the goa l in ques t ion . Whenevoked, t he gene ra to r p roposed one o r mo re m oves fo r advanc ing the goa l inques tion . These m oves were eva lua t ed by dy nam ic ana lys i s wh ich a ga in w assens i tive to fea tures not iced in n ew pos i t ions as they arose dur in g the ana lys i s .Hence the ove r- a ll o rgan iza t ion o f the p rog ram was qu i te c lose to t ha t o f t hehyp othe t ica l program we descr ibed earl ie r .

The p roposa l s fo r u s ing a p l ann ing m e thod in the G ene ra l P ro b lem S o lvercan a l so be i n t e rp re ted a s a way o f hand l ing p rob lem s tha t a r e no t com ple t e lywe l l s t ruc tu red . P l ann ing was done by abs t r ac t ing f rom the de t a i l o f a p rob lemspace , an d ca r ry ing ou t p re l im ina ry p rob lem so lv ing in t he abs t r ac t ed ( andconseq uent ly s impler ) space . But the p lan th en h ad to be tested by t ry ing to

r l i f ic ia l ln te ll ioence 4 1973 ) , 181 -201


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20 0 H F .R e~ r A. SLMONc a r r y i t o u t i n t h e o r i g i n a l p r o b l e m s p ac e . T h e d e t a il o f t h e p l a n w a s t h e r e b ye l a b o r a t e d a n d i ts f e a s ib i l it y t es te d . T h e r e l a ti o n b e t w e e n t h e a b s t r a c tp l a n n i n g s p a c e a n d t h e o r i g i n a l p r o b l e m s p a c e w a s q u i t e a n a l o g o u s t o t h er e l a t i o n w e h a v e d is c u s s e d b et w e e n a n i n t e r n a l p r o b l e m s p a c e o f a r o b o t a n dt h e e x t e r n a l r e al w o r l d i n w h i c h th e r o b o t p e r f o r m s .

W h a t h a s b e e n a b s e n t f r o m ( o r a t le a s t n o t p r o m i n e n t i n ) sc h e m e s l ik et h e s e i s a v e r y la r g e l o n g - t e rm m e m o r y o f p o t e n t i a ll y e v o c a b l e i n f o r m a t i o nt h a t c a n b e u s e d to b r i n g a b o u t r e p e a t e d m o d i f i c a ti o n s i n t h e p r o b l e m s p a ce .T h e r e c e n t g r o w t h o f in t e r e s t i n se m a n t ic s , i n t h e d e s ig n a n d c o n s t r u c t i o n o fs e m a n t i c n e t s, in t h e i n t e r p r e t a t i o n o f in s t r u c t io n s , a n d i n i n t e r f a c in g r o b o t sw i t h t h e ex t e r n a l w o r l d a r e a l l m o v e m e n t s i n t h e d i re c t i o n o f e n r i c h i n g o u ra r s e n a l o f a r ti fi ci al in t e ll ig e n c e m e t h o d s a l o n g t h e d i m e n s i o n s t h a t w i l lb e c o m e i n c r ea s in g l y i m p o r t a n t a s w e m o v e t o w a r d m o r e c o m p r e h e n s i v es c h e m e s f o r h a n d l i n g i ll s t r u c tu r e d p r o b l e m s o lv i ng . O u r a n a l y s i s g iv e s u sr e a s o n t o b e o p t i m i s t i c th a t p r o g r e s s w i l l n o t r e q u i re u s t o i n t r o d u c em e c h a n i s m s t h a t a r e q u a l i t a ti v e l y d i ff e re n t f r o m t h e o n e s a l r e a d y i n t r o d u c e di n a r t i f i c i a l i n t e l l i g e n c e s c h e m e s - - m e c h a n i s m s w i t h w h i c h w e h a v e a l r e a d yhad some , : i , n i t ed expe r i ence .

T h e b o u n d a r y b e t w e e n w e l l s t ru c t u r e d a n d i l l s t r u c tu r e d p r o b l e m s o l v in g i sin d e e d a va.,~ guea n d f l u id b o u n d a r y . T h e r e a p p e a r s t o b e n o r e a s o n t o s u p p o s et h a t c o n ce ~ t~ a s y e t u n i n v e n t e d a n d u n k n o w n s t a n d b e t w e e n u s a n d t h e f u ll e re x p l o r a t i o n o f t h o s e p r o b l e m d o m a i n s t h a t a r e m o s t o b v i o u s l y a n d v i s ib l y i lls t r u c t u r e d .

REFERENCES1. Alexaader, C. Notes on the Syn thes is o f Form. Harvard Un iv. Press, Cam bridge, Mass.1964.2. H ayes, .l . R . and Sim on , H . A . U nderstanding written problem instructions. Prec .9th Carnegie Syrup. on Cognition L. W . Grcgg (ed.), forthcoming 1974.3. Kling, R. D . A paradigm for reasoning by analogy. Prec . 2nd In tern . Join t Conf. onArtificial Intelligence British Com puter Society, Lond on, 1971, pp. 568-585.4. Minsky, M. (ed.) Semantic Information Processing. M .I.T. Press, Cambridge, M ass.,1969.5. M urray, S ir Osw yn A. R. T he adm inistration of a fighting service. J. Publ ic Admin. 1(.lu~y 1923), 216-217.6. ?~ewell, A. H eur istic program ming: ill structured problems. Progress in OperationsResearch V ol. 3, J. Aro nofsk y (ed.), ~J;iley,N ew York, 1969, pp. 360 -414.7. Newell , A. and Sim on, H. A. Human Problem Solv ing . Prentice-Hall, EnglewoodCliffs, N .J., 1972.8. N ew ell, Ao, Shaw , J. C. an d S imon, H. A., C hess-playing program s and the prob lemof complexity. I B M J . R e s . D v e i o p . 2 (1958 ), 320-335.9. Pitrat, J. R([alisation des p rogram m es de d6 m onstration des th(~or6mes utilisant desm6 thodes heuristiques. Doctoral Thesis, Faculty o f S ci., U niv . of Paris, 1966.10. Reitrnan, W. R. Heuristic decision procedures, open constraints, and the structure o f

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THE STRUCTURE OF ILL STRUCTURED PROBLEMS 201ill-defined problems. H um an Judgments and Optimality M. W . Shelley and G. L .Bry an (eds .) , Wiley, New Y ork , 1964, pp. 282-315,11. Rei tman, W. R. Cognition and Though t. W iley, Ne w Y ork, 1965.12. Sikl6ssy, L . and Simon, H. A. Some semantic methods for language processing.Representation and Meaning H. A. Simon and L. Siklbssy (eds . ) , Prent ice-Hall ,En glew ood Cliffs, N .J. , 1972.13. Sim on, H . A . Style in design, Proc. 2nd Ann. Environ. Design Re s. Assoc. Conf. 1-10,Oc tober 1970, J . Axcl~a an d C. E astm an (eds .) , Carnegie-M ellon Un iv. , Pi ttsburgh,Pa., 1971.14. Simon, H. A. The heuris t ic compiler . Representation and Meaning H. A . S im o n an dL. Sikl6ssy (eds.), Pre ntice-H all, Eng lew ood Cliffs, N .J. , 1972.15. W inograd , T . U nders tand ing natural language. Cog nitive Psychol. 3 (1) ( 973), 1-191.

Rece i ved 18 Ju l y 1973; rev i sed ve rs ion rece i ved 29 Oc tober 1973

Ar tificial Intelligence 4 (1973), 181-201

6 simon ill defined problem

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