learning and reasoning by analogy

8/13/2019 Learning and Reasoning by Analogy

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A r t i fi c i al I n t e ll i g e nc e a n d C . M o n t g o m e r yL a n g u a g e P r o c e s s in g E d i t o rLearning andReasoning by AnalogyPa t r i ck H . Wins tonAr t i fi c i al I n t e ll i gence La b o ra to ry , M IT

W e u s e a n a l o g y w h e n w e s a y s o m e t h i n g i s aC i n d ere l l a s tory an d w hen w e l earn ab out res i s tors b yth in kin g ab out w ater p i pes. We a l so use an a l ogy w henw e l earn sub jec t s l i ke ec on omi c s , med i c i n e , an d l aw .T hi s paper presen ts a theory o f an a l ogy an d d esc r i b esan i mpl emen ted sys tem that emb od i es the theory . T hespec i f i c c ompeten c e to b e un d ers tood i s that o f us i n gan al og i e s to d o c er ta i n k i n d s o f l earn i ng an d reason i n g .L earn i n g takes p l ac e w hen an a l ogy i s used to gen eratea constraint description in one domain , given ac on s tra i n t d esc r i pt i on i n an other , as w hen w e l earnO h m s l a w b y w a y o f k n o w l e d g e a b o u t w a t e r p ip e s .R e a s o n i n g t a k e s p l a c e w h e n a n a l o g y i s u s e d t o a n s w e rques t i on s ab out on e s i tuat ion , g i ven an other s i tuat ionthat i s supposed to b e a prec ed en t , as w hen w e an sw erques t i on s ab out H a m l et b y w a y o f k n o w l e d g e a b o u tM a c b et h

Key Word s an d Phrases : matc h i n g , c omputerl earn i n g , an a l og i c a l reason i n g , c ommon -sen sereasoning, information retrieval , s i tuation identi f icat ion

CR Categories: 3 .6 , 3 .61, 3 .62, 3 .64, 3 .65, 3 .7 , 3 .74,3 .7 5

1 . An al ogyM u c h t h i n k i n g i s d o n e b y a n a l o g y . W e f a c e a si tu a -t i o n , w e r e c a l l a s i m i l a r s i tu a t i o n , w e m a t c h t h e m u p , w e

r e a s o n, a n d w e l e a rn . W e u s e a n a l o g y w h e n w e s a y s o m es i t u a t i o n i s l i k e l y t o b e a C i n d e r e l l a s t o r y a n d w h e n w e

P e r mi s s i on t o c opy w i t hou t f e e a l l o r pa r t o f t h i s ma t e r i a l i sg r a n t e d p r o v i d e d t h a t t h e c o p i e s a r e n o t m a d e o r d i s t r i b u t e d f o r d i r ec tc o m m e r c i a l a d v a n t ag e , t h e A C M c o p y r i g h t n o t ic e a n d t h e t i tl e o f th epub l i c a t i on a nd i t s da t e a ppe a r , a nd no t i c e i s g i v e n t ha t c opy i ng i s byp e r m i s s i o n o f th e A s s o c i a t io n f o r C o m p u t i n g M a c h i n e r y . T o c o p yo t he r w i s e , o r t o r e pub l i s h , r e q u i r e s a f e e a nd / o r s pe c i f i c pe r mi s s i on .Th i s pa pe r de s c r i be s r e s e a r c h done a t t he A r t i f i c i a l I n t e l l i ge nc eL a b o r a t o r y o f t h e M a s s a c h u s e t t s I n s ti t u te o f T e c h n o l o g y . S u p p o r t f o rt he l a bo r a t o r y ' s a r t i f i c i a l i n t e l l i ge nc e r e s e a r c h i s p r ov i de d i n pa r t byt he O f f i c e o f N a v a l Re s e a r c h unde r c on t r a c t N 0 0 0 1 4 - 77- C - 0 38 9 a ndi n p a r t b y t h e A d v a n c e d R e s e a r c h P r o j ec t s A g e n c y o f t h e D e p a r t m e n to f D e f e n s e u n d e r O f f i c e o f N a v a l R e s e a r c h c o n t r a c t N 0 0 0 1 4 - 7 5 - C -0643.A u t h o r ' s p r e s e n t a dd r e s s : A r t i f i c ia l In t e l l i ge nc e L a bor a t o r y , R oom8 1 6, 54 5 Te c hno l ogy Sq ua r e , C a mb r i dge , M a s s a c hus e t t s 02 1 39 . 1 9 80 A C M 0 0 0 1 - 0 78 2 / 8 0 / 1 2 0 0 - 0 6 8 9 $ 0 0. 75 .6 8 9

l e a r n a b o u t r e s i s t o r s b y t h i n k i n g a b o u t w a t e r p i p e s .E x p e r t s i n e c o n o m i c s , m e d i c i n e , a n d l a w u s e a n a l o g y t or e l a t e n e w s i t u a t i o n s t o c a s e s t u d i e s.

T h i s p a p e r p r e s e n t s a t h e o r y o f a n a l o g y a n d d e s c r i b e sa n i m p l e m e n t e d s y s t e m t h a t e m b o d i e s t h e t h e o r y . T h ep a p e r b e g i n s w i th a p r e s e n t a t i o n o f s o m e e x a m p l e s t h a tf u r t h e r i ll u s t r a t e t h e s o r t o f r e a s o n i n g a n d l e a m i n g t o b eu n d e r s t o o d , f o l l o w e d b y a d i s c u s s io n o f h o w o n e c a n t e llt h a t t h e r e h a s b e e n s o m e s u c c e s s . N e x t , t h e r e i s a s p e c i -f i c a ti o n o f a r e p r e s e n t a t i o n a n d a n e x p l o r a t i o n o f p ri n -c i p l e s t h a t s e e m t o e n a b l e r e a s o n i n g a n d l e a r n i n g t o b ed o n e w i t h t h e a i d o f t h e re p r e s e n t a t i o n . F i n a l l y , a ni m p l e m e n t e d s y s t em is p r e s e n t e d t h a t a c t u a l l y d oe s r e a -s o n a n d l e a r n .

T h e i m p l e m e n t e d s y s t e m h a s a n u m b e r o f k e y in g r e -d i e n t s , t h e f o l l o w i n g i n p a r t i c u l a r :--Extensible-relations representation. S i t u a t i o n s a r e

r e p r e s e n t e d u s i n g r e l a t i o n s b e t w e e n p a i r s o f p a r ts .S u p p l e m e n t a r y d e s c r i p t i o n s c a n b e a t t a c h e d t o t h er e l a ti o n s w h e n e l a b o r a t i o n i s n e e d e d .

--Importance-dominated matching. T h e s i m i l a r i t y b e -t w e e n t w o s i t u a t io n s i s m e a s u r e d b y f i n d i n g t h e b e s tp o s s i b l e m a t c h a c c o r d i n g t o w h a t i s i m p o r t a n t i nt h e s i t u a t i o n s a s e x h i b i t e d b y t h e s i t u a t i o n s t h e m -s e lv e s . V a r i o u s k i n d s o f c o n s t r a i n t r e l a t i o n s h e l pd e t e r m i n e i m p o r t a n c e . C a u s e i s a c o m m o n i m p o r -t a n c e - d e t e r m i n i n g c o n s t r a i n t .

--Analogy-driven constraint learning. A c o n s t r a i n t s u c ha s O h m ' s l a w i s l e a r n e d a s a b y p r o d u c t o f m a p p i n gt h e p a r t s o f a s i tu a t i o n i n a w e l l - u n d e r s t o o d d o m a i ni n t o t h e p a r t s o f a n o t h e r s i t u a t i o n i n a n i l l- u n d e r -s t o o d d o m a i n .

--Analogy-driven reasoning. S o m e q u e s t i o n s a b o u t as i t u a t i o n a s k i f a p a r t i c u l a r r e l a t i o n h o l d s . C a u s e sf o u n d i n a r e m e m b e r e d s i t u a t i o n c a n s u p p l y su g g e s -t i v e p r e c e d e n t s .

--Classification-exploiting hypothesizing. M e m o r y i ss e a r c h e d f o r s i t u a t i o n s t h a t a r e l i k e l y t o b e s i m i l a rt o a n e w , g i v e n s i t u a t i o n . T h e s e a r c h a s s u m e s t h a tt h e u s e f u l r e m e m b e r e d s i t u a t i o n s w i l l i n v o l v e t h es a m e s o r ts o f th i n g s a s t h e n e w o n e a t s o m e l e v e l o fc l as s i f i ca t i o n .

T h e s y s t e m i s p r e s u m e d t o w o r k w i t h s i t u a t i o n s t h a ta r e su b j ec t t o ce r t a in r es t r i c t i o n s :

--Symbol ic suf f iciency. A s i t u a t i o n c a n b e d e s c r i b e db y u s i n g a r e p e r t o i r e o f c l a ss e s, p r o p e r t i e s , a c t s, a n do t h e r r e l a t i o n s . T h e r e p e r t o i r e n e e d n o t b e s o l a r g ea s to m a k e m a t c h i n g c o m p l i c a t e d .

--Description-determined similarity. A s i t u a t i o n i s s im -i l a r to a n o t h e r i f t h e i m p o r t a n t r e l a t i o n s i n t h e i rd e s c r i p t i o n s c a n b e p l a c e d i n c o r r e s p o n d e n c e .

--Constraint-determined importance. T h e i m p o r t a n tr e l a t i o n s o f a s i t u a t i o n a r e t h e o n e s e x p l i c i tl y sa i d t ob e i m p o r t a n t b y s o m e t e a c h e r o r i m p l i c it l y k n o w nt o b e i m p o r t a n t b y b e i n g i n v o l v e d i n c o n s t r a i n t

C o m m u n i c a t i o n s D e c e m b e r 1 98 0o f V o l u m e 2 3t h e A C M N u m b e r 1 2


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relations. Often the constraint relations have to dowith various forms of cause.- - H i s t o r i c a l c o n t i n u i t y . A situation that is similar to apast situation generally leads to similar results or

conclusions.

2 . T he C r i ter ia for Suc c es s an d the C om peten c e to b eU n d e r s t o o d

In any scientific work, it is necessary to have someway of determining success. For this work, claims forsuccess are with respect to the following criteria: (1) theremust be an implemented program that performs a spec-ified task; (2) the implemented program must performby virtue of identifiable principles.In Artificial Intelligence, having such criteria forsuccess in mind helps avoid tendencies either to beromantically speculative about the power of vague ideasor to be overcome by the performance of working, butad hoc programs. For this particular work, part of thespecified task is to do reasoning and learning by analogyas required by the following representative scenario:

A t e a c he r t e l l s a s t ude n t t ha t t he v o l t a ge a c r os s a r e s i s t o r c a n bec a l c u l at e d b y t h i n k i n g a b o u t t h e w a t e r p r e s s u r e a c r o ss a l e n g t h o fp i p e . T h e s t u d e n t c o r r ec t l y fi n d s t h e v o l ta g e w i t h o u t k n o w i n g O h m ' slaw.The t e a c he r i n s t r uc t s t he s t ude n t i n t w o d i f f e r e n t v o l t a ge - r e s i s t a nc e -c u r r e n t s i t ua t i ons a nd t e l l s t he s t ude n t t o f o r mul a t e a l a w . Thes t u d e n t i n v e n t s O h m ' s l a w .T h e t e a c h e r s u g g e s t s g e n e r a l i z i n g f r o m t h e w a t e r - p i p e l a w a n dO h m ' s l a w . T h e s t u d e n t f o r m u l a t e s a l i n e ar c o n s t r a i n t th a t i n v o l v e sf o r c e s a nd f l ow s .

Thus, practice with some specific situations in one do-main enables the invention of a specific law. In the otherdirection, once several forms of the same sort of law areknown, comparison enables generalization.Another part of the specified task is to reason byanalogy, as required in the following representative ex-amples:

A p l o t o u t l i ne i s g i v e n i n t e r ms o f 4 0 o r 50 f ac t s . Th e p l o ta p p e a r s r e m i n i s c e n t o f s e v e r a l o f S h a k e s p e a r e ' s t r a g e d ie s . A n a l y s i ss ugge s t s t ha t i t i s mos t l i ke Macbeth. S o m e o n e a s k s i f t h e p e r s o nt h a t c o r r e s p o n d s t o M a c b e t h w i l l e n d u p d e a d . R e a s o n i n g b y a n a l o g ys u g g e s t s a s k i n g i f th e p e r s o n t h a t c o r r e s p o n d s t o L a d y M a c b e t hp e r s u a d e d t h e M a c b e t h e q u i v a l e n t to m u r d e r t h e D u n c a n e q u i v a l e n t .T h e c a s e o f S m i t h v e r s u s W e s s o n e s t a b l i s h e s a p r e c e d e n t f o ra s s a u l t ca s e s. S m i t h p o i n t e d a r i fl e a t W e s s o n t o f r i g h t e n h i m . T h e

r i f le w a s no t l oa de d , a nd i t w a s t he r e f o r e ha r ml e s s . N e v e r t he l e s s , a na s s a u lt h a s t a k e n p l a c e b e c a u s e W e s s o n d i d n o t k n o w t h a t t h e r i fl ew a s n o t l o a d e d . S u b s e q u e n t l y , S m i t h v e r s u s W e s s o n i s r e t r i e v e dw h e n t h e c a s e o f V i l la i n v e r s u s V i c t i m i s c o n s i d e r e d . V i ll a i n p o i n t e da p i s t o l a t V i c t i m i n o r de r t o f r i gh t e n h i m . The p i s t o l w a s a ha r ml e s st o y . R e a s o n i n g b y a n a l o g y s u g g e s ts a sk i n g i f V i c ti m k n e w t h a t t h ep i s t o l w a s ha r ml e s s .All of these examples, having to do wi th both learningand reasoning, have been handled successfully in a seriesof experiments using an implemented system. Given thatthe examples suggest an interesting level of competence,

it remains to be more precise by showing the input toand the output from the implemented programs and todemonstrate that the implemented programs work byvirtue o f identifiable principles.The term c o m p e t e n c e , incidentally, is used in thesense intended by Chomsky, namely to refer to thek n o w l e d g e necessary for any part icular set of algorithmsto exhibit stated behavior. P e r f o r m a n c e has to do withthe use of knowledge to exhibit stated behavior. Imple-mentation of a particular set of algorithms, from thispoint of view, is done so that performance can helpevaluate progress toward understanding competence.

3 . R e p r e s e n t i n g S i t u a t io n s U s i n g E x t e n s i b l e R e l a t i o n sBroadly speaking, a representation is a vocabula ry of

symbols together with some conventions for arrangingthem. A good representation is one that has the followingcoupled characteristics:

It makes the important facts explicit;It suppresses irrelevant detail;It is perspicuous;It exposes constraint;It can be computed from a nat ural input.

In this section, a particular representation will beexplained. It is based on two key assumptions: first, thatwhat needs to be represented can be expressed in simpleEnglish and second, that much of what can be expressedin simple English can be thought of as consisting of anact-specifying verb and some noun-centered word groupsthat the act ties together.For the simplest sentences, the nouns involved arejust the agent and the object of the act. For others, theagent and object are supplemented by other things thatparticipate in act description, such as an instrument, atime or location, or perhaps a source or destination if theact involves motion. In the following, for example, aninstrument is specified:Prince Charming found Cinderella with her glass shoe.Knowing the kinds of things that are involved in describ-ing an act and understanding how to recognize thosethings in sentences is the objective of c a s e - g r a m m a rtheor i e s of sentence meaning. Agents, objects, instru-ments, and similar terms are used as names for case s l o t s .Sentence analysis is viewed as the job of filling case slotsusing sentences as raw material.3 .1 . E xten s i b l e -Re l at i on Rep resen tat i on

From the perspective of case grammar, the mostobvious way to strip a si tuation description of its syntac-tic nuances and to represent its approximate meaning isto use the material supplied by the sentences in thedescription to fill in an act-oriented schema, as illustratedby the following rendering.6 9 0 C o m m u n i c a t i o n s D e c e m b e r 1 98 0o f V o l u m e 2 3t h e A C M N u m b e r 1 2


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Action: F i n dAgent: C h a r m i n gObject: C i n d e r e l l aInstrument: [ n a m e f o r C i n d e r e l l a ' s s h o e ]T h e d i s a d v a n t a g e o f s u c h a r e p r e s e n t a t i o n i s t h a t i tf a v o r s s i t u a t i o n m a t c h i n g b y f i n d i n g c o r r e s p o n d e n c e s

b e t w e e n a c t - o r i e n t e d s c h e m a t a , r a t h e r t h a n b e t w e e n s i t -u a t i o n p a r t s . I n t r o s p e c ti v e l y , I f ee l t h a t I f o r m a n a l o g i e sb y p a i r i n g o f f s it u a t i o n p a r t s , u s i n g a c t s a n d o t h e r r e l a -t i o n s a s e v i d e n c e , n o t t h e o t h e r w a y a r o u n d . C o n s e -q u e n t l y , I u s e a n a l t e r n a t i v e , o b j e c t - o r i e n t e d r e p r e s e n -t a t i o n . P a r t s o f s i t u a t i o n s a re r e p r e s e n t e d a s n o d e s t h a ta r e t i e d to g e t h e r w i t h r e l a t i o n s f o r m i n g a k i n d o f s e m a n -t ic n et . W h e n m o r e t h a n a n a g e n t a n d a n o b j e c t isi n v o l v e d i n a n a c t , a s u p p l e m e n t a r y d e s c r i p t i o n is t i e d t ot h e a c t - s p e c i f y i n g r e l a t io n , m a k i n g t h e r e p r e s e n t a t i o nj u s t a s c a p a b l e o f b e a r i n g c a s e - l ik e i n f o r m a t i o n . T h es u p p l e m e n t a r y d e s c r i p t i o n i t s e l f c o n s is t s o f a n o d e r e -l a t e d t o o t h e r n o d e s a s i l l u s t r a t e d b y F i g u r e 1 . A s ac o n s e q u e n c e o f t h e a b i l it y o f t h e s u p p l e m e n t a r y d e s c ri p -t i o n n o d e t o s a y a l o t a b o u t a r e l a t io n , t h i s is c a ll e d a ne x t e n s i b l e - r e l a t i o n r e p r e s e n t a t i o n .

U s i n g t h i s e x t e n s i b l e - r e l a t i o n r e p r e s e n t a t i o n , t h ea g e n t a n d t h e o b j e c t i n v o l v e d i n a n a c t h a v e a n e x p l i c i tp r o m i n e n c e . S i n c e a g e n t s a n d o b j e c t s a r e g e n e r a l l ya m o n g t h e p a r t s o f a si t u a t i o n , t h e r e p r e s e n t a t i o n f a v o r ss i t u a ti o n m a t c h i n g b y f i n d i n g c o r r e s p o n d e n c e s b e t w e e ns i t u a t i o n p a r ts , w h i c h I t h i n k s e e m s n a t u r a l .

R e c a l l t h a t t h i s d i s c u s s i o n b e g a n w i t h t h e a s s u m p t i o nt h a t m u c h o f s i m p l e E n g l i s h c o n s i st s o f s e n t e n c e s w h o s ei n f o r m a t i o n c o n t e n t c a n b e c a p t u r e d b y a r e p r e s e n ta t i o nt h a t v i e w s se n t e n c e s f r o m t h e p e r s p e c t i v e o f c a s e g r a m -m a r . T h e r e a r e o t h e r k i n d s o f s e n t e n c es , h o w e v e r . S o m ei n d i c a t e t h a t a n o b j e c t b e l o n g s t o s o m e c l a s s ; s o m ei n d i c a t e t h a t a n o b j e c t h a s s o m e p r o p e r t y ; a n d s o m ei n d i c a t e t h a t a p a r t i c u l a r r e l a t i o n s h i p h o l d s b e t w e e n t w oob j ec t s :C h a r m i n g i s a p ri n c e .C i n d e r e l l a i s b e a u t i f u l .C i n d e r e l l a l o v es C h a r m i n g .

I n f o r m a t i o n a b o u t c l a s s e s a n d p r o p e r t i e s i s e a s i l yc o n v ey e d b y us in g A - K I N D - O F a n d H A S - P R O P E R T Yr e l a t i o n s . I n f o r m a t i o n a b o u t r e l a t i o n s h i p s b e t w e e n t w oo b j e c t s is h a n d l e d b y s t a t e r e l a t io n s s u c h a s L O V E S j u s ta s i f t h e r e l a ti o n s h ip w e r e a n a c t. N o t e t h a t A - K I N D -O F , H A S - P R O P E R T Y , a n d s t a t e r e l a t i o n s c a n b e t i e dt o s u p p l e m e n t a r y d e s c r i p t i o n n o d e s a l t h o u g h n o s u c hn o d e s a r e d e m a n d e d b y t h e e x a m p l e s j u s t g i v en .N o t e t h a t t h e r e la t io n s f r o m a n d t o a s u p p l e m e n t a r yn o d e a l l c o m e f r o m a l i m i t e d v o c a b u l a r y b e c a u s e t h ep u r p o s e o f a s u p p l e m e n t a r y n o d e i s t o t ie to g e t h e r a l lthe p a r t i c i p a n t s i n a c o n s t r a i n t . T h i s l i m i t e d v o c a b u l a r ycons i s t s o f the fo l lowing : f i r s t, c a s e nam es , s uc h a s i n s t r u -m e n t , u s e d t o d e s c r i b e c o n s t r a i n t s c o u c h e d i n t h e f o r mo f s i m p l e a c t - c e n t e r e d s e n t e n c e s ; s e c o n d , c a s e - l i k en a m e s , s u c h a s m u l t i p l i e r , u s e d t o d e s c r i b e a l g e b r a i cc o n s t r a i n t s ; a n d t h i r d , n a m e s l i k e c a u s e , u s e d t o s h o w

F i g . l. A F I N D r e l at i o n f u r t h e r d e s c r i b e d b y a s u p p l e m e n t a r y d e s c r i p -t i o n n o d e .

C h a r m i n gfind

~ l ~ C i n d e r e l l a

i n s t r u m e n tfind i s h o e - I

h o w c o n s t r a i n t s t h e m s e l v e s a r e c o n s t r a i n e d .T h e a c t u a l i m p l e m e n t a t i o n w a s d o n e u s i n g a v e r s io no f F R L , a n a c r o n y m f o r a L I S P - b a s e d F r a m e R e p r e s e n -t a t i o n L a n g u a g e , d e v e l o p e d b y R o b e r t s a n d G o l d s t e i n[ 1 4, 1 5 ]. F R L w a s u s ed b e c a u s e F R L h a s h a n d y m e c h -a n i s m s f o r a s s e r t i n g r e l a t i o n s a n d a t t a c h i n g s u p p l e m e n -t a r y d e s cr i p ti o n s to t h e m . I n F R L t e r m s , a n a g e n t - - a c t -o b j e c t c o m b i n a t i o n i s e x p r e s s e d a s a f r a m e , a s l o t i n t h ef r a m e , a n d a v a l u e i n t h e s l o t. A s u p p l e m e n t a r y d e s c r i p -t i o n n o d e f o r a n a g e n t - a c t - o b j e c t c o m b i n a t i o n i s e x -p r e s s e d i n t h e f o r m o f a s o - c a l le d c o m m e n t f r a m e a t -t a c h e d t o t h e f r a m e - s l o t - v a l u e c o m b i n a t i o n .

A s a c o n s e q u e n ce o f th e F R L i m p l e m e n t a t i o n , m yhab i t i s t o us e the t e r m s f r a m e a n d v a l u e w h e n r e f e r r i n gt o n o d e s , t o u s e t h e t e r m s l o t w h e n r e f e r r i n g t o r e l a t i o n so f a l l k i n d s , a n d t o u s e t h e t e r m c o m m e n t fr a m e w h e nr e f e r r i n g to t h e n o d e s w h i c h b e a r s u p p l e m e n t a r y d e s c r ip -t io n s . N o t e t h a t c o m m e n t f r a m e s a r e p a r t o f t h e k n o w l -e d g e r e p r e s e n t a t i o n - - t h e y a r e n o t n o t e s t o h u m a n p r o -g r a m m e r s .A s i t s t a n d s , m a n y s t a n d a r d q u e s t i o n s h a v e b e e n p u t o f f ,p a r t i c u l a rl y t h o s e i n v o l v e d i n t h e r e c o r d in g o f i n f o r m a -t i o n a b o u t q u a n t i f i c a t i o n , n e g a t i o n , d i s j u n c t io n , a n d p e r -s p e c ti v e . T h e s e q u e s t i o n s w e r e p u t o f f s in c e d e a l i n g w i t ht h e m w a s n o t f o r c e d b y t h e s i t u a t i o n s c o n s i d e r e d i n t h i sw o r k s o f a r .

3.2. English-Like InputI t w a s p o i n t e d o u t t h a t o n e c h a r a c t e r i s ti c o f a g o o d

r e p r e s e n ta t i o n i s t h a t i t c a n b e c o m p u t e d f r o m a n a t u r a li n p u t . T h i s m e a n s t h a t t h e e x t e n s i b l e - r e l a t i o n r e p r e s e n -t a t i o n o f a s i t u a t io n s h o u l d b e c o m p u t a b l e f r o m a s i m p l eE n g l i s h d e s c r ip t i o n o f t h e s i t u a t i o n o r f r o m s o m e t h i n gtha t i s a t l e a s t c los e to s imple E ng l i s h .I n f a c t , a t r a n s l a t o r t h a t t r a n s l a t e s E n g l i s h - l ik e s i t u -a t i o n d e s c r i p t i o n s i n t o d e s c r i p t i o n s i n e x t e n s i b l e - r e l a t i o nr e p r e s e n t a t i o n h a s b e e n d e s i g n e d a n d i m p l e m e n t e d . I tw a s d e s i g n e d w i t h a v i e w t o w a r d c o m p r o m i s e b e t w e e nm a x i m u m i n p u t t r an s p a r en c y a n d m i n i m u m t r an s la t o rc o m p l e x i t y . It r e q u i r e s o n l y m i n i m a l s y n t a c t i c, s e m a n t i c ,a n d r e f e r e n c e - f i n d i n g m a c h i n e r y s i n ce it a c c ep t s a k i n do f p a r e n t h e s iz e d E n g l i s h n o t a t i o n i n w h i c h t h e c a s en a m e s a r e e x p l i c i t l y g i v e n . F o r e x a m p l e , p a r t o f t h es e n t e n c e " P r i n c e C h a r m i n g f o u n d C i n d e r e l l a w i t h h e rg la s s s hoe , " i s expre s s ed a s fo l lows :C h a r m i n g f i n d C i n d e r e l l a [ i n s t ru m e n t s h o e - l ].

691 C o m m u n i c a t i o n s D e c e m b e r 1 98 0o f V o l u m e 2 3t h e A C M N u m b e r 1 2


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Fig . 2 . The input t ransla tor produces a conste l la t ion of nodes an drelations from a few English-like sentences.

k i s s e s kiss'I~ c a u s e

inst rument sh0e-1 // l \s h o e ~ a -k in d -o f / / /( /-k i n d -o fp r o p 4 1 raw materialgl ss

o w n e r

This sentence illustrates the basic form for conveying anagent-act-object combination with case information.Material enclosed in square brackets gives case-like in-formation to be hung on the comment frame that furtherdescribes the agent-act-object combination just asserted.Thus the expression [instrument shoe-1] generates a com-ment frame for the Charming-find-Cinderella combina-tion and hangs a case-filler combination on it. Moreabout the shoe is conveyed as follows:Shoe- 1 a-kind-of shoe prop- -raw-ma terial glass--ownerCinderella.This sentence illustrates that the input language permitsa kind of elision. When the same agent-act combinationis used with several objects, the objects are just enumer-ated one af ter the other. When the same agent is involvedwith several acts, hyphens keep things separated.A minimal reference feature makes it possible to usethe following, simpler forms, in which specific names areavoided:Charming find Cinderella [instrument a shoe].The shoe is a prop--raw-material glass--owner cinder-ella.Expressions like a shoe generate instances attached tothe named class, SHOE in this case. Expressions likethe shoe simply refer to the last instance created of thenamed class. Expressions like is a prop are taken tomean that an A-KIND-OF relation is implied.

Finally, it is often useful to have a direct way to referto an agent-act-object comment frame. This is done byembedding the agent, act, and object involved in curlybrackets. Thus either of the following indicates thatCharming's love for Cinderella causes him to kiss her:Charming love Cinderella [cause (Charming kiss Cin-derella}].(Charming love Cinderella} cause (Channing kiss Cin-derella}.

Figure 2 shows what all of this information looks likewhen translated into the graphical form of the extensible-relation representation.3.3. Demons /In addition to English-like input, it is good to havesome deductions made automatically, reducing the needfor tedious attention to details. For example, given thatCinderella is married to Prince Charming, PrinceCharming is clearly married to Cinderella. Similarlywhen one person kills another, it is clear that the personkilled is dead.One way to arrange for such obvious deductions is touse procedures that are invoked when relations are in-serted in the data base. Such procedures are commonlycalled i f -added demons. In the version of FRL used, if-added demons that trigger on the use of a particularrelation are placed in a frame describing that relation.In the end, demons prove so important that there hasto be some concern about whether they can be learned.In fact, they can be because using a demon is like doingan analogy in miniature. The ideas that make it possibleto accumulate big chunks of experience are the same asthe ideas that explain how it is possible to remembercause-effect relations at the level of demons.An immediate question is whether demon use shouldbe limited, and if so, by what control scheme. At themoment , there are no answers.3.4. Capturing Story Plots Requires Attent ion to CauseUsing extensible relations, ten story plots were setdown. The following is what one version of one of these,namely Macbeth, looks like in the English-like notation:

MA is a story.(Macbeth is a noble} before (Macbeth is a king}. Mac-beth marry Lady-macbeth. Lady-macbeth is a woman- -has-property greedy ambitious. Duncan is a king. Mac-duf f is a noble--has-pro perty loyal angry. Weird-sistersis a hag group--has-property old ugly weird--number 3.Weird-sisters predict (Macbeth murder Duncan). Mac-beth desire (Macbeth a-kind-of king} [cause (Macbethmurder Duncan)]. Lady-macbeth persuade (Macbethmurder Duncan). Macbeth murder Duncan [coagentLady-macbeth---instrument knife]. Lady-macbeth killLady-macbeth. Macbeth murder Duncan [cause (Mac-duf f kill Macbeth) ].

In addition to Macbeth, the plots set down includethree other Shakespearean tragedies, one of his comedies,two plays by Ibsen, and some random things, all selectedby thumbing through an encyclopedia of plots. Thepurpose was to discover if the representation and accom-panying vocabulary are adequate for reasoning withplots by analogy. The following observations were made:692 Co mm u n i ca t i o n s D ecem b e r 1980o f V o l u me 23t h e A C M N u m b e r 1 2


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A few bas ic E ng l i s h words adeq ua te ly s upp l ied by f a r the bu lk o fthos e need ed fo r s lo t nam e s and c las ses . Mos t o f the ones I u s e a r ein Ogde n ' s thous and w ord Bas ic E ng l i s h v ocab u la ry [1 2 ] and in thef i r st thous an d o r two m os t f r eq uen t E n g l i s h words [2 ].Caus e i s im po r tan t beca us e caus e cons t r a ins r e la t ions pa i r s .

M a n y p e o p l e h a v e a t t e n d e d t o t h e r o l e o f c a u se , p a r t ic -u l a r l y S c h a n k [ 17 ] a n d W i l k s [ 1 9] . T o h a n d l e c a u s e h e r e ,t h e f o l l o w i n g c o n v e n t i o n s w e r e h o n o r e d , b a s e d o n t h ew o r k o f G i v o n [ 5]:

A c t s , r e l a t i o n s , a n d p e o p l e c a n c a u s e o r p r e v e n ta c ts a n d r e l a ti o ns . T h e i n v e r s es o f C A U S E a n d P R E -V E N T a r e C A U S E D - B Y a n d P R E V E N T E D - B Y . S e eF i g u r e 3 ( a ) f o r w h a t h a p p e n s g i v e n t h i s fr a g m e n t :

L a d y - M a c b e t h c a u s e { M a c b e t h m u r d e r D u n c a n } .P e o p l e c a n p e r s u a d e a n d d i s s u a d e . P e r s u a d e i n d i c a t e sc a u s e a n d a C A U S E r e l a ti o n is th e r e f o r e g e n e r a t e d b ya d e m o n w h e n e v e r P E R S U A D E is u se d . D i ss u ad es i m i l a r l y i n d i c a t e s p r e v e n t . S i n c e p e r s u a d e r s a n d d i s -s u a d e r s n o r m a l l y i n t e n d f o r s o m e t h i n g t o h a p p e n ,I N T E N D r e l a t i o n s a r e g e n e r a t e d t o o , a g a i n b y d e -m o n s . S i n c e t h e p e r s o n p e r s u a d e d o r d i s s u a d e d r e t a i n sc o n t r o l o f w h a t i s h a p pe n i n g , a d e m o n - p l a c e d C O N -T R O L r e l a t i o n so in d i c a te s . S e e F i g u r e 3 ( b ) f o r a ne x a m p l e s h o w i n g w h a t h a p p e n s g i v e n t h i s :

L a d y - M a c b e t h p e rs u a d e { M a c b e t h m u r d e r D u n -c a n } .P e o p l e c a n a l s o o r d e r a n d f o r b i d . F o r t h e m o m e n tO R D E R a n d F O R B I D s i m p ly c a r ry d e m o n s th a tp la c e P E R S U A D E a n d D I S S U A D E r e l at io n s a n dt r i g g e r t h e i r d e m o n s i n t u r n .P e o p l e c a n f o r c e . F o r c e i s l i k e o r d e r a n d p e r s u a d e ,e x c e p t t h a t t h e p e r s o n f o r c i n g h a s c o n t r o l o f w h a t i sh a p p e n i n g . S e e F i g u r e 3 ( c ) f o r a n e x a m p l e s h o w i n gw h a t h a p p e n s g i v e n t hi s us e o f a F O R C E r e la t io n :

L a d y - M a c b e t h f o r c e { M a c b e t h m u r d e r D u n c a n } .4. Determining Analogous Parts Using Im portance-Dominated Matching

A n a l o g y i s b a s e d o n t h e a s s u m p t i o n t h a t i f t w os i t u a t i o n s a r e s i m i l a r in s o m e r e s p e c t s , t h e n t h e y m u s t b es i m i l a r i n o t h e r r e s p e c t s a s w e ll . T o d e t e r m i n e i f t w os i t u a t io n s a r e s i m i l a r , t h e p a r t s o f t h e s i t u a t io n s m u s t b ep l a c e d i n c o r r e s p o n d e n c e . T h e p u r p o s e o f m a t c h i n g i s toe s t a b l i s h t h e b e s t w a y t o d o t h is . I n g e n e r a l , t h e b e s t w a ywi l l leave so m e o f t h e p a r t s ' c l a s ses , p ro p e r t i e s , ac t s , an do t h e r r e l a t i o n s u n p a i r e d , b e c a u s e i f tw o s i t u a t i o n s w e r ee x a c t l y a l i k e , n o t h i n g c o u l d b e i n f e r r e d a b o u t o n e b yu s i n g t h e o t h e r . A m a t c h e r f o r u s e i n a n a l o g y m u s t b ef l ex ib l e , n o t r i g id .

I t is e a s y t o b e s e d u c e d i n t o w o r r y i n g a b o u t m a t c h i n gf o r i ts o w n s a k e , w i t h o u t a t t e n t i o n t o t h e s o r ts o f t h in g st o b e m a t c h e d . T h i s t y p i c a l l y l e a d s t o th e i n v e n t i o n o fa l l so r ts o f m e c h a n i s m s o f d o u b t f u l v a l u e i n p r a c t i c e .C o n s e q u e n t l y , t h e m a t c h e r d e s c r i b e d h e r e w a s d e v e l o p e db y i m p l e m e n t i n g o n l y t h o s e m e c h a n i s m s n e e d e d t o a t -t e n d t o t h e f a c t o r s th a t d e m o n s t r a b l y i n f l u e n c e s i m i l a r i ty .

F i g. 3. T h e r e l a t io n s pl a c e d b y C A U S E , P E R S U A D E , a n d F O R C E .~lacbethILady-Macbeth cause y murderDuncan

3a: Lady-Macbeth cause (Macbeth murder Duncan}.~ i a c b e t ~ c o n t r o l .

Lady-rlacbeth. cause der ~ wrtIDuncan

3b: Lady-Llacbeth persuade (,~lacbeth murder Duncan}._ co ntrol ~_~~lacbeth

jDuncan

c: Lady-~lacbeth force (Macbeth murder Duncan}.

R e c a l l t h a t t h e p a r t s o f a s i tu a t i o n a r e t h e n e wi n s t a n c e s g e n e r a t e d b y t h e i n p u t i n t e r f a c e w h e n e v e r t h ea r t i c l es a an d an a r e u s e d . G i v e n t h a t m a t c h i n g i s t o p a i rt h e p a r t s o f t w o s i t u a t io n s , t h r e e g e n e r a l i s s u e s r e q u i r et h o u g h t : f i r s t, h o w i s t h e s p a c e o f a ll p o s s ib l e m a t c h e s o ft h e p a r t s o f t w o s i t u a ti o n s t o b e s e a r c h e d ; s e c o n d , w h a ti s t o c o n s t i tu t e a q u a n t u m o f e v i d e n c e f o r a p a r t i c u l a rm a t c h , a n d t h i r d , h o w a r e t h e q u a n t a o f e v i d e n c e f o r ap a r t i c u l a r m a t c h t o b e c o m b i n e d t o p r o d u c e a n o v e r a l lm e a s u r e o f s i m i la r i ty .T h e i s su e o f h o w t o s e a r c h t h e s p a c e o f a l l po s s i b l em a t c h e s s e e m e d t h e b e s t i s s u e t o n e g l e c t i n t h e e a r l ys t a ge s o f th i s r e s e a r c h . T h e r e a s o n i s t h a t e f f i c i e n c y isb e s t a d d r e s s e d a f t e r i t i s e s t a b l i s h e d t h a t t h e r e i s s o m e -t h i n g w o r t h w h i l e t o b e e f f ic i e n t a b o u t . C o n s e q u e n t l y , t h ei m p l e m e n t e d m a t c h e r d o e s a b r u t e f o r c e s e a rc h o f th es p a c e o f p o s s i b l e m a t c h e s , c a l c u l a t e s h o w g o o d e a c h i s,a n d a n n o u n c e s t h e b e s t.

T h e p r i c e p a i d i s t h a t t h e s i tu a t io n s m a t c h e d m a y n o ti n v o l v e m o r e t h a n a h a n d f u l o f p a r t s . I n g e n e r a l , i f t h e r ea r e N 1 p a r t s i n o n e s i t u a t io n a n d N 2 i n a n o t h e r , t h e n t h en u m b e r o f w a y s th e s i t u a ti o n s c a n b e p a i r e d u p i s N l /( N 1 - N 2 ) , g i v e n t h a t N 1 i s e q u a l t o o r g r e a t e r t h a n N 2 .

A t f i r s t t h o u g h t , t r y i n g a l l p o s s i b l e p a i r i n g s s e e m sh o p e l e s s s i n c e t h e n u m b e r o f p o s s i b l e p a i ri n g s g e t s b i gf a s t . F o r s m a l l N 1 a n d N 2 , t h e n u m b e r i s m a n a g e a b l e .T h e i m p l e m e n t e d m a t c h e r , w h e n c o m p i l e d , h a n d l e s 1 00o r s o p a i r i n g p o s s i b i l i t i e s w i t h o u t e x c e s s i v e s t r a i n . F o r

6 9 3 C o m m u n i c a t i o n s D e c e m b e r 1 98 0of Vo lum e 2 3t h e A C M N u m b e r 1 2


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Fig . 4 . M atching Cinderella with Romeo and Juliet produces a matchscore of six . Having the sam e propert ies accounts for two points; hav ingthe same re la t ions between the people accounts for two more; andhaving corresponding causal re la t ions between the comment framesaccounts for the f inal two.~ k i s s . l ~ - " ~ Nkiss ~ ~cause

R o m e o ~ d u l i e tl has-propery I has-propery

srong beauUful h a s - p r o p e r t y l h a s - p r o p e r t y

Charmng _ ~7,--.~ ~caused-by~ve ~,[.~nderellak i s s ~ . ) - ~ s e )

larger numbers, something must be done to constrain thenumber of pairings considered.Given x way of searching the space of all possiblematches, the next issues have to do with finding andcombining evidence so that the best match can be iden-tified. Thought about these issues led to the followingconclusions:

-- To exploit an analogy between two situations startswith establishing the best correspondence betweenthe parts of the situations using the parts' classes,properties, acts, or other relations as evidence, de-pending on what is important.--To establish what is important in a situation mayrequire attention to constraint. This in turn usuallymeans looking at the causal relations exhibited in

the situation.-- To establish enough of what is important in a situ-ation may require expansion of some facts in thedirection of more detail or abstraction of some factsin the direction of more generality.-- To establish enough of what is important in a situ-ation may require asking some questions.-- To combine evidence, simply counting the individ-ual items of evidence is sufficient to handle theparticula r tasks involved in determining success.

Plainly, the issue of what constitutes an item ofevidence requires further discussion. Examples will dealwith both story plots and natural laws.4.1. Finding Correspondence C an Require Attention toProperties and Re lations

Suppose, for example, that Prince Charming andCinderella are the characters in one plot and Romeo andJuliet are the characters in another. (These names werepicked so that the combinations are mnemonic--theplots are not developed in this illustration.)

Charming job entertaining--has-property bravestrong--love Cinderella--ki ss Cinderella.Cinderella job cleaning--has-property beautiful.Romeo job fighting cleaning--has-property stron g--love Juliet--kiss Juliet.Juliet has-property beautiful.Knowing just these facts intuitively indicates thatCHARMING corresponds to ROMEO and CINDER-

ELLA to JULIET. The implemented matcher agreesbecause it tries all possible matches and because itssimple scoring module awards one point to each sharedrelation. In doing its job, the matcher produces a set ofpaired f rames for each possible match. Each set of pairedframes is referred to as a list of linked pairs. Each list oflinked pairs is evaluated by calculating a similarity scorefor each linked pair in the list and adding the resultstogether. The score for each linked pair is calculated byscoring one point if the two linked frames contain thesame value in some particular slot or if two linked framescontain the two parts of another linked pair in someparticular slot.The matcher therefore produces a score of four forthe intuitively correct match of CHARM ING and CIN-DERELLA with ROMEO and JULIET, but only onefor the incorrect one.The details of the matcher's scoring module are notimportant. The important thing is that it seems reason-able to use both relations and properties as evidence inlieu of specific information about what is important. Wewill see that relations and properties are not sufficient,however.4.2. Finding Correspondence C an Require Attention toCorresponding Comments

For the sake of illustration, suppose Prince Charm-ing's love for Cinderella causes him to kiss her andRomeo's iove for Juliet has the same result, indicated bythe following:{Charming love Cinderella} cause {Charming kiss Cin-derella}.{Romeo love Juliet} cause {Romeo kiss Juliet}.

Certainly there is evidence for pairing CH ARM INGwith ROMEO and CI NDEREL LA with JULIET sincesuch a pairing places the LOVE and the KISS slots incorrespondence. However it is evident that pairing thecharacters in this way also puts LOVE-1 and KISS-1 incorrespondence with LOVE-2 and KISS-2, which putsa CAUSE and a CAUSED-BY relation in correspond-ence, producing additional evidence of similarity.To account for the additional similarity available incomment frames, the implemented matcher adds corre-sponding comment frames to each possible list of linkedpairs after it is formed but before it is scored. Thus thecorresponding comment frames are considered linkedwhen scoring other frames, and they themselves arescored. Thus the total score should be six for the two

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s i t u a t i o n s u n d e r c o n s i d e r a t i o n . F i g u r e 4 i l l u s t r a t e s t h ec o m b i n a t i o n s t h a t l e a d t o t h i s s c o r e i n g r a p h i c f o r m .4 .3 . F i n d i n g C orrespon d en c e C an Requi re At ten t i on toC l ass i f i c at i on In format i onS o f a r it w o u l d n o t h e l p t o a d d t h e f o l l o w i n g i n f o r m a t i o n :C h a r m i n g i s a p r in c e . R o m e o i s a b o y .C in d ere l l a i s a p r i n cess . Ju l i e t i s a g i r l .

K n o w in g th a t C H A R M I N G is A - K I N D - O FP R I N C E a n d R O M E O is A - K I N D - O F B O Y l en ds nod i r e c t s t r e n g t h t o t h e i r s i m i l a r i t y , n o r d o e s i t h e l p t ok n ow th at C I N D E R E L L A is A - K I N D - O F P R I N C E S Sa n d J U L I E T is A - K I N D - O F G I R L . T h e s e fa ct s d o le n di n d i r e c t s t r e n g t h t o t h e t w o p a i r s b e c a u s e t h e g i v e nc l a s s i f i c a t i o n s i n d i c a t e c o m m o n c l a s s i f i c a t i o n a t h i g h e rl e v e l s . A f t e r a l l , a p r i n c e a n d a b o y a r e t h e s a m e s e x a sa re a p r i n cess an d a g i r l .

T o a c c o u n t f o r t hi s i n d i r e c t e v i d e n c e o f s i m i l a ri t y ,t h e i m p l e m e n t e d m a t c h e r tr e a t s a l l A - K I N D - O F s lo ts a si f t h e y c o n t a i n e d e v e r y t h i n g t h a t i s f o u n d b y t r a c i n gt h r o u g h th e A - K I N D - O F h i e r ar c h y t h a t le a ds f r o mt he m . T h e A - K I N D - O F s lo t o f C H A R M I N G c o nt ai nso n l y P R I N C E , b u t i t is t re a t e d a s i f i t c o n t a i n e dP R I N C E , M A N , a n d P E R S O N . S i m i la rl y R O M E O ' sA - K I N D - O F s lo t is t re a t e d a s i f i t c o n t a i n e d n o t o n l yB O Y , b u t a ls o M A N a n d P E R S O N . C o n s e q u e n tl y t h eA - K I N D - O F S L O T c o n t r ib u t e s a s co re o f t w o w h e nC H A R M I N G a n d P R I N C E a re pa ir ed . S im i la rl y C I N -D E R E L L A is a P R I N C E S S , a W O M A N , a n d a P E R -S O N w h il e J U L I E T is a G I R L , a W O M A N a n d a P E R -S O N . T h e i r A - K I N D - O F s lo ts c o n tr i b u te a s c o re o f t w oa s w e ll . T h u s t h e A - K I N D - O F s lo ts o f a l l t h e p a r ts l e a dt o a m a t c h s c o re o f te n , f o u r m o r e t h a n b e f o r e . F i g u r e 5s h o w s th e A - K I N D - O F h i e r a r c h y th a t g iv e s t h e s e e x t r ap o in t s .A n o b j e c t i o n t o t h is t y p e o f s c o ri n g is t h a t t h e A -K I N D - O F h i e r a r c h y m i g h t i n v o l v e l o n g c h a i n s t h a tw o u l d t e n d t o c a u s e c l a s s i f i c a t i o n i n f o r m a t i o n t o d o m i -n a t e m a t c hi n g . H a p p i ly , lo n g A - K I N D - O F c h a in s d on o t o c c u r i n t h e s i t u a t io n s c o n s i d e r e d i n t h i s w o r k s o f a r ,s o t h e o b j e c t i o n h a s b e e n n o t e d , b u t n o t t h o r o u g h l ys tu d i ed .

I f l o ng A - K I N D - O F c h a in s s h o u ld p r o v e to b e ap r o b l e m , t h e w o r k o f R o s c h e t a l. m a y b e r e l e v a n t [ 1 6] .T h e y a r g u e t h a t t h e w o r l d o f h u m a n e x p e r i e n c e i s s u c ht h a t t h e r e i s a s o - c a l l e d b a s i c l e v e l o f c la s s a b s t r a c t i o n i nt h e A - K I N D - O F h i e r a r c hy . A t t hi s b a si c le v e l, t w ot h i n g s a r e t r u e : a t t h e n e x t l e v e l u p , t h e m e m b e r s o f t h ec l a ss e s s h a r e s u b s t a n t i a l l y f e w e r p r o p e r t i e s t h a n a t t h eb a s i c l e v e l; a n d a t t h e n e x t l e v e l d o w n i n t h e h i e r a r c h y ,t h e m e m b e r s o f t h e c la s se s s h ar e a b o u t t h e s a m e n u m b e ro f p r o p e r t i e s a s a t t h e b a s i c l e v e l . C o n c e p t s l i k e g u i t a r ,a p p l e , h a m m e r , s h i r t , ta b l e , a n d c a r a r e a t t h e b a s i c l e v e l .M u s i c a l i n s t r u m e n t , f r u i t , t o o l , c l o t h i n g , f u r n i t u r e , a n dv e h i c l e a r e h i g h e r. G r a n d p i a n o , M a c i n t o s h a p p l e , b a l l-p e e n h a m m e r , d r e s s s h i r t , k i t c h e n t a b l e , a n d s p o r t s c a ra r e l o w e r .

F i g . 5 . T h e A - K I N D - O F h i e r a r c h y i s e x p l o i t ed i n m a t c h i n g . T h e A -K I N D - O F s l o ts c o n t ri b u t e f o u r p o i n t s to t h e s c o r in g o f t h e m a t c h w i t hR O M E O p a ir ed w it h C H A R M I N G a n d C I N D E R E L L A w i th J U L I E Te v e n t h o u g h e a c h h a s s o m e t h i n g d i f fe r e n t i n i ts A - K I N D - O F s l o t.

. . . . _ _ _ _ . _ . _ _ _ _ ~ p e r s 0 % ~ _ _ _ . _ ~man w0maR0 S\o / \ 0 iCinderella Juliet

A b o v e t h e b a s i c le v e l, c o m m o n c l as s m e m b e r s h i pm e a n s l i t tl e . B e l o w t h e b a s i c l e v el , c o m m o n c l a ss m e m -b e r s h i p a d d s l i t t l e . C o n s e q u e n t l y , i t m i g h t b e r e a s o n a b l et o s c o r e m a t c h i n g p o i n ts o n l y f o r c o m m o n c l a ss i fi c a ti o na t t h e b a s i c l e v e l , i g n o r i n g c o m m o n c l a s s i f i c a t i o n a b o v ea n d b e l ow , f i ne s si ng t h e p r o b l e m o f lo n g A - K I N D - O Fch a in s .4 .4 . C on s tra i n t Makes Some Re l at i on s More Importan tt h a n O t h e r s

T h e r e i s s o m e d e b a t e a b o u t w h e t h e r a m a t c h e r s h o u l dd i s ti n g u is h a m o n g t h e k i n d s o f i n f o r m a t i o n a v a i l a b l e f o rm a t c h i n g . O n e v i e w i s t h a t c l a s s i f i c a t i o n i n f o r m a t i o n i st h e m o s t i m p o r t a n t w h i l e a n o t h e r v i e w f a v o r s p r o p er t ie s .S t i l l a n o t h e r , m i l d e r v i e w i s t h a t a l l i n f o r m a t i o n i s i m -p o r t a n t , b u t t o a v a r y i n g d e g r e e t h a t h a s t o b e a c c o u n t e df o r b y a w e i g h t i n g s c h e m e , p o s s i b l y c o n t e x t d e p e n d e n t .T h i s c a n q u i c k l y g i v e t h e m a t c h e r a n a d h o c f e e l . I t i sd i s t u r b i n g w h e n a p r o g r a m m u s t b e t u n e d u p b y f o o l in gw i t h a s y s t e m o f p a r a m e t e r s .

N e v e r t h e l e s s , so m e r e l a t i o n s a re m o r e i m p o r t a n t t h a no t h e r s b e c a u s e t h e y l e a d t o th e c o n c l u s i o n s t h a t a r e t o b ee x p l o i t e d i n t h e a n a l o g y p r oc e s s . T h e i m p o r t a n t r e l a t i o n sa r e s o m e t im e s A - K I N D - O F s , s o m e t im e s H A S - P R O P -E R T Y s , a n d s o m e t i m e s o t h e r r el a ti o n s, s o m e o f w h i c ha r e n o r m a l l y i n c i d e n t a l .

T h a n k f u l l y , i m p o r t a n c e t e n d s t o b e t a u g h t b y t e a c h -e r s , e i t h e r e x p l i c i t l y o r i m p l i c i t ly . E x p l i c i t t e a c h i n g i sd o n e w h e n a t e a c h e r s a ys , p e r h a p s w i t h o u t j u s t i f i c a t io n ,t h a t s o m e f a c t i s i m p o r t a n t . I m p l i c i t t e a c h i n g i s d o n ew h e n a t e a c h e r i n c l u d e s s o m e f a c t i n a c o n s t r a i n t , t y p i -c a l l y i n t h e f o r m o f a c a u s a l c h a i n . T h u s I ta k e t h ef o l l o w i n g p o s i t i o n :

Any relation can be important in matching. The importance of a~articular relation can be determined by remem beringwhat teachersave said about it or by noting whether it is involved n constrainingsomething. Causing something is an impo rtant way of constraining.F o r t h e m o s t p a r t , t h e e x a m p l e s i n th i s p a p e r a s s u m e

a b e n e f i c i e n t t e a c h e r w h o g i v e s o n l y t h e r e l e v a n t f a c t sa n d w h o d o e s n o t d e l i b e r a t e l y t ry t o c o n f u s e t h e s y s t emb y s h o v e l i n g d e t r i t u s a t i t . I t i s i m p o r t a n t , h o w e v e r , t o

695 Comm unications Decem ber 1980of Volume 23the ACM Num ber 12


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u n d e r s t a n d t h a t m e c h a n i s m s h a v e b e e n i m p l e m e n t e dt h a t p a y a t t e n t io n t o i m p o r t a n c e o n d e m a n d .

I n p a r t i c u l a r , t h e m a t c h e r c a n b e t o l d t o u s e o n l yr el at io n s th a t h av e c o m m e n t f r am e s w it h I M P O R T A N Ti n t he H A S - P R O P E R T Y s lo t . T h e H A S - P R O P E R T Ys lo t o f a c o m m e n t f r a m e c a n h av e I M P O R T A N T p l ac e di n i t d i r e c t l y a s i n t h e f o l l o w i n g e x a m p l e :M a c b e t h k i ll D u n c a n [ h a s - p r o p e r t y i m p o r t a n t ] .A l t e rn a t iv e l y , t h e H A S - P R O P E R T Y s lo t c a n h a v e I M -P O R T A N T p u t in b y a d e m o n p l a ce d in th e C A U S Ef r a m e . U s i n g t h i s d e m o n , a l l f r a m e s a t e i t h e r e n d o f ac a u s e r e l a t i o n a r e n o t e d t o b e i m p o r t a n t , a s w e l l a s t h ec a u s e r e l a t io n i t s e l f .

A c t u a l l y , t h e i m p l e m e n t e d s t r a t e g y r e p r e s e n t s o n ee n d o f a s p e c t r u m o f p o s s ib i l i t ie s . A s i t s t an d s , r e l a t i o n sn e v e r b e c o m e g l o b a l l y i m p o r t a n t . A l o o s e r s t r a t e g yw o u l d m a k e a r e l a t i o n i m p o r t a n t e v e r y w h e r e in a s i tu a -t i o n i f i t i s d e t e r m i n e d t o b e i m p o r t a n t s o m e w h e r e i n t h es i t u a t i o n . A s t i ll l o o s e r s t r a t e g y w o u l d m a k e a r e l a t i o ni m p o r t a n t e v e r y w h e r e i n a s i t u a ti o n i f i t i s i m p o r t a n ts o m e w h e r e i n s o m e o t h e r s i t u a t io n o f t h e sa m e g e n e r a lc lass .4 . 5. M a t c h i n g L a r g e G r o u p s M a y R e q u i re S o m ePre l i mi n ary C l ass i f i c at i on

A s t h e s iz e o f t w o g r o u p s t o b e m a t c h e d b e c o m e sl a r g e , t r y i n g a l l p o s s i b i l i t i e s b e c o m e s i n t r a c t a b l e . T h e r ea r e t w o c ho i c es : T h r o w a w a y t h e e x h a u s t i v e m a t c h e r a n dd o s o m e t h i n g e l s e , o r s o m e h o w p r u n e t h e c o l l e c t i o n o fm a t c h i n g a l t e r n a t i v e s t h a t th e m a t c h e r g e n e r a t es . T h ei m p l e m e n t e d m a t c h e r p r u ne s :

One way to limit the m atching alternatives is to restrict the pairingsto those that link together only fram es of the sam e class, as specifiedby instructions to the m atcher.F o r e x a m p l e , i f t h e r e a r e t w o g r o u p s o f p e o p l e to b em a t c h e d , a n d e a c h c o n t a i n s, s a y , t h r e e m e n a n d f o u rw o m e n , t h e n t h e t o ta l n u m b e r o f m a t c h a l t e r n a t i v e s is:NI /(N 1-N 2) = 7 = 5040.B u t i f th e m a t c h e r i s i n s t ru c t e d t o l in k m e n o n l y w i t hm e n a n d w o m e n o n l y w it h w o m e n , t h e n t h e n u m b e r i s:MI / (MI -M2) x WI / (W1-W2 ) = 3 x 4 = 6 x 24= 144.T h e s m a l l e r n u m b e r i s o n l y 3 p e r c e n t o f th e l a r ge r . O fc o u r s e i t i s n o l o n g e r p o s s i b l e t o d i s c o v e r a m a l e C i n d e r -e l la , a d e f e c t t h a t m a y s u g g e s t a si m i l a r d i f f i c u l t y w h e np e o p l e m u s t d e a l w i t h a n a l o g i e s i n v o l v i n g m a n y p a r t s .T o p r e v e n t t o o m a n y b l u n d e r s o f t h is s o rt r e q u i re s s o m ew a y o f s e l e c t i n g a g o o d s e t o f c l as s e s f o r t h e m a t c h e r .T h e r e m a y b e s o m e w a y o f d o i n g t hi s b y in s p e c t in g t h eA - K I N D - O F h i e r a rc h y i n th e v i ci n it y o f t h e f ra m e si n v o l v e d i n t h e m a t c h .4.6 . Ma tching Finds Corresponding P arts in Plo ts

H e r e a r e s o m e r e s u l t s s h o w i n g t h e m a t c h s c o r e sb e t w e e n t h e f o u r S h a k e s p e a r e a n t r a g e d i e s a n d o n e c o m -e d y :

MA HA J U OT TAMA cbeth 78 49 45 21 9H Am let 49 108 35 22 9JUlius Caesa r 45 35 91 28 8OT hello 21 22 28 71 10TA ming of the Shrew 9 9 8 10 50

T h e c h o i c e o f S h a k e s p e a r e a n t r a g e di e s w a s s o m e w h a ti l l - a d v i s e d s i n c e t h e y l e a n t o w a r d t h e m a c a b r e . N e v e r -t h e l e s s , i t i s i n t e r e s t i n g t h a t t l ; e t e n d e n c y t o h a v e e v i l ,m u r d e r , a n d d e a t h e v e r y w h e r e i n s i g h t d o e s m a k e t h e mm o r e s i m i l a r t o e a c h o t h e r t h a n t o t h e c o m e d y .

T h e a v e r a g e s c o r e o n t h e d i a g o n a l i s 8 0 . E v i d e n t l yt h e a v e r a g e n u m b e r o f fa c t s k n o w n a b o u t e a c h p l o t ist h e r e f o r e 8 0 . S o m e o f th e f a c t s a r e d e r i v e d b y d e m o n sa n d o t h e r s ar e i m p l ie d b y th e A - K I N D - O F c o n n e c ti o n s.A d e m o n o n M U R D E R c r ea t es a K I L L a n d l in k s t h eM U R D E R a n d t he K I L L t o g e th e r w i th a C A U S E r el a-t i o n. A d e m o n o n K I L L l e a d s t o i n s t an c e s o f H A S -P R O P E R T Y a n d C A U S E b e c au s e k il li ng s o m e o n ec auses t h a t p e r s o n t o h a v e t h e p r o p e r t y o f b e i n g d e a d .A l s o , m u r d e r e r s a r e n o t e d t o h a v e t h e E V I L p r o p e r t y .

I t i s i n s t r u c t i v e t o l o o k a t t h e b e s t a n d w o r s t o f f -d i a g o n a l m a t c h e s t o s e e if th e y m a k e s e ns e . E v i d e n t l yMacbeth a n d Hamlet s h o w t h e m o s t s i m i l a r i t y . T h em a t c h e r a n n o u n c e s i ts v i e w a s fo l lo w s :4 9 . V a l u e s m a t c h w i t h 78 . a n d 1 0 8. p o s s i b l e - - B e s t

m a t c h i s 1 3 . b e t t e r t h a n n e x t b e s t .(49 . (1 0. M A C B E T H C L A U D I U S )(5 . D U N C A N G H O S T )

(4 . L A D Y - M A C B E T H G E R T R U D E )(4 . M U R D E R - 1 M U R D E R - 2 )(4 . K I L L - 1 K I L L - 4 )(4 . K I L L - 3 K I L L - 5 )(3 . M A C D U F F H A M L E T )(3 . K I L L - 2 K I L L - 8 )( 2. H Q - 3 H Q - 5 )(2 . H Q - 2 H Q - 9 )(2. HQ-1 HQ-4)(1 . W E I R D - S I S T E R S L A E R T E S )(1 . C A U S E - 6 C A U S E - 1 1 )(1 . C A U S E - 5 C A U S E - 2 0 )(1 . C A U S E - I C A U S E - 8 )(1 . C A U S E - 2 C A U S E - 9 )(1 . C A U S E - 7 C A U S E - 1 2 )(0 . A K O - 2 A K O - 3 ) )

T h i s m a k e s s o m e s e n s e . M a c b e t h a n d C l a u d i u s b o t h k i l la k i n g s o a s t o b e c o m e k i n g a n d b o t h a r e k i l l e d i n t u r n .T h e i r v i c t im s a re D u n c a n a n d t h e G h o s t . M a c d u f f a n dH a m l e t k i l l t h e m . T h e i r w i v e s a r e L a d y M a c b e t h a n dG e r t r u d e .O n t h e o t h e r h a n d , The Taming of the Shrew a n dJulius Caesar s h o w l i tt l e si m i l a r i t y . I n f a c t , t h e r e a r e o n l y

696 Comm unications Decem ber 1980of Volume 23the ACM Numb er 12


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t w o p o i n t s o f s i m i l a r i t y b e y o n d t h e f a c t th a t t h e r e aref o u r p e o p l e t o p a i r u p a n d t w o o f th e f o u r h a v e t h e s a m es e x. T h e s c o r e o f e i g h t is a t t h e l e v e l o f b a c k g r o u n dn o i se .E v i d e n t l y , t h e p l o t s a s g i v e n t o t h e m a t c h e r d o n o te x h i b i t m u c h d i v e r t i n g d e t a i l b e c a u s e t h e g e n e r a l s h a p eo f th e t a b l e i s th e s a m e w h e n t h e m a t c h e r c o u n t s o n l yt h e r e l a t i o n s t h a t a r e d e m o n s t r a b l y i m p o r t a n t . T h e f o l -l o win g r ev i sed t ab l e sh o ws t h i s :

MA HA JU OT TAMA cbeth 16 12 11 5 0HA mlet 12 28 9 5 0JUlius Caesa r 11 9 21 7 0OThello 5 5 7 21 0TAm ing of the Shrew 0 0 0 0 11T h e s c o r e s a r e m u c h r e d u c e d , b u t s t i l l M a c b e t h a n dH a m l e t a r e s i m i l a r w h i l e T h e T a m i n g o f t h e S h r e w a n dJ u l iu s C a e s a r are n o t .

I n p r o d u c i n g t h e s c o r e s i n t h i s t a b l e , t h e m a t c h e rc o u n t e d o n l y r e la t io n s m a r k e d a s im p o r t a n t . D e m o n s o nC A U S E a n d P R E V E N T d o th e m ar k in g .

4 .7 . Ab s trac t i on May B e N ec essary B efore Matc h i n gM a t c h i n g m a y r e q u i r e s o m e p r e l i m i n a r y a c t a b s t ra c -t i o n , e x p l o i t i n g t h e f a c t t h a t a c t s l i k e K I L L i m p l y m o r e

a b s t r a c t a c t s l i k e H U R T . S u p p o s e , f o r e x a m p l e , t h a t t w os i t u a t i o n s a r e p r o p o s e d , o n e i n v o l v i n g a t r a g i c e v e n t , a n dth e o th e r , a p e r so n i n co n f l i c t wi th h im se l f :

T R A G I C - E V E N T is a si tu a ti on .E v i l - p e r s o n i s a p e r s o n . G o o d - p e r s o n i s a p e rs o n . E v i l -p e r s o n h u r t G o o d - p e r s o n . E v i l - p e r s o n h a s - p r o p e r t ye v il . G o o d - p e r s o n h a s - p r o p e r t y g o o d .S E L F - C O N F L I C T is a s it ua ti on .G r u b b l a is a p e r so n . G r u b b l a h a s - c o n fl i c t- w i t h G r u b -b l a .

A s t h e y s t a n d , t h e s e s i t u a t i o n s a r e a b s t r a c t i o n s o f s o m eo f t h e t h i n g s t h a t g o o n i n t h e t e n e x p e r i m e n t a l p l o t s,b u t n e i t h e r h a s a n y t h i n g e x p l i ci t ly i n c o m m o n w i t h a n yo f t h e m , o t h e r t h a n t h a t p e o p l e a r e i n v o lv e d a n d t h a ts o m e e x p l i c i t h u r t i n g g o e s o n i n I b s e n ' s A D o l l s H o u s ea n d S h a w ' s P y g m a l i o n . G o o d a n d e v il a r e n o w h e r e t o b ef o u n d .A k i n d o f a b s t r a c ti o n c a n m a k e g o o d m a t c h e s h a p p e na n y w a y . I t is e a s y t o p u t d e m o n s o n H A S - P R O P E R T Ya n d M U R D E R s o t h a t lo y a l p e o p l e a r e n o te d to b eG O O D a n d m u r d e r e r s a r e n o t e d t o b e E V I L . O t h e rd e m o n s c a n g e ne r at e H U R T a n d H A S - C O N F L I C T -W I T H r e la t io n s , g iv e n K I L L . F o r t h e t r a gi c e v e n t si tu -a t i o n , t h e s e d e m o n s e n a b l e t h e m a t c h e r t o p r o d u c e t h ef o l l o w i n g r e s u l t s , w h e r e t h e n u m b e r s g i v e t h e a c t u a lm a t c h i n g s c o re s a n d t h e p e r c e n t a g e s o f t h e m a x i m u mp o ss i b l e sco res :

T h e m a t c h e s , i n o r d e r o f q u a l i ty , a r e :5 . 8 3 . % M a c b e t h5 . 8 3 . % H a m l e t5 . 83 .% Oth e l l o5 . 83 .% Ju l i u s Ca esa r4 . 6 6 .% D o l l s H o u s e4 . 6 6 . % P y g m a l i o n4 . 6 6 .% A d a m a n d E v e3 . 5 0 .% Cin d ere l l a2 . 3 3 .% T a m i n g o f t h e S h r e w2 . 3 3. % H e d d a G a b b i e r

T h e a c t o f m u r d e r m a d e M a c b e t h a n e v il p e r s o n a n de s t a b l i s h e d t h a t h e h u r t D u n c a n . T h e p l o t l a c k s p e r f e c tm a t c h w i t h t h e d e s c r i p t i o n o f a t r a g i c e v e n t b e c a u s e i tw a s n o t s t a t e d t h a t D u n c a n w a s a g o o d p e r s o n , n o r w a si t d e d u c e d . H a m l e t a n d J u l i u s C a e s a r s i m i l a r l y f a i l t om a t c h p e r f e c t ly . T h e G h o s t a n d C a e s a r a r e no t k n o w nt o b e g o o d .

O t h e l l o f a i l s b e c a u s e O t h e l l o k i l l s D e s d a e m o n a , b u tk i l li n g , u n l i k e m u r d e r i n g , d o e s n o t i m p l y a p e r s o n i s e v i l.D e s d a e m o n a , h o w e v e r , i s g o o d b e c a u s e s h e i s l o y a l .

N o w c o n s i d e r t h e o t h e r s i t u a t i o n , t h e o n e t h a t i n -vo lves se l f - co n f l i c t :T h e m a t c h e s , i n o r d e r o f q u a l i t y , ar e :2 . 100 .% H am le t2 . 100 .% Oth e l l o2 . 100 .% Ju l i u s Ca esa r2 . 1 00 .% H e d d a G a b b i e r1 . 5 0 .% M a c b e t h1. 5 0 .% T a m i n g o f t h e S h r e w1 . 5 0 .% Do l l s H o u s e1 . 5 0 .% P y g m a l i o n1 . 5 0 .% Cin d ere l l a1 . 5 0 .% A d a m a n d E v eT o k i l l m e a n s t o h u r t w h i c h m e a n s t o h a v e c o n f l i c t w i t h .E v i d e n t l y t h e g o o d m a t c h e s a r e t h e o n e s w i t h s u i c i d e s .

A f o r m o f i r o n y , i n c i d e n t a l ly , c o u l d b e f o u n d t h es a m e w a y . B u t t h e r e w e r e n o s u c h i n c i d e n t s , a t l e a s t a sd e s c r i b e d :I R O N I C - E V E N T is a si tu a ti on .U n f o r t u n a t e - p e r s o n i s a p e r s o n . U n f o r t u n a t e - p e r s o nw a n t a d e s i r e d - a c t - - a t t e m p t t h e d e s i r e d - a c t [ c a u s e a na c t u a l - a c t ] . T h e d e s i r e d - a c t o p p o s i t e t h e a c t u a l - a c t .A l l t h e s e e x a m p l e s a r g u e f o r t h e f o l l o w i n g c o n c lu s i o n :S i m p l e d e d u c t i o n i n t h e d i r e c t i o n o f a b s t r a c t i o n f a c il -

i t a t e s s o m e m a t c h e s .4 .8 . M an y S i mi l ar i ty Me asure s Are Poss i b l eT h e s i m i l a r i t y m e a s u r e u s e d i n t h e i m p l e m e n t e dm a t c h e r i s j u s t t h e t o t a l n u m b e r o f p o in t s o f e v i d e n c ee x h i b i t e d w h e n t h e p a r t s i n t w o s i t u a t i o n s a r e o p t i m a l l yp a i r e d . T h u s t h e s i m i l a r i t y i s a m e a s u r e o f o v e r l a p .

M a n y o t h e r a u t h o r s h a v e c o n s i d e r e d t h e q u e s t i o n o fs i m i l a r i t y m e a s u r e m e n t , a l t h o u g h n o t i n t h e c o n t e x t o ft h e r e p r e s e n t a t i o n u s e d i n t h i s p a p e r . I n p a r t i c u l a r ,T v e r s k y c o n s i d e r s s it u a t i o n s i n w h i c h t w o o b j e c t s d e f i n e db y f e a t u r e s e t s a r e t o b e c o m p a r e d [ 1 8 ] . H e a r g u e sp e r s u a s i v e l y t h a t s i m i l a r i t y s h o u l d b e d e t e r m i n e d n o t

697 Communications Decem ber 1980of Volume 23the ACM Num ber 12


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Fig. 6 . W ate r - s i tua t io n-3, a s i tua t io n invo lv ing a wate r pipe , can be Fig. 7 . Resis tor - s i tua t io n-6 , a s i tua t ion invo lv ing a r es i s tor , can bema t c he d t o t he ge ne r a l w a t e r p i pe de s c r i p t i on e a s il y , ma t c h e d t o t he ge ne r a l w a t e r p i pe de s c r i p t ion .plpe-lawpto o-1 o l l l o r t

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II I p"rtr e s t s t o r - s t t ua t i on - 6

o n l y b y t h e f e a t u r e s t h a t c o r r e s p o n d , b u t a l s o b y t h o s et h a t d o n o t . F o r d e t e r m i n i n g t h e s i m i l a r i t y o f f e a t u r e s e tA t o f e a t u r e s e t B , h e r e c o m m e n d s t h i s f o r m u l a :SIMILA RITY(A, B)

= O f ( A U B ) - ~ f ( A - 8 ) - ~ f ( , - A )

F o r s o m e O , a , a n d f l w h e r e f i s t y p i c al l y a f u n c t i o n t h a tsa t i s f i e s ad d i t i v i t y :f ( X O Y ) = f ( X ) + f ( Y ) .I n t h i s p a p e r s i m i l a r i t y i s m e a s u r e d b e t w e e n g r o u p s o ff r a m e s r a t h e r t h a n f e a t u r e s e t s . A U B i s a n a l o g o u s t o t h es l o t- v a l u e c o m b i n a t i o n s t h a t a r e i n o n e o r b o t h o f t h eg r o u p s o f f r a m e s ; A - B a n d B - A w o u l d b e a n a l o g o u st o t h e s l o t- v a l ue c o m b i n a t i o n s t h a t a r e i n o n e g r o u p o ff r a m e s b u t n o t i n t h e o t h e r ; f i s j u s t a f u n c t i o n w h i c hco u n t s ; 0 i s 1 ; an d bo th a an d f l a r e 1 . I f t h e an a lo g s t oA - B a n d B - A w e r e u s e d w i t h u n e q u a l a a n d f l, t h em e a s u r e w o u l d b e u n s y m m e t r i c - - o n e s i t u a t i o n w o u l db e m o r e s i m i l a r to a s e c o n d t h a n t h e s e c o n d w o u l d b e t oit.4 . 9. M a t c h i n g W o r k o n P h y s i c a l L a w s a s w e l l a s o nP l o t s

C o n s i d e r t h e r e l a t i o n b e t w e e n t h e w a t e r p r e s s u r e a n dw a t e r f l o w i n a p i p e . I t is p o s s ib l e t o d e s c r i b e t h e k i n d o ft h i n g e a c h i s , a s w e l l a s a b o u t h o w e a c h i s r e l a t e d t o t h e6 9 8

o t h e r a n d t o t h e r e s i s t a n c e o f t h e p i p e , u s i n g t h e s a m es y m b o l - a r r a n g e m e n t c o n v e n t i o n s t h a t w e h a v e b e e nw o r k i n g w i th . A n e w v o c a b u l a r y i s n e e d e d , h o w e v e r :

P I P E - L A W is a c o n s tr a i n t - -d e p e n d e n t - v a r i a b l ep r e s s u r e - p i p e - l a w - - i n d e p e n d e n t - v a r i a b l e f l o w - p i p e -l a w - - m u l t i p l i e r r e s is t a nc e - p ip e - la w .P r e s s u r e - p i p e - l a w i s a w a t e r - p r e s s u r e . F l o w - p i p e - l a wi s a w a t e r - f l o w . R e s i s t a n c e - p i p e - l a w i s a w a t e r - r e s i s t a n c e .P r e s s u r e - p i p e - l a w i s p r o p o r t i o n a l - t o f l o w - p i p e - l a w[ m u l t i p l i e r r e s i s ta n c e - p i p e - l a w ] .

M a t c h i n g a s p e c i f ic s i t u a t i o n a g a i n s t t h is c o n s t r a i n ti s l i k e m a t c h i n g o n e p l a y p l o t a g a i n s t a n o t h e r . M o r e o v e r ,a s p e c i f ic s i t u a t i o n a n d a g e n e r a l l a w n e e d n o t b e s oc l o s e l y r e l a t e d , a s w h e n a n e l e c t r i c a l s i t u a t i o n i n v o l v i n ga r e s i s t o r i s m a t c h e d a g a i n s t t h e p i p e l a w .N o t e t h a t a b s t r a c t i o n m a y b e n e c e s s a r y w i t h p h y si c a ll a w s ju s t a s i t i s w i t h p l o t s . S u p p o s e , f o r e x a m p l e , t h a t Ai s p r o p o r t i o n a l t o B i n o n e s i t u a t i o n w h i l e X i s d e t e r -m i n e d b y Y i n t h e o th e r . O r s u p p o s e t h a t A i s k n o w n t ob e a k i n d o f f o r c e i n o n e s i t u a t i o n a n d X is k n o w n t oc a u s e s o m e t h i n g i n t h e o t h e r . M a t c h i n g s h o u l d b e p o s -s i b l e b e c a u s e b e i n g p r o p o r t i o n a l t o s o m e t h i n g i s a w a yo f b e i n g d e t e r m i n e d b y s o m e t h i n g a n d f o r ce s a r e th i n g st h a t c a u s e . A s w i t h p l o t s , w h e n m a t c h i n g s e e m s t o od i f f i c u l t a t f i r s t , s o m e d e m o n s a r e r e q u i r e d t o m a k es i m p l e a b s t r a c t i o n - o r ie n t e d d e d u c t i o n s. N o c h a n g e s a r em a d e t o t h e m a t c h e r i t s e l f .C o m m u n i c a t i o n s D e c e m b e r 1 9 80o f V o l u m e 2 3t h e A C M N u m b e r 1 2


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Fig. 8. The d escriptive par t of Oh m's law, as abstracted from two Fig. 9. The descriptive part of the general linear law, as abstractesituations analyzed hrough the water-pipe analogy, from the water pipe law and Ohm 's law.ohms-aw

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U n d e r s t a n d i n g m a t c h i n g h a s p r e p a re d u s f o r u n d e r -s t a n d i n g h o w k n o w l e d g e f r o m o n e d o m a i n c a n b e t r an s -f e r re d t o a n o t h e r a s w h e n w e l e a rn O h m ' s l a w b y b e i n gto ld tha t r e s i s to r s a re l i k e wa te r p ipe s .T h e r e a s o n m a t c h i n g h e l p s i s t h a t a p p l y i n g a c o n -s t ra in t c an be v i ewed a s cons i s t ing o f two s t eps : F i r s t ,i d e n t i f i c a t i o n o f t h e r o l e e a c h p a r t p l a y s i n t h e c o n s t r a i n ta n d s e c on d , c o m p u t a t i o n o f a r e su l t. T h u s m a t c h i n ghe lps becaus e i t i den t i f i e s the ro le e ach pa r t p l ays in ac o n s t r a i n t , m a k i n g i t p o ss i b l e t o p a i r o f f t h e p a r a m e t e r so f a c o m p u t a t i o n a g a i n s t t h e a v a i l a b l e a r g u m e n t s . T h i sp o i n t o f v i e w is r e m i n i s c e n t o f a s u g g e s t i o n in M o o r ea n d N e w e l l [ 1 1] .

F i g u r e 6 i l l u s t r a t e s t h e r o l e o f m a t c h i n g i n a p p l y i n gg e n e r a l k n o w l e d g e a b o u t w a t e r p i p e s to a s p e c if i c w a t e rp i p e s i t u a t i o n . T h e g e n e r a l d e s c r i p t i o n o f w a t e r p i p es i t u a t i o n s i d e n t i f i e s t h e p a r t s t h r o u g h b o t h t h e P A R Tr e l a t i o n a n d t h r o u g h t h e r o l e - e s t a b l i s h i n g r e l a t i o n sD E P E N D E N T - V A R I A B L E , I N D E P E N D E N T - V A R I -A B L E , a n d M U L T I P L I E R . T h e d e sc r ip t io n o f th e s pe -c i fi c w a t e r p i p e s i t u a t i o n o n l y i d e n t i f i e s t h e p a r t s t h r o u g ht h e P A R T r e l a t io n , p r o v i d i n g n o e x p l i c i t m e a n s o f id e n -t i f y i n g t h e r o l e t h e p a r t s a r e t o p l a y i n c o m p u t i n g , s a y ,t h e w a t e r p r e s s u r e , g i v e n t h e p i p e r e s i s t a n c e a n d w a t e rf lo w . A p r o c e d u re l o o k i n g f o r t h e D E P E N D E N T - V A R -I A B LE , I N D E P E N D E N T - V A R I A B L E , a nd M U L T I -P L I E R r e l a t i o n s c a n n o t w o r k o n t h e s p e c i f i c s i t u a t i o nu n t i l t h e p a r t s o f t h e s p e c i fi c s i tu a t i o n a r e i d e n t i f i e d w i t ht h o s e o f t h e g e n e r a l s i t u a t i o n .

I n t h e e x a m p l e g i v e n , e s t a b l i s h i n g t h e m a t c h i s n op r o b l e m b e c a u s e t h e p a r t s o f t h e s p e ci f ic s it u a t i o n h a v ee n o u g h c l a s s i f ic a t i o n , p r o p e r t y , a n d o t h e r i n f o r m a t i o n t oi n s u r e m a t c h .

5.1. M atching Ena bles Com putation in Ana logousDomainsS o f a r w e h a v e l o o k e d a t a n e x a m p l e i n w h i c h i t w a sn e c e s s a r y t o m a t c h t h e p a r t s o f a s p e c if i c s it u a t i o n a g a i n s t699

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t h o s e o f a g e n e r a l d e sc r i p ti o n w i t h i n o n e d o m a i n . N o ww e l o o k a t a n e x a m p l e i n w h i c h t h e s p e c i f ic si t u a t i o n a n dt h e g e n e r a l s i t u a t i o n a r e i n d i f f e r e n t d o m a i n s .

F i g u r e 7 i l lu s t r a te s a n e x a m p l e i n w h i c h i t is d e s ir e dto ca lcu la t e the vo l t age ac ros s a re s i s to r . As s hown , thep a r t s o f t h e s p e c i f ic r e s i st o r s i t u a t i o n a r e d e s c r i b e d b yc l a s s i f i c a t i o n , p r o p e r t y , a n d o t h e r i n f o r m a t i o n , b u t i t i sa s s u m e d t h a t t h e r e i s n o g e n e r a l d e s c r i p t i o n o f r e s i s t o rs i t u a t i o n s a n d n o p r o c e d u r e f o r c o m p u t i n g t h e v o l t a g eacross a res is tor .

I f a t e a c h e r a n n o u n c e s t h a t r e s is t o rs a r e l i k e w a t ep i p e s , h o w e v e r , t h e v o l t a g e c a n b e c o m p u t e d . I t i s o n l yn e c e s s a r y t o m a t c h t h e p a r t s o f t h e s p e c i f i c r e s i s t o rs i t u a t i o n w i t h t h o s e o f t h e g e n e r a l w a t e r p i p e s i t u a t i o na n d t o u s e t h e p r o c e d u r e f o r c a l c u l a t i n g w a t e r p r e s s u r eo n t h e r e s i s t o r - s i t u a t i o n p a r t s i d e n t i f i e d a s t h e I N D E -P E N D E N T - V A R I A B L E a n d th e M U L T I P L I E R . A s is t a n d s , t h e r e i s e n o u g h e v i d e n c e t o i n s u r e t h e c o r r e c tm a t c h o f t h e p a r ts , a l t h o u g h t h e s t r e n g t h o f t h e m a t c h in a t u r a l l y w e a k e r t h a n i t w a s w h e n t h e s p e c i f ic s i t u a t i o na n d t h e g e n e r a l s i t u a t i o n b o t h i n v o l v e d w a t e r .5.2. Speci f ic Laws Can Be Learned

I t i s p o s s i b l e t o g e n e r a t e a g e n e r a l d e s c r i p t i o n or e s is t o r s i t u a t io n s o n c e t w o s p e c i f ic s i t u a t i o n s h a v e b e e na n a l y z e d t h r o u g h t h e w a t e r - p i p e a n a l o g y . T h e i d e a i ss i m p l e : C o p y t h e c l a s s i f i c a t i o n , p r o p e r t y , a n d o t h e r i n -f o r m a t i o n t h a t i s c o m m o n t o b o t h s p e c i f i c s i t u a t i o n s .F igu re 8 i l lu s t ra t e s the re s u lt , g iven two ana ly zed re s i s to rs i tua t ions .W i t h t h e n e w d e s c r i p t i o n o f r e s is t o r s it u a t io n s , t h ep r o c e d u r e t h a t c o m p u t e s w a t e r p r e s s u r e c a n b e a p p l i e dto re s i s to r s i tua t ions w i th more conf idence , s ince re s i s to rs i t u a t i o n s w i l l m a t c h t h e g e n e r a l r e s i s t o r - s i t u a t i o n d e -s c r i p t i o n b e t t e r t h a n t h e y w i l l m a t c h t h e g e n e r a l w a t e rp i p e s i t u a t i o n . T h e n e w l y g e n e r a t e d , g e n e r a l d e s c r i p t i o no f r e s i s t o r s i t u a t i o n s , t o g e t h e r w i t h t h e s a m e p r o c e d u r et h a t w o r k e d w i t h w a t e r p i p e s , c o n s t i t u t e O h m ' s l a w .G e n e r a t i n g t h e d e s c r i p t i o n c o n s t i t u te s a k i n d o f l e a rn i n g .L e t u s recap i tu l a t e the s t eps :

T w o s p e c i f ic s i tu a t i o n s a r e a n a l y z e d u s i n g a g e n e r a ls i t u a t i o n d e s c r i p t i o n i n a n o t h e r d o m a i n .Com munications Decem ber 1980of Volume 23the ACM Num ber 12


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F i g . 1 0 . Th e c a us a l c o nne c t i ons i n M a c b e t h . I f M a c b e t h i s m a t c h e dw i t h a s i t u a t i o n h a v i n g n o c o n n e c t i o n s , t h e n a s k i n g i f t h e M a c b e t hp e r s o n d i e s l e a d s t o a s k i n g q u e s t i o n s d e t e r m i n e d b y t h e c a u se s . T h i s i sd o n e b y o v e r l ay i n g t h e C A U S E c o n n e c t io n s in M a c b e t h o n t h o s e i nt h e n e w s i t u a t i o n , a s t r i p p e d d o w n v e r s i o n o f H a m l e t he r e . The f i r s tq u e s t i o n i s a b o u t G e r t r u d e a n d t h e c a u s e o f a m u r d e r . I f t h e a n s w e r i su n k n o w n , t h e s e c o n d q u e s t i o n i s a b o u t t h e C l a u d i u s p e r s o n a n dw h e t h e r h e d e s i r e s t o b e k i n g .

s u g g e s t t h e r i g h t r e l a t i o n s t o c h e c k a n d t h e r i g h t q u e s -t i o n s t o a s k . H e r e w e c o n s i d e r o n l y s p e c i a l c a s e s o fc o n s t r a i n t i n v o l v i n g c a u s e . T h e k e y a s s u m p t i o n i s t h a tt h e c a u s e s t r u c t u r e o f a w e l l - u n d e r s t o o d s i t u a t i o n i s l i k e l yt o s a y s o m e t h i n g a b o u t t h e p o s s i b l e c a u s e s t r u c t u r e i n as i t u a t i o n t o b e a n a l y z e d .

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- - T h e c o m m o n p a r t s o f t h e s p ec i fi c s i t u at i o n d e s c ri p -t i o n s d e t e r m i n e a g e n e r a l d e s c r i p t i o n i n t h e s a m ed o m a i n .

- - T h e p r o c e d u r a l p a r t o f t h e la w i n t h e o t h e r d o m a i nis b r o u g h t o v e r w i t h o u t c h a n g e .I t is p o ss i b l e t o p u s h t h e l e a r n i n g f u r t h e r b a c k , a c q u i r i n gt h e p r o c e d u r a l p a r t o f t h e l a w b y e x a m p l e s , r a t h e r t h a nb y c o p y i n g , b u t w o r k o n t h i s i s n o t y e t s o l i d e n o u g h t or e p o r t .5 .3 . G e n e r a l L a w s C a n B e L e a r n e d

S p e c i f i c l a w s a r e l e a r n e d b y j o i n t l y a n a l y z i n g t w ow o r k e d - o u t s i t u a t i o n s i n o n e d o m a i n . G e n e r a l l a w s a r el e a r n e d b y j o i n t l y a n a l y z i n g t w o s p e c i f i c l a w s i n d i f f e r e n td o m a i n s . T h e l e a r n in g p r o c e d u r e i s t h e s a m e .

F i g u r e 9 i l l u s t r a t e s t h e r e s u l t , g i v e n t h e w a t e r - p i p el a w a n d O h m ' s l a w . A g a i n t h e k e y s te p is to f o r m a n e wd e s c r i p ti o n o u t o f w h a t i s c o m m o n t o b o t h g i v e n d e s c r i p-t io n s. T h e p r o c e d u r a l p a r t, n o t e d t o b e t h e s a m e i n b o t hs p e c i f ic la w s , i s a d o p t e d w i t h o u t c h a n g e .6 . R e a s o n i n g U s i n g A n a l o g y - D r i v e n S i tu a t i o n A n a l y s i s

H o w i s it p o s s ib l e t o k n o w i f s o m e r e l a t i o n h o l d s i no n e s i t u a t i o n , g i v e n t h a t t h e s i t u a t i o n i s a n a l o g o u s t oa n o t h e r , w e l l - u n d e r s t o o d s i t u a t i o n ? T h e a n s w e r i s t h a tt h e c o n s t r a i n t r e l a t i o n s i n t h e w e l l - u n d e r s t o o d s i t u a t i o n

6 . 1 . T h e C a u s e R e l a t i o n s i n S i t u a t i o n s M a k eC o m m o n - S e n s e R e a s o n i n g P o s s i b l e

T o b e m o r e p r e c i s e , t h e f o l l o w i n g s t e p s a r e t a k e n i nt h e c u r r e n t im p l e m e n t a t i o n w h e n a u s e r as k s a b o u t s o m ere l a t i o n :

- - F i r s t , t he r e l a t i on i n q ue s t i on ma y a c t ua l l y be i n t he s i t ua t i onbe i ng a na l yz e d . I f s o , no f u r t h e r a c t i on i s ne e de d .- - S e c o n d , i n t h e w e l l - u n d e r s t o o d s i t u a ti o n , t h e r e l a t io n i n q u e s t i o nm a y b e c a u s e d b y a p e r s o n . I f so , a s k i f t h e c o r r e s p o n d i n g p e r s o ni n t he s i t ua t i on be i ng a na l yze d c a us e s t he r e l a t i on .- - T h i r d , i n t h e w e l l - u n d e r s t o o d s it u a t io n , t h e r e l a ti o n i n q u e s t i o nm a y b e c a u s e d b y a n o t h e r r e l a t i o n . I f so , t ry t o ju s t i f y t h a t o t h e rr e l a t i on i n t he s i t ua t i on be i ng a na l yze d by r e c u r s i on .I f t h e r e a r e s e v e r a l c a u s e s f o r a r e l a t i o n i n t h e w e l l -

u n d e r s t o o d s i t u a t i o n , a ll m u s t b e v e r i f ie d . I f a n y P R E -V E N T E D - B Y r e la t io n s a re e n c o u n t e r e d a l on g t he w a y ,t h e y a r e i n v e s t i g a t e d a s f o l l o w s :

I f , i n t he w e l l - u nde r s t ood s i t ua t i on , a p e r s on p r e v e n t s a r e l a t i on ,a s k i f t h e c o r r e s p o n d i n g p e r s o n i n t h e s i t u a t i o n b e i n g a n a l y z e dpr e v e n t s t he r e l a t i on .I f , i n t he w e l l - und e r s t oo d s i t ua t ion , a r e l a t i on i s p r e v e n t e d b ya no t he r r e l a t i on , t r y t o j u s t i f y t ha t o t he r r e l a t i on i n t he s i t ua t i onb e i n g a n a l y z e d b y r e c u r s i o n .

S u c ce s s i n p u rs u i ng a n y o f a r e la t io n 's P R E V E N T E D -B Y v a l u e s m e a n s t h e c o r r e s p o n d i n g r e l a t i o n in t h e g i v e ns i t u a t i o n c a n n o t b e e s t a b l i s h e d .

T o s e e h o w a l l t h i s w o r k s o u t , c o n s i d e r t h e f o l l o w i n gs t r i p p e d - d o w n v e r s i o n o f Ha m le t :H A i s a s t o r y .G h o s t is a k in g . C l a u d iu s i s a m a n - - m a r r y G e r t r u d e .G e r t r u d e i s a w o m a n . H a m l e t i s a m a n - - h a s - p r o p e r t ylo y a l .A s i t s t a n d s , t h e r e i s b a r e l y e n o u g h s a i d t o d o a n u n -a m b i g u o u s m a t c h a g a i n s t Ma cb e th , b u t g i v e n t h a t a u s e ra s k s q u e s t i o n s , i t m a y s t i ll m a k e s e n s e t o u s e t h e a n a l o g y .I n p a r t i c u l a r , t h e f o l l o w i n g t r a c e s w h a t c a n b e d o n eg i v e n t h e c a u s e c o n n e c t i o n s i n Ma cb e th , s h o w n i n F i g u r e1 0 , t o g e t h e r w i t h a q u e s t i o n a b o u t w h e t h e r C l a u d i u sd ies:( C H E C K t C L A U D I U S v H A S - P R O P E R T Y v D E A DI N H A U S I N G M A )D o e s G E R T R U D E c au se th e M U R D E R slo t o f C L A U -D I U S t o h a v e G H O S T i n it?> N O ( m e a n i ng t h e u se r d oe s n ot k n o w )D o es C L A U D I U S D E S I R E [ C L A U D I U S A - K I N D - O FK I N G ] ?> Y E S ( a s s u m e d f o r il l u st r a ti o n )E v id e nt ly C L A U D I U S D E S I R E [ C L A U D I U S A -K I N D - O F K I N G ] .E v i d e n t ly t he r e is s uf fi c ie n t C A U S E f o r t h e M U R D E Rs lo t o f C L A U D I U S t o ha v e G H O S T i n it.

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E v i d e n t l y t h e r e i s s u f f i c i e n t C A U S E f o r t h e K I L L s l o to f H A M L E T t o h a v e C L A U D I U S i n it.E v i d e n t l y t he r e is s u f fi c ie n t C A U S E f o r t h e H A S - P R O P -E R T Y s lo t o f C L A U D I U S t o h a v e D E A D i n it.[ C L A U D I U S H A S - P R O P E R T Y D E A D ] is v e ri fi ed b yt h e p r e c e d e n t i n M AI t m a k e s s e ns e . B y u s in g a n a l o g y , a k i n d o f c o m m o n -s e n s e r e a s o n i n g i s e x h i b i t e d . I n i t i a l e x p e r i m e n t s i n d i c a t et h a t t h e s a m e i d e a s w o r k i n la w w h e r e d e a l i n g w i t h l e ga lp r e c e d e n t s e e m s l i k e a c o m b i n a t i o n o f s i t u a t i o n i d e n ti -f i c a t i o n a n d a n a l o g y - d r i v e n s i t u a t i o n a n a l y s i s .7 . F in d in g A n a log ie s b y C lass i f i c a t ion - Ex plo i t in gH y p o t h e s i z i n g

B e f o r e t w o s i t u a t i o n s c a n b e m a t c h e d , i t i s n e c e s s a r yt o f r e d th e r e m e m b e r e d s i t u a t i o n t h a t i s m o s t r e l e v a n t tot h e s i t u a ti o n u n d e r a n a ly s is . T w o m e c h a n i s m s f o r su c hh y p o t h e s i z i n g

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