Analogical Reasoning in Problem Solving

David T. Chen* and N icho las V. F i n d l e r Dept. of Computer Sc ience, SUNY at Bu f f a l o Amherst , N.y. 14226 INTRODUCTION Our a b i l i t y to cope w i t h the environment i s the r e s u l t o f c o n t i n u a l l e a r n i n n from exper ience . Learn ina "makes sense" on lv because s i t u a t i o n s resemble each o t h e r , and some i n f o r m a t i o n obta ined in one s i t u a t i o n is of use in o the rs — o r , expressed more b r o a d l y , s i m i l a r s i t u a t i o n s c a l l f o r s i m i l a r a c t i o n s . We a l so l e a r n to e x t r a c t the e s s e n t i a l c h a r a c t e r i s t i c f e a t u r e s o f the s i t u a t i o n s we become f a m i l i a r w i t h , which then he lp us i n r e t r i e v i n a the s i t u a t i o n s most s i m i l a r to the one we are faced w i t h . S i m i l a r i t y can be of d i f f e r e n t types and a t d i f f e r e n t l e v e l s o f c o m p l e x i t y . I t s d i scove ry i s o f t e n the r e s u l t o f a goa l o r i e n t e d process assoc ia ted w i t h problem s o l v i n g a c t i v i t y . Once s i m i l a r i t y betxween a problem w i t h a known s o l u t i o n and an unso lved problem has been recogn i zed , Anal o g i c a l Reasoning (AR) is no rma l l y c a l l e d i n t o a c t i o n by humans to generate p o s s i b l e s o l u t i o n s to be t e s t e d then f o r adequacy. We have a t tempted to i n v e s t i g a t e Alt detached f rom s p e c i f i c tasks and to fo rmu la te i t s gene ra l p r i n c i p l e s . Our o b j e c t i v e has been to c r e a t e an AR component f o r problem s o l v i n g proarams and to assume f o r i t the l e v e l o f g e n e r a l i t y the means-ends ana l ys i s was shown to have in GPS. WORKING HYPOTHESES OF ANALOGICAL REASONING The u n d e r l y i n g r a t i o n a l e of AR can be expressed by a few work ing hypotheses: ( i ) Each problem is d e s c r i b a b l e aS an (ordered) c o l l e c t i o n o f , p o s s i b l y o v e r l a p p i n g , f e a t u r e s . (A f e a t u r e rep resen ts one or s e v e r a l chunked p r o p e r t i e s . Whereas p r o p e r t i e s are atomic and d i r e c t l y meas u r a b l e , f ea tu res can in genera l be measured as p resen t or absent o n l y . ) The i d e n t i f i c a t i o n and e x t r a c t i o n o f f ea tu res a r e , however, l e f t e i t h e r to a program component e x t e r n a l to AR or to the user . ( i i ) S o l u t i o n s are assoc ia ted w i t h r e s p e c t i v e problems in a w e l l d e f i n e d , det e r m i n i s t i c manner. Th is assumption goes beyond the usua l concept o f c a u s a l i t y . I t r e q u i r e s t h a t the f ea tu res be i d e n t i f i a b l e and s t r o n g l y enough c o r r e l a t e d w i t h the s o l u t i o n s so t h a t the l a t t e r can be d e r i v e d d i r e c t l y f rom the fo rmer . ( i i i ) I n the task domains o f i n t e r e s t t o us , s i m i l a r problems have s i m i l a r s o l u t i o n s . ( S i m i l a r i t y must be measured a long c e r t a i n dimensions t h a t depend on a p r i o r i f e a t u r e s o f bo th problems and s o l u t i o n s . ) ( i v ) When two problems have s i m i l a r sol u t i o n s , the f ea tu res p resen t i n one p r o blem b u t no t i n the o the r are l i k e l y to be o f l e s s e r impor tance . I n t u r n , f ea tu res shared by problems which have s i m i l a r sol u t i o n s are l i k e l y to be i m p o r t a n t . These can be s t reng thened q u a n t i t a t i v e l y the