The Use Of Informal Calculus in Problems Of Artificial Intellect

The e s s e n t i a l c r e d i t o f t h e s e o p e r a t i o n s i s t h e i r n o n d e t e r m i n a t i o n , i . e . a m b i g u i t y and i n f o r m a l i t y o f t h e i r r e s u l t s . Consequently, t h e r e a l i z a t i o n o f v a r i o u s i n t e l l e c t u a l problems may p r o ceed in d i f f e r e n t ways. Thus we have a c a l o u l u s o n hand ( 2 , p.203), i . e . w e have p e r m i s s i o n t o c a r r y out some o p e r a t i o n s . For example, i f w e add 1 and 8 w i t h t h e aim of g e t t i n g an a r i t h m e t i c sum, we s h a l l g e t number 9. However, if we add 1 and 8 w i t h t h e i n t e n t i o n o f g e t t i n g a new t w o f i g u r e number, we s h a l l g e t 18 F u r t h e r , i f w e add 1 and 8 w i t h t h e a i m of g e t t i n g a new s y m m e t r i c a l f i g u r e , we s h a l l g e t @ , b u t i f w e s i m p l y aim a t any new f i g u r e , w e s h a l l get f i g u r e s i 8 or 4 or 81 , i . e . t h r e e d i f f e r e n t poss i b l e r e s u l t s . O b v i o u s l y , i t i s t h e r e a l i z a t i o n o f some g e n e r a l summation o p e r a t i o n t h a t below w i l l be r e f e r r e d t o as t h e system summation o p e r a t i o n . I t s h o u l d a l s o b e n o t e d t h a t f o r t h e man i n f o r m a l c a l c u l u s o p e r a t i o n s a r e s t r i c t l y enough d e t e r m i n a b l e by i n t u i t i o n a s t h e y , f i r s t and f o r e m o s t , f o r m a l i z e oommon a r i t h m e t i c o p e r a t i o n s w i t h o b j e c t s and n o t i o n s . However, t h e use o f such o p e r a t i o n s i n i n t e l l e c t u a l problems does n o t serve t h e purpose o f c o p y i n g t h e s t r u c t u r e o f man's t h i n k i n g . For r e a l i z i n g o f i n f o r m a l c a l o u l u s o p e r a t i o n s i t i s neoessary t o g i v e r u l e s g o v e r n i n g t h e r e p r e s e n t a t i o n o f r e a l system on t h e l e v e l of a computer w h i o h