Numerical Quantifiers and Their Use in Reasoning with Negative Information

Numer i ca l q u a n t i f i e r s p r o v i d e s imp le means o f f o r m a l i z i n g such s ta temen ts a s , " a t l e a s t t h r e e peop le a re i n t h a t r o o m " , " a t most f i f t e e n peop le a re i n the e l e v a t o r " , and "everybody has e x a c t l y two p a r e n t s " . A l t h o u g h n u m e r i c a l q u a n t i f i e r s g e n e r a l i z e the e x i s t e n t i a l q u a n t i f i e r , they have d i f f e r e n t uses i n r e a s o n i n g . The e x i s t e n t i a l q u a n t i f i e r i s most u s e f u l f o r s u p p l y -­ i n g r e f e r e n t s f o r d e s i g n a t i n g phrases w i t h n o p r e v i o u s l y e x p l i c i t l y men t ioned r e f e r e n t . Numer-­ i c a l q u a n t i f i e r s a re most u s e f u l f o r r e a s o n i n g b y the process o f e l i m i n a t i o n . Numer i ca l q u a n t i f i e r s w o u l d , t h e r e f o r e , be a u s e f u l a d d i t i o n to the o p e r a t o r s o f a r e a s o n i n g program o r d e d u c t i v e q u e s t i o n -­ a n s w e r i n g sys tem. They have been added to SNePS, the Semantic Network P r o c e s s i n g System, t o f u r t h e r enhance i t s i n f e r e n c e c a p a b i l i t i e s .