Short Time Periods

Abstract

E a r l i e r papers ( A l l e n and Hayes 1985,1986) d e s c r i b e d a compact a x i o m a t i c t h e o r y which p r o v i d e d a f o r m a l b a s i s f o r tempora l r e a s o n i n g . Th is t h e o r y makes a sharp d i s t i n c t i o n between t ime p o i n t s and p e r i o d s of t i m e . We show he re , by c o n s i d e r i n g p o s s i b l e models o f t he t h e o r y , t h a t i t can b e s l i g h t l y extended t o g i v e a b e t t e r f i t t o i n t u i t i o n . I n p a r t i c u l a r , t he extended t h e o r y i s p rese rved under changes o f tempora l g r a n u l a r i t y . TIMEPERIODS AND MEETING The o r i g i n a l p e r i o d t h e o r y ( A l l e n 1984, A l l e n & Hayes 1986 ) used p e r i o d s r a t h e r than p o i n t s as i t s t empora l p r i m i t i v e . ( The t e r m i n o l o g y used e a r l i e r was ' i n t e r v a l ' r a t h e r than ' p e r i o d ' . We have changed to a v o i d con fus ion w i t h the mathemat i ca l use o f ' i n t e r v a l ' . ) The t h i r t e e n p o s s i b l e r e l a t i o n s h i p s between p e r i o d s , i n c l u d i n g f o r example o v e r l a p p i n g , i n c l u s i o n , and be fo re are d e f i n e d in terms of MEETS, which we w i l l w r i t e a s i n i n f i x c o l o n , w i t h p : q : r meaning p :q and q : r . The b a s i c axioms of the t h e o r y are then as f o l l o w s : Ml f o r a l l p , q , r , s . ( p :q and p :s and r : q ) i m p l i e s r : s M2 f o r a l l p , q , r , s . ( p : q and r : s ) i m p l i e s ( p :s xor e x i s t s t . p : t : s xor e x i s t s t . r : t : q ) M3 f o r a l l p . e x i s t s q , r . q : p : r M4 f o r a l l p , q , r , s . ( p : q : s and p : r : s ) i m p l i e s q r M5 f o r a l l p , q . p : q i m p l i e s e x i s t s r , s . r : p : q : s and r : ( p + q ) : s These f i v e axioms a re a l l t h e assumptions which t h e t h e o r y makes. For a l onge r d i s c u s s i o n of t h e i r i m p l i c a t i o n s and j u s t i f i c a t i o n , see ( A l l e n

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Cite this paper

@inproceedings{Hayes1987ShortTP, title={Short Time Periods}, author={Patrick J. Hayes and James F. Allen}, booktitle={IJCAI}, year={1987} }