The Specification of Time Meaning for Machine Translation

(I) k p 3 I , , I=, . . .S time ( R e l , ( I j , l , ) k . . ° & Pred. ( l . J & m. ! & AT ( I , , p) ) where the I, are i n t e r v a l s , the Relj are binary r e l a t i ons between i n t e r va l s l i k e : b e f o r e , the Predw are p r e d i c a t e s l i k e yes te rday ~, and p is a basic p r o p o s i t i o n , from which a l l t imere levant parts have been removed. The category of expression (I be applied to a basic proposi funct iona l way. ) is t / t ; i t can t ion in a The i n t e r p r e t a t i o n of (I) is the set of proposi t ions that are true at some given i n te r va l I , . This is s im i la r to Kr ipke 's d e f i n i t i o n of the not ion of 'possib le wor ld ' : 'A possible world is given by the desc r ip t i ve condi t ions we associate with i t . . . . ' (1972, p. 44). Analogously, a time i n te r va l can be i d e n t i f i e d with the co l l ec t i on of proposi t ions that are true at i t . 2. A t heo ry of time meanings. In many discussions of time meaning, a O is t inc t ion is made between an in te rna l and an external temporal system. The external system represents the t empora l r e l a t i o n between the state of affairs as described by the basic proposi t ion and the time at which the utterance takes place. This system always re fers to the speaker or w r i t e r , and consequently i t is a de i c t i c system. The in te rna l system is about such things as whether the state of a f f a i r s expressed in the basic propos i t ion is described as going on, hav ing l u s t s t a r t e d , hav ing been comp le ted , etc. This type of informat ion is often ca l led aspectual. In th is paper, we adopt the fo l lowing three basic p r i nc ip les for the representat ion of time meanings: (I) Each time meaning representat ion contains exact ly three time i n t e r v a l s : the time of speech or nar ra t ion (S) the time of event (E), i . e . the i n t e r va l at which the basic propos i t ion is said to be true one time of r e f e r e n c e (R) The Sin te rva l consists of one point only: i t is a s ing le ton. The Rand E i n te rva l s are non-empty subsets of t ime. ( I I ) The de i c t i c part of time meaning is represented by a binary r e l a t i o n between S and R and o p t i o n a l l y by one p r e d i c a t e ove r R, ( I l l ) Aspect is represented by a binary r e l a t i o n between R and E, and o p t i o n a l l y by one predicate over E. Pr inc ip les (1), ( I I ) , and ( I l l ) together imply that the general form of a time meaning representat ion can be somewhat s i m p l i f i e d . I t w i l l now be: (2) k p 3 S,R,E ~ t ime ( R e l t ( R , S ) & Pred . (R) & Rel=(E,R) & Pred=(E) & AT(E,p ) ) Apart from the const ra in ts on possible time meaning representat ions there are some const ra in ts on the r e l a t i o n between the time meanings and the language spec i f i c morphosyntactic forms for expressing those meanings: (IV) The p r e d i c a t e s over R are those t ime adverbia ls that can be used as answers to when-questions, such as (3) yesterday, now, next week, on Tuesday (V) The p r e d i c a t e s over E are ( a . o . ) the durat ion time adverb ia ls , such as (4) for an hour, f i ve weeks, since Christmas, u n t i l ~une (vI ) The r e l a t i o n s between R and S and between E and R a r e determined by the i n te rac t i on of the verbal tense forms and the time adverbia ls in ways to be speci f ied and exempl i f ied in section three. We w i l l now present the d e i c t i c and the aspectual components of the temporal system in some d e t a i l . 2.1. The de i c t i c system. As possible r e l a t i ons between S and R we w i l l take ( i ) before (R,S), defined as in I . ( i i ) a f te r (R,S), defined analogously ( i i i ) contain (R,S), defined as fo l lows : t s time (t ~ S -> t ~ R)