Iterative Operations

ITERATIg-E O P E R A T I O N S Sae Y a m a d a

Notre Dame S e i s h i n U n i v e r s i t y Ifuku-Ch5 2 - 1 6 - 9

700 Okayama, Japan

A B S T R A C T

We p r e s e n t in this article, as a part of a s p e c t u a l o p e r a t i o n s y s t e m , a gene- r a t i o n system of iterative e x p r e s s i o n s using a set of operators called iterative operators. In order to execute the itera- tive operations efficiently, we have c l a s s i f i e d p r e v i o u s l y p r o p o s i t i o n s

d e n o t i n g a single occurrence of a single event into three groupes. The d e f i n i t i o n of a single event is given recursively. The c l a s s i f i c a t i o n has b e e n carried out e s p e c i a l l y in c o n s i d e r a t i o n of the d u r a - tire / n o n - d u r a t i v e c h a r a c t e r of the denoted events and also in c o n s i d e r a t i o n of existence / n o n - e x i s t e n c e of a cul- m i n a t i o n point (or a boundary) in the events. The o p e r a t i o n s c o n c e r n e d w i t h iteration have e i t h e r the effect of g i v i n g a b o u n d a r y to a n event ( in the case of a n o n - b o u n d e d event) or of e x t e n d i n g an event t h r o u g h repetitions. The operators c o n c e r n e d are: N,F .. d i r e c t iterative operators; I,G .. b o u n d a r y giving opera- tors; I .. e x t e n d i n g operator. There are d i r e c t and indirect operations: the d i r e c t ones change a n o n - r e p e t i t i o u s p r o p o s i t i o n into a r e p e t i t i o u s one directly, w h e r e a s the indirect ones change it indirectly. The indirect i t e r a t i o n is indicated w i t h

. The scope of each operator is not u n i q u e l y definable, t h o u g h the m u t u a l r e l a t i o n of the operators can be given more or less explicitly.

I I N T R O D U C T I O N

The system of the iterative opera- tions, w h i c h makes a part of a s p e c t u a l operation system, is based on the assump- tion that the general m e c h a n i s m of

r e p e t i t i o n is language independent and can be reduced to a small number of operations, though language expressions of r e p e t i t i o n are d i f f e r e n t from language to language. It must be noticed that even in one language there are u s u a l l y several means to express r e p e t i t i o u s events. We know that "il lui cognait la t~te contre l e m u r " and "il lui a cogn~ deux ou trois fois la t~te contre l e m u r " , the examples given by W. Pollak, express the same event.

We have also l i n g u i s t i c means for iterative e x p r e s s i o n s on all lin- guistic levels: morphological,

syntactical, semantic, p r a g m a t i c etc. As the general form of r e p e t i t i o n we use ~ = ( ~ i ~ in w h i c h ~ is the whole event, ~ia single occurrence of a single event a n d * an iteration indicator. For example:

: (a series of) e x p l o s i o n s took place

93: a single e x p l o s i o n took place : indefinit n u m b e r of times ~i d e n o t e s a c t u a l l y a p r o p o s i t i o n

d e s c r i b i n g a single event S i. ~ sign w i l l be r e p l a c e d later b y a singIe or c o m p l e x operator or operators, w h i c h operate(s) on ~i-

We hope also to be able to give various e x p r e s s i o n s to the same event and for that purpose we are p l a n n i n g to have a set of i n t e r p r e t a t i o n rules.

The language m a i n l y c o n c e r n e d is Japanese, but in this article examples are given in French, in E n g l i s h or in German.

2 BASIC C O N D I T I O N OF THE I T E R A T I O N The iterative aspect is one of s e n t e n t i a l aspect and d e n o t e s plural occurrence of an event or an action. The iterative aspect concerns therefore the p r o p e r t y of countability. The itera- tire operations give the iterative a s p e c t to a p r o p o s i t i o n and are c o n c e r n e d w i t h the p l u r a l i t y of occurrences of the event.

As we d i s t i n g u i s h count nouns (count terms) from n o n - c o u n t nouns (mass terms), we d i s t i n g u i s h countable events from non- countable events, or more precisely, the events of w h i c h the n u m b e r of occur- r e n c e s is c o u n t a b l e and those of w h i c h the number of occurrences is n o n - c o u n - table.

As a count noun has a clear boundary, a countable event also has to have a clear boundary. Countable events are for instance: he opens a window; he reads a book; he kicks a ball etc. N o n - c o u n t a b l e events are for instance: he swims; he sleeps deeply; he runs fast,etc.

Only a countable event can be repeated: he opens three windows; he kicked the ball twice,etc. A n ~ n - c o u n t a b l e event can't be repeated: ~he sleeps twice.

The d i s t i n c t i o n of two kinds of events (and of two kinds of propositions),

w h i c h also is called t e l i c - a t e l i c , cyclic- non-cyclic or b o u n d e d - n o n b o u n d e d dis- tinction" is therefore n e c e s s a r y for the execution of the iterative operations.

It must be useful to give here some remarks on the terminology.

The terms such as 'iterative', 'repeti- tive', 'frequentative' and 'multiplica- tire' are used very often as synonyms. However there are some works w h i c h d i s t i n g u i s h them one from the other The term repetitive is used sometimes to indicate only one r e p e t i t i o n and the term iterative to indicate more than two repetitions. And sometimes the term iterative is used for one r e p e t i t i o n and the term f r e q u e n t a t i v e is used for several repetitions.

We use both of the terms 'iterative' and 'repetitive'~ (hence 'iteration' and 'repetition'~as synonyms. In this article 'repetition' means, in most of cases, two or more occurrences of a same event. But in order to prevent a m i s u n d e r s t a n - ding, we rather use the term 'iteration'.

A 'proposition' denotes an event and it is a neutral e x p r e s s i o n in the sense that the tense, aspect and mode operators operate on it.

3 SOME PREVIOUS R E M A R K S ON ITERATION 3.1 Regular and irregular iteration

Two kinds of iterations are distin- guished: regular and irregular iterations, i.e. the iterations w h i c h correspond to cardinal count adverbials and the itera- tions which correspond to frequency adverbials.

A regular iteration is defined either by a regular f r e q u e n c y of the occurrence of the event, (called 'fixed frequency' b y Stump), or by a constant l e n g t h of intervals between occurrences.

(I) We ate supper at six o'clock every night last week. (Frequency)

The busses started at five-minute

intervals. (Interval)

I These termes are used by Garey, Bull and Allen respectively.

The extreme case of the r e g u l a r itera- tion is called 'habitude'.

(2) En ~t~, elle se levait ~ quatre heure s.

A r e g u l a r f r e q u e n c y or a constant inter- val is indicated by the operator F. An irregular iteration is indicated

either w i t h a number of occurrences of an event or w i t h irregular lengths of

intervals b e t w e e n occurrences.

(3) L i n d a called you several times last

night. (Frequency)

Nous avons e n t e n d u le m~me bruit par

intervalles. (Interval)

B o t h the n u m e r i c a l indications and the indications of irregular intervals are given w i t h the operator N.

3.2 Repeated c o n s t i t u e n t of the event C o n s i d e r i n g the structure of a repeated event, we can d i s t i n g u i s h several forms of repetitions, a c c o r d i n g as which constituent is affected. If we say,"She changes her dress several times a day", it is the object w h i c h is affected b y the repetition.

Using grammatical c a t e g o r y - n a m e s we can indicate the r e p e a t e d c o n s t i t u e n t as the following.

Simple r e p e t i t i o n

(4) Subj (Pred)~: Mr. Wells is p u b l i s h i n g a novel year b y year; L'une apr~s l'autre le pilote v ~ r i f i a des c h i f f r e a

(Subj P r e d ~ : People walked across the lawn; Each boy in the room stood up and gave his name.

Complex r e p e t i t i o n

(5)(Subj(Pred)~)*: L o r s q u ' e l l e venait avec sa m~re, souvent celle-ci cares- salt ce vieux pilier central...

((Subj Pred) ~ : Les habitants de ce q u a r t i e r r ~ p ~ t e n t toujours:~Si nous avions un arr~t d'autobus pr%s d'ici.~ On the actual stage we have no such a detailed mechanism to be able to diffe- rentiate the repeated constituent. Nor do we consider the d i f f e r e n t i a t i o n neces- sary. We treat all these r e p e t i t i o n s as having the type (Subj P r e d ) ~ , ( i n a more general form ~ ) , and we find no incon- venience doing so.

3.3 Repeated phase of the event

A s for the r e p e t i t i o n is c o n c e r n e d only a p h a s e i n c l u d i n g a c u l m i n a t i o n point is capable of repetition, because the repe- tition p r e s u p p o s ~ that the event has a

(real or hypothetical) boundary.

(6) (Inchoative)~: L o r s q u ' i l a r r i v a i t .., M~re e t M m e van D a a n se m e t t a i e n t pleurer ~ chaque fois.

~

(Imminent Phase)*: Trois fois ou quatre fois au cours de l ' e n t r e t i e n le commissaire avait ~t~ sur le point de lui a p p l i q u e r sa main sur la figure. (Hypothetical c u l m i n a t i o n point)

( R e s u l t a t i v e ~ : Chaque fois que je vais chez elle, je trouve toute l a m a i s o n bien nettoy~e.

Like the d i s t i n c t i o n of the r e p e a t e d constituent, the d i s t i n c t i o n of the r e p e a t e d phase is not e s p e c i a l l y signifi- cative in the iterative operations.

Besides, if necessary, we can treat each phase as an i n d e p e n d e n t event: the b e g i n - ning part ~' of the event ~ can be

c o n s i d e r e d as an event. Thus, for the time being, the d i s t i n c t i o n of phases is also n e g l e c t e d in the iterative opera- tions.

3.4 H o m o g e n e o u s i t e r a t i o n and h e t e r o - geneous iteration

A h o m o g e n e o u s i t e r a t i o n is an o r d i n a r y i t e r a t i o n of the type(~)~ and a h e t e r o - geneous iteration is what is called by Imbs 'la r ~ p ~ t i t i o n d ' a l t e r n a n c e ' . It is not the iteration of a simple event but the iteration of two or more m u t u a l l y related events. It has the form:

(~'÷~' '...)~

(7) J'allume et j'~teins une fois par minute.

The most frequent case is the c o m b i n a - tion of two events, but the c o m b i n a t i o n of three events is still possible:

(8) Depuis une heure il v a ~ la fen~tre t o u s l e s trois minutes, s'arr~te un moment et r e v i e n t encore.

The c o m b i n a t i o n of more than three events is not natural.

4 A P P L I C A T I O N ORDER OF TENCE A N D A S P E C T OPERATOR

In the present article we are e x c l u - sively c o n c e r n e d w i t h aspect operators and tense operators are not treated, t h o u g h past tense sentenses are used as examples. We will b e c o n t e n t e d just to say that tense operators come after aspect opera- tors in the o p e r a t i o n order.

(9) I1 travaille. --- I1 se met enfin travailler. (Inchoative) --- I1 s'est nis e n f i n ~ travailler. (Inchoative + Past)

C L A S S I F I C A T I O N OF BASIC P R O P O S I - TIONS

A sentential a s p e c t is the sythesis of the a s p e c t u a l meanings of all c o n s t i - tuents of the sentence.

For the e f f i c i e n t e x e c u t i o n of iterative o p e r a t i o n s as well as all a s p e c t u a l o p e r a t i o n s we have to c l a s s i f y p r e v i o u s l y p r o p o s i t i o n s ~i d e n o t i n g events S i. For this c l a s s i f i c a t i o n we take accoufit of d u r a t i v e / n o n - d u r a t i v e and b o u n d e d / n o n - bounded c h a r a c t e r s of events.

The d i s t i n g u i s h e d p r o p o s i t i o n s are: ~ = d u r a t i v e proposition; ~2 = a c c o m - p l i s h m e n t proposition; ~ = m o m e n t a n e o u s (or n o n - d u r a t i v e ) proposltion. This clas- sication is b a s i c a l l y identical w i t h Verkuyl's. The c r i t e r i a we have used and examples of p r o p o s i t i o n s of e a c h groupe are as the following. (For pragmatic reason, sentences are given instead of p r o p o s i t i o n s . )

C r i t e r i a

~I: the event is r e p r e s e n t e d with an open interval; satisfies the a d d i t i v i t y (or partitivity) condition; c o - o c c u r r e n c e with durative a d v e r b i a l s such as a yea~ an hour .. Ok; c o - o c c u r r e n c e w i t h m o m e n t a n e o u s adverbials such as in five minutes, at that m o m e n t .. No

~2: the event is r e p r e s e n t e d w i t h a closed interval; a c u l m i n a t i o n point

(or a boundary) is included; if the c u l m i n a t i o n point is excluded, it satisfies the a d d i t i v i t y condition, otherwise .. ~o

~ : the event can be c o n s i d e r e d as a ~ m o m e n t a n e o u s one; c o - o c c u r r e n c e w i t h

d u r a t i v e a d v e r b i a l s .. No; c o - o c c u r - rence w i t h m o m e n t a n e o u s a d v e r b i a l s ..Ok

I Cf. V e r k u y l (80) p145. Verkuyl distin- guishes durative VP, terminative VP and m o m e n t a n e o u s VP.

Examples of e x p r e s s i o n s

~I: he sleeps, he sings, he walks ~2: he swims across the river, he

reaches the top of the hill, he builds a sandcastle

@3: he hits the ball, a bombe explodes, -he kicks at a ball

This c l a s s i f i c a t i o n is n e c e s s a r y also for other aspectual operations. In order to show the v a r i d i t y of the classifi- cation, we give an example of other aspectual operations: the inchoative operation. Inch is a b o u n d a r y giving operator and gives the initial border to any proposition, but the meaning of Inch(@ i) is d i f f e r e n t according to @i- W i t h ~[, which doesn't imply any b o u n d a r z Inch functions to give the initial boun- dary.

ex. ~I it rains; Inch(~l) .. It begins to rain

With @o, which implies an end point, inch fiEes the initial boundary.

ex. @2 "" Bob builds a sandcastle; Inch(@2) .. Bob began to build a sand- castle.

The length of the event is the time stretch, at the end of which Bob is supposed to complete the sandcastle.

With @3 the condition is quite different. ~3, momentaneous proposition, implies no l e n g t h (or no meaningful length) and the beginning point and the end point overlap each other. Inch(~3) gives a u t o m a t i c a l ] y the iteration of the event and the initial b o u n d a r y becoms the initial boundary of the prolonged event.

ex. @3 "" he knocks (one time) on the door; Inch(@3) .. He began k n o c k i n g

(repeatedly) on the door.

The function of the Inch is the same for all of three examples, but the meaning of the b e g i n n i n g is different one from another. The third case (that of ~3) is an example of the fact that a non-repe- titious operator can produce certain repetitions. This is the repetitious effect of a n o n - r e p e t i t i o u s operator, to which we will return later.

6 BASIC OPERATORS

An iterative operation is noted as Rj(~i), of w h i c h Rj is either a single operator or operators. As it was already said t a n e c e s s a r y c o n d i t i o n of the itera- tion is that the event in question has a clear boundary. Thus the operators

c o n c e r n e d w i t h the iterative operations have either the effect of giving a certain boundary, (in the case of n o n - b o u n d e d event): B@i , or the effect of repetition.

The following operators indicated w i t h capital letters are not individual opera- tors,but group names. An individual operator has for instance a form like N 2 or F1/w(eek).

Operators

N: operators indicating directly the num- ber of r e p e t i t i o n s

F: operators indicating a f r e q u e n c y or regular intervals between occurrences I: operators indicating a temporal

length; effect of prolonging and b o r d e r i n g

B: b o u n d a r y giving operators G: prolonging operators

Examples of expressions

N: two times, three times, several times F: every day, three times a week,

several times a day

I: for an hour, from one to three

B: begin to, finish -ing, (teshimau..J) G: continue to, used tO, (te iru.. J)

7 OPERATIONS

7.1 Single operators N~F~I

7.1.1 Direct operations

The operation of N, F, r e p e t i t i o u s operators, on ~2, ~3 give as the output N~2, N~ 3, F~2, F ~ . These are direct (ex- plicit) repetitiofis operations, n a m e l y those w h i c h change a n o n - r e p e t i t i o u s proposition into a repetitious one. The result of the operations is exactly what the operators indicate.

(lO)

a week.

F~3: It s~arkles every two minutes.

7.1.2 Indirect Operations

The operator I gives a temporal limit to a proposition. Usually it ope- rates on ~I"

It is not a proper r e p e t i t i o u s operator. However, if the operator I operates on 92 or on 9x, a bounded proposition, it turns the p r o p o s i t i o n into that of r e p e a t e d event. In this case, the i t e r a t i v e opera- tion is effectuated indirectly. We call this iteration 'implicative iteration'.

ex. 92 -- John walks to the door; I .. for hours; I92 .. John walked to the door for hours.

In order to d i f f e r e n t i a t e this I92 from I91, we use the symbolXfor an implicative iteration: I ( ~ 9 2 ) . ( e x a c t l y ~ i s ~ 1 oral2)

~ a p p e a r s not only w i t h the operator I, but also w i t h N and F.

(11) N ( ~ 93): The top spun three times (= several times on three occasionsl).

F ( ~ 9 3 ) : The bell rings three times a day.

As we have already seen, other aspectual operators can also have the effet of repetition.

(12) Inch 93 = I n c h ( ~ 93): It began to spin.

Term 93 = T e r m ( ~ 9 3 ) : It stopped to beat.

As for the strings N91 and F91, they don't satisfy the basic c o n d i t i o n of the iteration, i.e. 91 has no boundary. W i t h some special i n t e r p r e t a t i o n rules, how- ever, we can interprete them as N92 and F92 respectively.

ex. F91: ?He walks three times a week. --@ He walks from the house to the station three times every week (F92).

7.2 C o m p l e x operators of N,F,I

7.2.1 Direct Operations

The above operators N,F,I can be applied successively one after the other, but not every c o m b i n a t i o n nor every a p p l i c a t i o n order is acceptable. F.I,

I.F, F-N and N-I are acceptable, but N.F is not natural.

(13) F(I91): Ii y alla souvent pendant une quinzaine de jours; I .. 15 jours, F .. souvent, 91 .. il y alla (pour y rester)

N(I91): J'~tais ~ Tokyo en tout trois fols, chaque lois pendant quel- ques semaines;N .. trois fois; I ..

I The d i s t i n c t i o n of the situation and the occasion is clear in Mourelatos.

quelques semaines; 91 .. J'gtais Tokyo

I(F93): Ii prend le m e d i c a m e n t trois lois par Sour pendant une semaine; I .. une semaine; F .. trois fois par jour; 93 .- il prend le medi- cament

I~N gives in a certain operational order the same effect as a single opera- tor F, but in other o r d e ~ other effects. Using c o m p l e x operators, we get the out- put I(F92), I(F93!, F(N92), F!N93), N(I91), F(I91), I(N92), I(N93).

C o m b i n a t i o n of more than two operators are also possible.

(14) II(F(I291)): Es hat heute ab und zu eine Stunde lang geregnet; II heute F .. ab und zu; 12 .. eine Stunde; 91 .. es regnete

Cf. Es hat heute eine Stunde lang ab und zu geregnet.

II(F(I291)!: Toutes les fins de semaine en gte, on gtait toujours parti; II .. en gt~; F .. chaque semaine; !o -- pendant le week-end 91 -. on @~ait parti I

II(F(I291)): Ein Jahr fang hat Peter t~glich 3 Stunden lang trainiert;

I1 .. ein Jahr; F .. t~glich; I2 .. d~ei Stunden; 91 .. P e t e r trainierte

7.3 Operators B and G

7.3.1 Direct Operations

Adding B, b o u n d a r y giving operators, and G, p r o l o n g i n g operators, to the above operators, we can further extend the iterative operations. B is by it-self no r e p e t i t i o u s operator. Its proper f u n c t i o n is to give a b o u n d a r y to a n o n - b o u n d e d proposition. One of the B - o p e r a t o r s is Inch: Inch 91 .. he begins to write. Once a event gains a boundary, it can be repeated.

(15) N(B91): He began to write three times.

Another a p p l i c a t i o n order of N and B gives another kind of output.

(16) B(N92): Bob began to build three sandcastles; N .. 3; B .. Inch; 92 -. Bob built a sandcastle

I Example borrowed from Sankoff/Thibault. 'en ~te' can be also interpreted as F. In this case, we have two F - o p e r a t o r s F I and F2: FI (F2(I~I)); FI .. en ~t~ = chaque ~t~; F2 .. chaque semaine.

The p r o l o n g i n g operators G is not a r e p e t i t i o u s operator either. If G performs on ~I, it has only the effect of prolon- ging o r e x t e n d i n g the event•

(17) G~I: He is working; G .. ING; ~I -- he works

7.3.2 Indirect Operations

In some cases, the operation of B brings about repetitions, as we have seen with the operator Inch. It is done in the c o m b i n a t i o n of B and ~3"

(18) B~ = B ( ~ 3 ) : She began to cough; it began to sparkle; I stopped his calling you.

B(I~ I) = B(F(I~I)): He began jog- ging of half an hour (= half an hour each day).

G gives the effect of iteration too, if G is associated w i t h a bounded p r o p o s i t i o ~ such as ~2, ~3' I~I"

(19) G~ 2 = ~ 2 : He continues going to Tokyo Station; G .. Cont; ~2 .- he goes to Tokyo Station

C o m b i n a t i o n of the operators F,G w i t h other operators can also give similar effects•

(20) I ( G ~ ) = I ( ~ ~3): It was sparkling for an hour.

G ( F ( X ~ ) ) = F ( ~ ~3): It continued to s p a r k ~ ~very two mlnutes.

7.4 Multiple Structure of Iteration A repeated event, (which in fact has durative character like ~I), can again be given a boundary. And this renewed b o u ~ ded event can again be repeated• T h i s makes a multiple iteration• The iteration can be explicit or implicative.

(21) G~2: Elle prend des legons de piano. B ( Z ~2): Elle a commenc~ ~ prendre des le$ons de piano.

N ( B ( X ~2)): A trois reprises elle a commenc~ ~ prendre des legons de piano. The following examples given by Freed have also a multiple iterative structure,

'a series of series' according to her ter- minology.

(22) N ( ~ ~3): She sneezes a lot. B ( G ( ~ 3 ) : She began to cough

(after years of smoking)• 7.5 Order of Operations

The scope of each operator is not u n a m b i g u o u s l y definable. However their mutual r e l a t i o n can be indicated more or less like the following•

f • N ~

• F ~ i

• • B ~

. G-- Figure I

The d i r e c t i o n of an arrow in the figure indicates the written order of two ooera- tors in a form. The order of a p p l i c a t i o n in the operation is therefore inverse.

8 EVENT AND B A C K G R O U N D

It is often p r o p o s e d t o d i s t i n g u i s h an event from its b a c k g r o u n d (or its occasion)• The b a c k g r o u n d is a time stretch in w h i c h the event takes place•

From a pure theoretical viewpoint, the idea of the double structure of event- b a c k g r o u n d is very helpful for analysis of ambiguous structures•

I ex. La toupie a tourn~ trois fois. In this expression, 'trois fois' can be either the number of occurrences of the event (i.e. number of spins of the top) or the number of occasions on w h i c h the top spun. With the iterative operators the difference can be given clearly: N~3 and N ( ~ 3 ) • In the former case, the top spun three times on one occasion and in the latter case, the top spun several times on three occasions.

The operators N,F,I are related w i t h b o t h the event and the background. G r a p h i c a l l y the difference can be indi- cated as the figure 2. 2

La toupie a tourn4 trois fois.

La toupie a tourn~ trois foiso (= ~ trois occasions)

La toupie a tourn~ pendant une minute.

N(Z ~3)

N=3

I(x

~3)

~ ~ ' I& I minute

Figure 2

Operationally, if we d i f f e r e n t i a t e the b a c k g r o u n d from the event on the level of iterative operations, the rules must be too complicated. For the time being the operators N,F, I are used r e g a r d l e s s whether they operate on the event or on the occasion.

9 N A G A T I O N OF THE ITERATIVE P R O P O S I T I O N S

As for the negative cases of itera- tire operations, there are several

possibilities. E i t h e r a negeted iterative p r o p o s i t i o n remains still iterative or it becomes a non-iterative proposition. In other words, the n e g a t i o n affects the whole p r o p o s i t i o n in the case of total negation, and affects just the number of r e p e t i t i o n s or the f r e q u e n c y in the case of partial negation. In the former case

the scope of the n a g a t i o n is larger than that of the iteration, and in the latter case, the scope of the n e g a t i o n is smaller than that of the iteration.

(23) N @ 3 : I 1 est venu d e u x fois ~(N@5) or r a t h e r ~ 3 : I 1 n'est jamais venu. (Total negation)

( ~ N ) @ 3 : I 1 n'est pas venu deux fois. (En effe%, il n'est venu qu'une lois.)

(Partial negation)

N(~@3): I1 n'esz pas venu deux fois. D4j~ deux fois il n'est pas venu.

F ~ 3 : I 1 sortait trois fois par semalns.

~(F~3) or rather ~ @ 3 : I 1 n'est

jamais sorti. (Total negation)

( ~ F ) @ 3 : I 1 ne sortait pas trois fois par semaine: en effet il ne sortait que d e u x fois par semaine. (partial negation)

F ( ~ 3 ) : Trois jours par semaine, il ne sortait pas.

It depends on w h i c h stage of the opera- tions the n e g a t i o n is applied.

10 I N T E R P R E T A T I O N AND C O N C O R D A N C E RULES

Several kinds of i n t e r p r e t a t i o n rules are in view. The i n t e r p r e t a t i o n rules of the first c a t e g o r y are those w h i c h give adequate i n t e r p r e t a t i o n s to N@I, F~ I etc, in c o n s i d e r a t i o n of the context on the pragmatic level. N@I gains u s u a l l y an i n t e r p r e t a t i o n of N~2, and F~I that of F@2. For example, "I walked three times this week" can be interpreted as: "I walke@ three times from the house to the station this week."

The second i n t e r p r e t a t i o n rules are concordance rules, w h i c h connect diverse expressions w i t h one same event.

D i f f e r e n t e x p r e s s i o n s in appearence or d i f f e r e n t means of e x p r e s s i o n s are inter- connected by these rules. Eventually, the d i s t i n c t i o n of the b a c k g r o u n d from the event can be e f f e c t u a t e d by certain rules.

R E F E R E N C E S

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Aspectual C o m p l e m e n t a t i o n , D . R e i d e l . Imbs,P. 1960: L'emploi des temps verbaux

en fran~ais moderns,Paris.

Mourelatos,A.P.D. 1981: Events, P r o c e s s e s and States; S y n t a x and Semantics vol 14 191-212.

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Stump,G.T. 1981: The I n t e r p r e t a t i o n of Fr F r e q u e n c y Adjectives; L i n g u i s t i c s and P h i l o s o p h y 4, 221-257.

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