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<Paper uid="E83-1003">
  <Title>ITERATIg-E OPERATIONS</Title>
  <Section position="4" start_page="0" end_page="14" type="metho">
    <SectionTitle>
2 BASIC CONDITION OF THE ITERATION
</SectionTitle>
    <Paragraph position="0"> The iterative aspect is one of sentential aspect and denotes plural occurrence of an event or an action. The iterative aspect concerns therefore the property of countability. The iteratire operations give the iterative aspect to a proposition and are concerned with the plurality of occurrences of the event.</Paragraph>
    <Paragraph position="1"> As we distinguish count nouns (count terms) from non-count nouns (mass terms), we distinguish countable events from noncountable events, or more precisely, the events of which the number of occurrences is countable and those of which the number of occurrences is non-countable. null  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. Non-countable events are for instance: he swims; he sleeps deeply; he runs fast,etc.</Paragraph>
    <Paragraph position="2"> Only a countable event can be repeated: he opens three windows; he kicked the ball twice,etc. A n~n-countable event can't be repeated: ~he sleeps twice.</Paragraph>
    <Paragraph position="3"> The distinction of two kinds of events (and of two kinds of propositions), which also is called telic-atelic, cyclicnon-cyclic or bounded-non bounded distinction&amp;quot; is therefore necessary for the execution of the iterative operations.</Paragraph>
    <Paragraph position="4"> It must be useful to give here some remarks on the terminology.</Paragraph>
    <Paragraph position="5"> The terms such as 'iterative', 'repetitive', 'frequentative' and 'multiplicatire' are used very often as synonyms. However there are some works which distinguish them one from the other The term repetitive is used sometimes to indicate only one repetition and the term iterative to indicate more than two repetitions. And sometimes the term iterative is used for one repetition and the term frequentative is used for several repetitions.</Paragraph>
    <Paragraph position="6"> 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.</Paragraph>
    <Paragraph position="7"> But in order to prevent a misunderstanding, we rather use the term 'iteration'. A 'proposition' denotes an event and it is a neutral expression in the sense that the tense, aspect and mode operators operate on it.</Paragraph>
  </Section>
  <Section position="5" start_page="14" end_page="15" type="metho">
    <SectionTitle>
3 SOME PREVIOUS REMARKS ON ITERATION
</SectionTitle>
    <Paragraph position="0"/>
    <Section position="1" start_page="14" end_page="14" type="sub_section">
      <SectionTitle>
3.1 Regular and irregular iteration
</SectionTitle>
      <Paragraph position="0"> Two kinds of iterations are distinguished: regular and irregular iterations, i.e. the iterations which correspond to cardinal count adverbials and the iterations which correspond to frequency adverbials.</Paragraph>
      <Paragraph position="1"> A regular iteration is defined either by a regular frequency of the occurrence of the event, (called 'fixed frequency' by Stump), or by a constant length of intervals between occurrences.</Paragraph>
      <Paragraph position="2"> (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.</Paragraph>
      <Paragraph position="3"> The extreme case of the regular iteration is called 'habitude'.</Paragraph>
      <Paragraph position="4"> (2) En ~t~, elle se levait ~ quatre heure s.</Paragraph>
      <Paragraph position="5"> A regular frequency or a constant interval is indicated by the operator F. An irregular iteration is indicated either with a number of occurrences of an event or with irregular lengths of intervals between occurrences.</Paragraph>
      <Paragraph position="6">  (3) Linda called you several times last night. (Frequency)  Nous avons entendu le m~me bruit par intervalles. (Interval) Both the numerical indications and the indications of irregular intervals are given with the operator N.</Paragraph>
    </Section>
    <Section position="2" start_page="14" end_page="14" type="sub_section">
      <SectionTitle>
3.2 Repeated constituent of the event
</SectionTitle>
      <Paragraph position="0"> Considering the structure of a repeated event, we can distinguish several forms of repetitions, according as which constituent is affected. If we say,&amp;quot;She changes her dress several times a day&amp;quot;, it is the object which is affected by the repetition.</Paragraph>
      <Paragraph position="1"> Using grammatical category-names we can indicate the repeated constituent as the following.</Paragraph>
      <Paragraph position="2">  On the actual stage we have no such a detailed mechanism to be able to differentiate the repeated constituent. Nor do we consider the differentiation necessary. We treat all these repetitions as having the type (Subj Pred)~,(in a more general form ~), and we find no inconvenience doing so.</Paragraph>
    </Section>
    <Section position="3" start_page="14" end_page="15" type="sub_section">
      <SectionTitle>
3.3 Repeated phase of the event
</SectionTitle>
      <Paragraph position="0"> An event consists of several phases: the beginning, the middle, the end and eventually the result and the imminent phase, i.e. the phase directly preceding the beginning point.</Paragraph>
      <Paragraph position="1">  As for the repetition is concerned only a phaseincluding a culmination point is capable of repetition, because the repetition presuppos~ that the event has a (real or hypothetical) boundary.</Paragraph>
      <Paragraph position="2">  (6) (Inchoative)~: Lorsqu'il arrivait ..,  M~re et Mme van Daan se mettaient pleurer ~ chaque fois. ~ Terminative~ : Une ~ une les villes talent englouties.</Paragraph>
      <Paragraph position="3"> (Imminent Phase)*: Trois fois ou quatre fois au cours de l'entretien le commissaire avait ~t~ sur le point de lui appliquer sa main sur la figure. (Hypothetical culmination</Paragraph>
      <Paragraph position="5"> vais chez elle, je trouve toute la maison bien nettoy~e.</Paragraph>
      <Paragraph position="6"> Like the distinction of the repeated constituent, the distinction of the repeated phase is not especially significative in the iterative operations. Besides, if necessary, we can treat each phase as an independent event: the beginning part ~' of the event ~ can be considered as an event. Thus, for the time being, the distinction of phases is also neglected in the iterative operations. null</Paragraph>
    </Section>
    <Section position="4" start_page="15" end_page="15" type="sub_section">
      <SectionTitle>
3.4 Homogeneous iteration and hetero-
</SectionTitle>
      <Paragraph position="0"> geneous iteration A homogeneous iteration is an ordinary iteration of the type(~)~ and a heterogeneous iteration is what is called by Imbs 'la r~p~tition d'alternance'. It is not the iteration of a simple event but the iteration of two or more mutually related events. It has the form: (~'/~' '...)~ (7) J'allume et j'~teins une fois par minute.</Paragraph>
      <Paragraph position="1"> The most frequent case is the combination of two events, but the combination of three events is still possible: (8) Depuis une heure il va ~ la fen~tre tousles trois minutes, s'arr~te un moment et revient encore.</Paragraph>
      <Paragraph position="2"> The combination of more than three events is not natural.</Paragraph>
    </Section>
  </Section>
  <Section position="6" start_page="15" end_page="15" type="metho">
    <SectionTitle>
4 APPLICATION ORDER OF TENCE AND
ASPECT OPERATOR
</SectionTitle>
    <Paragraph position="0"> In the present article we are exclusively concerned with aspect operators and tense operators are not treated, though past tense sentenses are used as examples.</Paragraph>
    <Paragraph position="1"> We will be contented just to say that tense operators come after aspect operators in the operation order.</Paragraph>
    <Paragraph position="3"/>
  </Section>
  <Section position="7" start_page="15" end_page="16" type="metho">
    <SectionTitle>
CLASSIFICATION OF BASIC PROPOSI-
TIONS
</SectionTitle>
    <Paragraph position="0"> A sentential aspect is the sythesis of the aspectual meanings of all constituents of the sentence.</Paragraph>
    <Paragraph position="1"> For the efficient execution of iterative operations as well as all aspectual operations we have to classify previously propositions ~i denoting events S i. For this classification we take accoufit of durative/non-durative and bounded/nonbounded characters of events.</Paragraph>
    <Paragraph position="2"> The distinguished propositions are:</Paragraph>
    <Paragraph position="4"> (or non-durative) proposltion. This classication is basically identical with Verkuyl's. The criteria we have used and examples of propositions of each groupe are as the following. (For pragmatic reason, sentences are given instead of propositions.) Criteria ~I: the event is represented with an open interval; satisfies the additivity (or partitivity) condition; co-occurrence with durative adverbials such as a yea~ an hour .. Ok; co-occurrence with momentaneous adverbials such as in five minutes, at that moment .. No ~2: the event is represented with a closed interval; a culmination point (or a boundary) is included; if the culmination point is excluded, it satisfies the additivity condition, otherwise .. ~o ~: the event can be considered as a ~momentaneous one; co-occurrence with durative adverbials .. No; co-occurrence with momentaneous adverbials ..Ok I Cf. Verkuyl (80) p145. Verkuyl distinguishes durative VP, terminative VP and momentaneous VP.</Paragraph>
    <Paragraph position="5">  ~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 classification is necessary also for other aspectual operations. In order to show the varidity of the classification, we give an example of other aspectual operations: the inchoative operation. Inch is a boundary giving operator and gives the initial border to any proposition, but the meaning of Inch(@ i) is different according to @i-With ~\[, which doesn't imply any boundarz Inch functions to give the initial boundary. null ex. ~I it rains; Inch(~l) .. It begins to rain With @o, which implies an end point, inch fiEes the initial boundary.</Paragraph>
    <Paragraph position="6"> ex. @2 &amp;quot;&amp;quot; Bob builds a sandcastle; Inch(@2) .. Bob began to build a sandcastle. null The length of the event is the time stretch, at the end of which Bob is supposed to complete the sandcastle.</Paragraph>
    <Paragraph position="7"> With @3 the condition is quite different. ~3, momentaneous proposition, implies no length (or no meaningful length) and the beginning point and the end point overlap each other. Inch(~3) gives automatical\]y the iteration of the event and the initial boundary becoms the initial boundary of the prolonged event.</Paragraph>
    <Paragraph position="8"> ex. @3 &amp;quot;&amp;quot; he knocks (one time) on the door; Inch(@3) .. He began knocking (repeatedly) on the door.</Paragraph>
    <Paragraph position="9"> The function of the Inch is the same for all of three examples, but the meaning of the beginning is different one from another. The third case (that of ~3) is an example of the fact that a non-repetitious operator can produce certain repetitions. This is the repetitious effect of a non-repetitious operator, to which we will return later.</Paragraph>
  </Section>
  <Section position="8" start_page="16" end_page="16" type="metho">
    <SectionTitle>
6 BASIC OPERATORS
</SectionTitle>
    <Paragraph position="0"> An iterative operation is noted as Rj(~i), of which Rj is either a single operator or operators. As it was already said t a necessary condition of the iteration is that the event in question has a clear boundary. Thus the operators concerned with the iterative operations have either the effect of giving a certain boundary, (in the case of non-bounded event): B@i , or the effect of repetition.</Paragraph>
    <Paragraph position="1"> The following operators indicated with capital letters are not individual operators,but group names. An individual operator has for instance a form like N 2 or F1/w(eek).</Paragraph>
    <Paragraph position="2"> Operators N: operators indicating directly the number of repetitions F: operators indicating a frequency or regular intervals between occurrences I: operators indicating a temporal length; effect of prolonging and bordering B: boundary 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)</Paragraph>
  </Section>
  <Section position="9" start_page="16" end_page="18" type="metho">
    <SectionTitle>
7 OPERATIONS
</SectionTitle>
    <Paragraph position="0"/>
    <Section position="1" start_page="16" end_page="16" type="sub_section">
      <SectionTitle>
7.1 Single operators N~F~I
</SectionTitle>
      <Paragraph position="0"> The operation of N, F, repetitious operators, on ~2, ~3 give as the output N~2, N~ 3, F~2, F~. These are direct (explicit) repetitiofis operations, namely those which change a non-repetitious proposition into a repetitious one. The result of the operations is exactly what the operators indicate.</Paragraph>
      <Paragraph position="1"> (lO) N~: He crossed the road twice.</Paragraph>
      <Paragraph position="2"> N~: He knocked on the door twice.</Paragraph>
      <Paragraph position="3"> F~2: He goes to Tokyo Station once a week.</Paragraph>
      <Paragraph position="4"> F~3: It s~arkles every two minutes.</Paragraph>
      <Paragraph position="5">  The operator I gives a temporal limit to a proposition. Usually it operates on ~I&amp;quot; ex. ~I .. he walks; I~I .. he walks for two hours  It is not a proper repetitious operator. However, if the operator I operates on 92 or on 9x, a bounded proposition, it turns the proposition into that of repeated event. In this case, the iterative operation 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.</Paragraph>
      <Paragraph position="6"> In order to differentiate this I92 from I91, we use the symbolXfor an implicative iteration: I(~92). (exactly~is~1 oral2) ~appears not only with the operator I, but also with N and F.</Paragraph>
      <Paragraph position="7"> (11) N(~ 93): The top spun three times (= several times on three occasionsl). F(~93): The bell rings three times a day.</Paragraph>
      <Paragraph position="8"> As we have already seen, other aspectual operators can also have the effet of repetition.</Paragraph>
      <Paragraph position="9"> (12) Inch 93 = Inch(~ 93): It began to spin.</Paragraph>
      <Paragraph position="10"> Term 93 = Term(~93): It stopped to beat.</Paragraph>
      <Paragraph position="11"> As for the strings N91 and F91, they don't satisfy the basic condition of the iteration, i.e. 91 has no boundary. With some special interpretation rules, however, we can interprete them as N92 and F92 respectively.</Paragraph>
      <Paragraph position="12"> ex. F91: ?He walks three times a week. --@ He walks from the house to the station three times every week (F92).</Paragraph>
    </Section>
    <Section position="2" start_page="16" end_page="16" type="sub_section">
      <SectionTitle>
7.2 Complex operators of N,F,I
</SectionTitle>
      <Paragraph position="0"> The above operators N,F,I can be applied successively one after the other, but not every combination nor every application order is acceptable. F.I, I.F, F-N and N-I are acceptable, but N.F is not natural.</Paragraph>
      <Paragraph position="1"> (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 quelques semaines;N .. trois fois; I .. I The distinction of the situation and the occasion is clear in Mourelatos.</Paragraph>
      <Paragraph position="2"> quelques semaines; 91 .. J'gtais Tokyo I(F93): Ii prend le medicament trois lois par Sour pendant une semaine; I .. une semaine; F .. trois fois par jour; 93 .- il prend le medicament null I~N gives in a certain operational order the same effect as a single operator F, but in other orde~ other effects. Using complex operators, we get the output I(F92), I(F93!, F(N92), F!N93), N(I91), F(I91), I(N92), I(N93).</Paragraph>
      <Paragraph position="3"> Combination of more than two operators are also possible.</Paragraph>
      <Paragraph position="4">  (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.</Paragraph>
      <Paragraph position="5"> 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</Paragraph>
    </Section>
    <Section position="3" start_page="16" end_page="18" type="sub_section">
      <SectionTitle>
7.3 Operators B and G
</SectionTitle>
      <Paragraph position="0"> Adding B, boundary giving operators, and G, prolonging operators, to the above operators, we can further extend the iterative operations. B is by it-self no repetitious operator. Its proper function is to give a boundary to a non-bounded proposition. One of the B-operators is Inch: Inch 91 .. he begins to write.</Paragraph>
      <Paragraph position="1"> Once a event gains a boundary, it can be repeated.</Paragraph>
      <Paragraph position="2"> (15) N(B91): He began to write three times.</Paragraph>
      <Paragraph position="3"> Another application order of N and B gives another kind of output.</Paragraph>
      <Paragraph position="4"> (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-operators F I</Paragraph>
      <Paragraph position="6"> The prolonging operators G is not a repetitious operator either. If G performs on ~I, it has only the effect of prolonging orextending the event* (17) G~I: He is working; G .. ING; ~I -he works  In some cases, the operation of B brings about repetitions, as we have seen with the operator Inch. It is done in the combination of B and ~3&amp;quot; (18) B~ = B(~3): She began to cough; it began to sparkle; I stopped his calling you.</Paragraph>
      <Paragraph position="7"> B(I~ I) = B(F(I~I)): He began jogging of half an hour (= half an hour each day).</Paragraph>
      <Paragraph position="8"> G gives the effect of iteration too, if G is associated with a bounded propositio~ such as ~2, ~3' I~I&amp;quot;</Paragraph>
    </Section>
    <Section position="4" start_page="18" end_page="18" type="sub_section">
      <SectionTitle>
7.4 Multiple Structure of Iteration
</SectionTitle>
      <Paragraph position="0"> A repeated event, (which in fact has durative character like ~I), can again be given a boundary. And this renewed bou~ ded event can again be repeated* This makes a multiple iteration* The iteration can be explicit or implicative.</Paragraph>
      <Paragraph position="1"> (21) G~2: Elle prend des legons de piano.</Paragraph>
      <Paragraph position="2"> B(Z ~2): Elle a commenc~ ~ prendre des le$ons de piano.</Paragraph>
      <Paragraph position="3"> 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 terminology. null  The scope of each operator is not unambiguously definable. However their mutual relation can be indicated more or less like the following*</Paragraph>
      <Paragraph position="5"> The direction of an arrow in the figure indicates the written order of two ooerators in a form. The order of application in the operation is therefore inverse.</Paragraph>
    </Section>
  </Section>
  <Section position="10" start_page="18" end_page="18" type="metho">
    <SectionTitle>
8 EVENT AND BACKGROUND
</SectionTitle>
    <Paragraph position="0"> It is often proposedto distinguish an event from its background (or its occasion)* The background is a time stretch in which the event takes place* From a pure theoretical viewpoint, the idea of the double structure of eventbackground is very helpful for analysis of ambiguous structures* I ex. La toupie a tourn~ trois fois.</Paragraph>
    <Paragraph position="1"> 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 which 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.</Paragraph>
    <Paragraph position="2"> The operators N,F,I are related with both the event and the background.</Paragraph>
    <Paragraph position="3"> Graphically the difference can be indicated as the figure 2. 2 I This example is borrowed from Rohrer.</Paragraph>
    <Paragraph position="4">  Operationally, if we differentiate the background 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 regardless whether they operate on the event or on the occasion.</Paragraph>
  </Section>
  <Section position="11" start_page="18" end_page="18" type="metho">
    <SectionTitle>
9 NAGATION OF THE ITERATIVE PROPOSITIONS
</SectionTitle>
    <Paragraph position="0"> As for the negative cases of iteratire operations, there are several possibilities. Either a negeted iterative proposition remains still iterative or it becomes a non-iterative proposition. In other words, the negation affects the whole proposition in the case of total negation, and affects just the number of repetitions or the frequency in the case of partial negation. In the former case the scope of the nagation is larger than that of the iteration, and in the latter case, the scope of the negation is smaller than that of the iteration.</Paragraph>
    <Paragraph position="1"> (23) N@3:I1 est venu deux fois ~(N@5) or rather ~3:I1 n'est jamais venu. (Total negation) (~N)@3:I1 n'est pas venu deux fois.</Paragraph>
    <Paragraph position="2"> (En effe%, il n'est venu qu'une lois.) (Partial negation) N(~@3): I1 n'esz pas venu deux fois.</Paragraph>
    <Paragraph position="3"> D4j~ deux fois il n'est pas venu.</Paragraph>
    <Paragraph position="4"> F~3:I1 sortait trois fois par semalns.</Paragraph>
    <Paragraph position="5"> ~(F~3) or rather ~@3:I1 n'est jamais sorti. (Total negation) (~F)@3:I1 ne sortait pas trois fois par semaine: en effet il ne sortait que deux fois par semaine. (partial negation) F(~3): Trois jours par semaine, il ne sortait pas.</Paragraph>
    <Paragraph position="6"> It depends on which stage of the operations the negation is applied.</Paragraph>
  </Section>
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