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<Paper uid="E85-1003">
  <Title>DISTRIBUTIVES, QUANTIFIERS AND A MULTIPLICITY OF EVENTS</Title>
  <Section position="4" start_page="16" end_page="16" type="metho">
    <SectionTitle>
2. ITERATIVES
</SectionTitle>
    <Paragraph position="0"> The following are examples iterative clauses in English: of (3)a Each day Mary wrote a letter to her sister.</Paragraph>
    <Paragraph position="1"> b Every time John went abroad he bought a souvenir.</Paragraph>
    <Paragraph position="2"> c Vesuvius erupted three times.</Paragraph>
    <Paragraph position="3"> Iterativity is an aspectual parameter which in English is marked mainly adverbially, with the presence of what are called 'frequency adverbials' or 'temporal quantifiers' (underlined in the examples). Iterative markers on a clause indicate the repetition of the event described in the clause, and also provide information about the frequency of repetition. The key requirement is couched in terms of an entailment condition: iteratives entail that there was more than one occasion on each of which an event of type E occurred, where 'occasion' is defined as spatiotemporal location. So there is a necessary requirement of seauentiality: that the events in question occurred on different occasions, in sequence.</Paragraph>
  </Section>
  <Section position="5" start_page="16" end_page="19" type="metho">
    <SectionTitle>
3. GENERALISATION
</SectionTitle>
    <Paragraph position="0"> On the basis of the descriptions given in sections I and 2 we can argue for a generalisation over distributives and iteratives such as is represented in Figure I (cf. Forsyth, 1970: 154).</Paragraph>
    <Paragraph position="1">  There are a number of intuitive arguments for the prima facie plausibility of such a generalisation, two of which will be considered here.</Paragraph>
    <Paragraph position="2"> First, it is clear that from one point of view, distributives and iteratives differ just in the nature of what is quantified over: distributives, where the marking of repetition is normally on the NP, involve quantification over individuals, while the temporal adverbial expressions in the iterative examples are normally taken to involve quantification over times or events. That is, the iterative markers can be seen as introducing distributive quantification. Secondly, perhaps the strongest argument for generalisation is that inferential set construction occurs with iteratives. Some iteratives, like distributives, contain indefinite NPs whose instantiations may vary across the repetition of the event. ~ sQuvenir in example (4), and a letter in example (5)  are just such NPs.</Paragraph>
    <Paragraph position="3"> (4) EverYtime John went abroad he bought A souvenir.</Paragraph>
    <Paragraph position="4"> a Sometimes it was a silver teaspoon, sometimes an antique vase.</Paragraph>
    <Paragraph position="5"> b They just lie around the house, cluttering it up.</Paragraph>
    <Paragraph position="6"> (5) Each day, Mary wrote ~ letter  to her sister.</Paragraph>
    <Paragraph position="7"> a It was usually ten pages long.</Paragraph>
    <Paragraph position="8"> b They were chatty letters.</Paragraph>
    <Paragraph position="9"> The solution to the set construction problem should if possible be a general one, covering both distributive and iterative cases.</Paragraph>
    <Paragraph position="10"> The ultimate defensibility, and explanatory value, of making such a generalisation will depend on whether it accurately reflects the facts about the temporal or event-theoretical structure of distributive clauses. It was said that are customarily defined as entailing a seauence o_~f events, each associated with a different occasion or spatiotemporal location. A generalisation of the kind envisaged would suggest that distributives might be regarded as having such an entailment as well, and the question we have to consider is whether this is so.</Paragraph>
    <Paragraph position="11"> Certainly, some distributives clearly * involve multiple occasions, that is, spatiotemporal locations. For example (6a), where it's one and the same book which is lent, and (6b).</Paragraph>
    <Paragraph position="12"> (6)a Mary lent each boy the book.</Paragraph>
    <Paragraph position="13"> b John visited each of his aunts.</Paragraph>
    <Paragraph position="14"> On the other hand, take an example like (2) above (Mary gave each boy ~9~)o This could easily describe a single occasion of giving, taking place once only. One could even imagine Mary handing a book to each of two boys simultaneously, with either hand. Or consider (7), on the interpretation where it was the same message and I did it on one occasion.</Paragraph>
    <Paragraph position="15"> Iteratives such as these manifest the same scope ambiguities as distributives and are open to the same mechanism of 'set construction' which as we saw operates in distributive clauses on the NPs which are distributed over. So in (4), ~ ~ is in the scope of a restricted universal quantification over times, and the sentence in question could be followed by  (b) where they refers to the set of souvenirs such that John bought each one on some trip abroad. (4a) and (5a) show that something like the 'bound variable' anaphora of example (2a) is possible here too \[I\] (7) Yesterday I sent each student  a message via computer mail.</Paragraph>
    <Paragraph position="16"> Intuition is clearly not enough, and in sections 4 and 5 we shall consider evidence from the discourse phenomena mentioned earlier, but first, what would constitute such a generalisation over iteratives and distributives: a generalisation which would indicate their similarities and differences, and provide a way in which the entailment of multiple temporal entities/events could be said to be true of distributives? \[I\] The expression 'variable binding', traditionally taken to describe an intrasentential phenomenon, is used with a less restrictive sense in this paper.  We can regard a clause as providing, at one level of description, a natter~ or temnl~t@, with specification of an event type with respect to placeholders for the following elements: one or more participants, and spatiotemporal location. Figure 2 is the skeleton of such templates or 'case specifications', which will be fleshed out for individual clauses.</Paragraph>
    <Paragraph position="17"> Distributive and iterative markers alike then contribute the following information: - first, that there are multiple instantiations of this pattern rather than a single instantiation; - and, in conjunction with other grammatical features of the clause, they provide information about which of these elements remain constant across such instantiations and which are variable. For example, take the sentence Each day, Mary wrote ~ letter to her sister (Figure 3). This specifies a event type which (as indicated by 'R') is repeatedly instantiated. Two of the participants, Mary and her sister, remain constant across these repetitions. The other participant, the letter, varies and will be instantiated by a (possibly) different entity on each occasion of repetition. There is also variation in the spatiotemporal element. This element is represented here by the time variable, ~\[me while t represents the reference ' * r of the Iterated complex as a whole. It is w~th r~spect to this second kind of information, about which of the elements vary, that iteratives and distributives differ. In iterative but not in distributive clauses the spatiotemporal location will necessarily be among those elements which are variable; other elements may also vary if they are introduced by expressions in a  scopal dependency relation with the temporal quantifier phrase* In \[2\] 'Case' in the sense of Lewis (1975) rather than Fillmorean Case Gram null Each day, Mary wrote ~ letter to her sister. distributives, at least one of the participant elements must vary - the one introduced by the distributive NP - and in addition so may other elements, including spatiotemporal location, if they are in a dependency relation with this NP. If no other participant element is in a dependency relation with the distributive NP, that is if all other participant elements are held constant, then variation in spatiotemporal location will entail, as in example (6a). Which elements vary tells us which inferential sets to construct.</Paragraph>
    <Paragraph position="18"> The similarities between the informal proposal which has just been sketched and Lewisdegs (1975) account of temporal quantifiers in terms of cases will be obvious. Lewis defines a case as an n-tuple of its participants (i.e. the values of free variables in the sentence) and a time coordinate \[the 'case specifications' represented above include in addition an event type label, such as 'writing'\]. He argues that iterative markers involve quantification over cases rather than over times or events. My proposal could be interpreted as a claim that we can extend some version of a case analysis to include distributives: these, too, would be taken to involve quantification over cases.</Paragraph>
    <Paragraph position="19"> Quantification over times or participants would then represent particular ways of realising the multiple instantiation of the case. The advantages of an account such as this are that it allows generalisation over a wide variety of phenomena, including numerous ways of marking iteration or distribution on the clause, and that it provides an appropriate level of description to be referred to in accounting for discourse anaphoric relations.</Paragraph>
    <Paragraph position="20"> The question of the individuation of events is a controversial one, and the terms 'event' and 'event type' have so far been used rather loosely. Suppose we first follow Mourelatos (1981) in making a distinction between events and the spatiotemporal locations with which they are associated, and secondly, suggest that  events should be regarded as particular instantiations of case specifications of the type described. Then iteratives entail a multiplicity of cases/events + spatiotemporal locations (which are in some isomorphic relationship), whereas distributives likewise entail a multiplicity of cases/events, but merely allow the possibility of multiple spatiotemporal locations (i.e., events and spatiotemporal locations may not be in an isomorphic relationship) - as we shall see, in the case of any particular distributive, this question may be resolved by following anaphoric reference. visit signifies a representative event of the type described: (10) John visited each of his maiden aunts, but the visit didn't make him popular with any of them.</Paragraph>
    <Paragraph position="21"> A second type of singular anaphora occurs, as in (11): in this case the anaphoric pronoun that appears to refer to the whole distributive episode, of John visiting each aunt, described in the preceding clause.</Paragraph>
  </Section>
  <Section position="6" start_page="19" end_page="20" type="metho">
    <SectionTitle>
4. ANAPHORIC REFERENCE TO EVENTS
</SectionTitle>
    <Paragraph position="0"> (8) John visited each of his great aunts.</Paragraph>
    <Paragraph position="1"> a The visits were much appreciated by the old ladies.</Paragraph>
    <Paragraph position="2"> b These ~ were a source of torment to him.</Paragraph>
    <Paragraph position="3"> (9) Everytime John went to Namibia he visited an old friend.</Paragraph>
    <Paragraph position="4"> a He found the visits distressing. b He was upset on these Q~casions, Examples (8) and (9) indicate that after a distributive or iterative clause,  speakers can refer using a plural definite NP, to a set of entities which are something like 'events' or 'occasions' and which appear to correspond to the' distributive or iterated situation of the preceding clause. Note thetwo types of example (a and b): in the first, the common noun head of the anaphoric expression is a nominalisation of the verb in the antecedent sentence (such NPs are normally taken to refer to event entities); in the second the noun is a much more general one. Both kinds of example appear to represent a phenomenon of the same type as the inferential set construction described in section I: it is as if the initial distributive or iterative clause introduces an 'event' variable and the anaphoric NPs represent a referential/extensional cashing out of this.</Paragraph>
    <Paragraph position="5"> Continuing the parallel with anaphoric reference to nominally-introduced entities, example (10) shows that with respect to event entities too, singular anaphoric NPs occur which are of the 'bound variable' type. Thus in (10) the (11) John visited each of his aunts. Tha___~t was a thoughtful thing to do.</Paragraph>
    <Paragraph position="6"> Finally, examples (12) and (13) show that, although plural definite NPs can be used to access the set of events or occasions resulting from distributive/iterative clauses (as in (8) and (9)), plural pronouns cannot. In (12) they and ~hem can only be interpreted with reference to the aunts - compare the same sentences with the pronouns replaced by the NP the visits. Explanation of this, which there is not space to elaborate here, must take account of the obvious fact that a requirement of nominalisation is involved. Meanwhile the important point to note is the clear distinction between the distribution of definite NP and pronominal anaphors.</Paragraph>
    <Paragraph position="7"> (12) John visited each of his aunts.</Paragraph>
    <Paragraph position="8"> a * They were a dismal failure.</Paragraph>
    <Paragraph position="9"> b * He had a good time on all of them.</Paragraph>
    <Paragraph position="10"> c * Each of them went well.</Paragraph>
    <Paragraph position="11"> (13) John flew to Paris twice.</Paragraph>
    <Paragraph position="12"> a He enjoyed both trips.</Paragraph>
    <Paragraph position="13"> b the enjoyed both of them.</Paragraph>
    <Paragraph position="14"> Example (11) shows that sinaular pronominal reference does occur, but this seeming inconsistency may be explained in terms of the nature of the entity being referred to: the plural NPs seem to refer to events whereas the singular ones refer to 'facts' or 'propositions' (in the sense of the distinction argued for in Vendler (1967)). \[3\] \[3\] There is clearly much more to be</Paragraph>
  </Section>
  <Section position="7" start_page="20" end_page="21" type="metho">
    <SectionTitle>
5. TEMPORAL BINDING PHENOMENA
</SectionTitle>
    <Paragraph position="0"> First it is necessary to review some claims of theories of temporal reference.</Paragraph>
    <Paragraph position="1"> Consider the following example: (14) When John made the cake, he broke the oven.</Paragraph>
    <Paragraph position="2"> Whe~, like other 'temporal connectives' such as before and after, indicates a particular relationship between the two clauses it connects: normally such relationships are considered to consist in specification of the relative ordering in time of the two events describe~ by these clauses. The basic claim, then, is that such connectives give a specification of a kind of 'temporal binding' between the two clauses such that the reference time of one is dependent on that of the other. This claim is independent of the particular nature of the ordering or binding hypothesised. (This idea is clearly on a par with claims that certain temporal phenomena should be understood on analogy with nominal anaphora, for example that the (past) tense morpheme should be taken to refer to a time, and to receive its reference either from some antecedent tense morpheme in the text, or from some adverbial expression, or deictically.) Kamp (1979), Hinrichs (1982&gt; and Partee (1984), who subscribe to a discourse theory of temporal (ordering) relations, argue that (in narrative discourse) the reference time of any main clause will be dependent on that of the preceding clause; that is, that just the same kinds of temporal binding dependencies occur at the level of discourse, between clauses which are syntactically independent as well as between those which are linked by temporal connectives.</Paragraph>
    <Paragraph position="3"> With this background, we can consider cl&amp;uses which involve iteration, marked by temporal quantification, in addition to temporal connection of the type just described. For example (15).</Paragraph>
    <Paragraph position="4"> (15) When Max left the office, he always turned the lights off.</Paragraph>
    <Paragraph position="5"> It seems that such sentences said with respect to the phenomena examined in this section; this wil~ be dealt with in forthcoming work.</Paragraph>
    <Paragraph position="6"> constitute a binding or dependency, between two clauses describing distinct types of event, which puts a condition on the pairwise mapping of instantiations of such events. Thus, in this case, every event of Max leaving the office is said to have been paired with (at least one) event of his turning the lights off. This kind of dependency relation seems to be exactly parallel to that which holds between the distributive NP each qirl and the indefinite NP ~ book in Mary qave each ~ book. In terms of the schema in Figures 2 and 3, binding is of the temporal variable t of clause one, and v the t v of clause two.</Paragraph>
    <Paragraph position="7"> Notice that the when clause restricts the range of the iterative quantifier always in the following clause. Examples like (15) are a special case of temporal quantification in that the condition on the range of quantification is explicitly stated in the subordinate clause. But it is true in general that temporal quantifiers like alwaTs or each time do not range over all of time, but over some contextually fixed interval. They thus conform to the claim made in section I that distributive NPs normally have their range of quantification restricted to some otherwise-specified 'witness set' The reference time t of Figure 3 represents this kind of witness set.</Paragraph>
    <Paragraph position="8"> The main point to be made in this section is that distributive clauses, with no explicit temporal quantification, can also act as sources for temporal binding, ~and restrict the range of subsequent temporal quantification, in just the same way that the iterati~e clauses do. Hence we find examples like (16) and (17).</Paragraph>
    <Paragraph position="9"> (16) Mary gave each boy a book.</Paragraph>
    <Paragraph position="10"> Sometimes the boy thanked her, but more often he did not.</Paragraph>
    <Paragraph position="11"> (17) Harry invited each of his relatives to stay. On each occasion he bought in enough food to feed an army.</Paragraph>
    <Paragraph position="12"> Here, the range of the quantifier phrases sometimes, mote often and on each is restricted by the set of events determined by the preceding distributive clause - that is, by something like the set of instantiations of the case specification, perhaps more specifically, instantiations of the temporal variable t . There is binding between the event~ described in the two sentences: in (16) some of the 'times' (occasions) on which Mary gave Some boy a  book are such that the boy in question thanked her; in (17) each occasion on which Harry\[s relatives came to stay is paired with an event of his buying in lots of food.</Paragraph>
    <Paragraph position="13"> Example (18), which is from a university library photocopying machine, is exactly parallel to the temporally quantified and connected example given in (15). Here, each plays the same role as always does in (15).</Paragraph>
    <Paragraph position="14"> (18) Please wait until machine is completely silent before inserting each 5p coin.</Paragraph>
    <Paragraph position="15"> This example is (theoretically) ambiguous in the scope of the distributive marker: does the first clause represent a condition for the iterated event, so that we are to wait until the machine is silent and then insert all the 5ps one after another, or is it part of an iterated condition + event sequence, so that on each occasion of inserting 5p, we must wait until the machine is silent first? (In actuality, it is of course the second reading which is intended.) Now consider the following examples, with another temporal connective, then. (19) Mary gave each boy a book.</Paragraph>
    <Paragraph position="16"> a Then she marked his name Off her list ashaving received it.</Paragraph>
    <Paragraph position="17"> b Then she dismissed them.</Paragraph>
    <Paragraph position="18"> (20) Everytime John went abroad he brought back a souvenir.</Paragraph>
    <Paragraph position="19"> a Then he put it in the cupboard with the rest of them.</Paragraph>
    <Paragraph position="20"> b Then he stopped going abroad and threw them all away.</Paragraph>
    <Paragraph position="21"> These examples indicate that the initial distributive or iterative sentence can be viewed either in terms of its unity as a complex situation, or in terms of the constituent phases which that total comprises (cf. examples (8) and (11) in section 4). Hence in (19) the reference time of (b), the dismissal, will be after the completion of the complex event of giving out books, (in terms of the case specification in Figures 2 and 3 the t of (b) will be after the t of the initial sentence). In contrast, t~e sequence in (19a) is such that the then clause is 'in the scope of' the distributive and there is a pairwise binding between the event type of giving out a book and the event type of marking off a&amp;quot; name, such that each instantiation of the former will be followed by an instantiation of the latter. That is, there is a temporal ordering condition on the temporal variables t of the two clauses. The whole sequence will have the same t ; overall reference time or 'witness set r. If we regard temporal connectives as indicating a relationship defined over reference times, then we are put in the position of racognising two possibilities with respect to distributive/iterative sentences: these seem to involve something like 'nested reference times', with the ordering relation being able to hold over either t v or t r, Consider also examples (21) and (22).</Paragraph>
    <Paragraph position="22"> (21) Mary gave each boy a book.</Paragraph>
    <Paragraph position="23"> a On each occasion the boy thanked her.</Paragraph>
    <Paragraph position="24"> b On that occasion they were grateful to her.</Paragraph>
    <Paragraph position="25"> (22) John visited each of his maiden aunts. Each one gave him a cup of tea.</Paragraph>
    <Paragraph position="26"> Example (22) is particularly interesting, because we have a sequence of two clauses which are not syntactically linked by a temporal connective, and neither of which contains a temporal quantifier phrase. Yet there is an implication that there is a pairwise dependency relation between teas and visits. The generalised binding relationship appears to hold across the sentence boundary, just as Kamp, Hinrichs and Partee postulated with respect to ordering relations between clauses describing single rather than repeated situations. Any analysis of this discourse which assigns each sentence a single reference time, and which then, following Hinrichs and Partee, requires that the reference time for the second follow that of the first, will give the wrong results. \[4\] The observations which have been made evince a close analogy with the facts of \[4\] Their response to this might be that we are not here dealing with narrative discourse, a denial which is more plausibly made of earlier examples, or even (19) or (20), than it is of (22).</Paragraph>
    <Paragraph position="27"> 22, nominal anaphora which were outlined in section 1 of the paper. The (a) examples in (19), (20) and (21) in each case represent something like maintenance of the binding: we are still specifying the type of the event sequence which is iterated, and all the clauses in the sequence have the same t ; reference time or witness set. In the (~) examples, on the other hand, the description of the iterated event is finished: there is a discourse-level division between the initial distributive/iterative sentence and sentence (b), representing the end of the rhetorical mode of generalisationthrough-singularisation, and closure of the interval t . One indication of this is that any p~onouns occurring in the (b) sentence, and anaphoric to distributive NPs or their dependent expressions in the first sentence, will necessarily be plural. The use of a plural NP, which as I have said represents 'referential cashing out', indicates that the iterated sequence is over and we can now assume its completion and move on. In contrast, in the (a) sentences anaphoric pronouns referring to entities which were introduced by the nominals in the distributive/iterative sentence, are normally singular.</Paragraph>
  </Section>
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