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<Paper uid="E85-1003">
  <Title>DISTRIBUTIVES, QUANTIFIERS AND A MULTIPLICITY OF EVENTS</Title>
  <Section position="3" start_page="0" end_page="16" type="intro">
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ABSTRACT
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    <Paragraph position="0"> With the intention of indicating some temporal/event-theoretic characteristics of distributive clauses, a generalisation is made over distributives and clauses marked for iterative aspect: two kinds of semantic phenomena which have normally been confined to separate theoretical domains. It is shown that in particular, both give rise to an 'inferential set construction' problem. An informal outline is given of what might constitute such a generalisation. The generalisation is proposed intially on grounds of prima facie plausibility, but its ultimate defensibility and explanatory value will depend on the validity of its consequence, that distributive clauses entail a multiplicity of temporal entities or events. This proposal is considered with respect to two types&amp;quot; of discourse phenomena; anaphoric reference to event entities, and temporal binding. These provide further support for making the generalisation, clarify its nature and indicate in what respect the entailment claim can be true of distributives. The set construction problem is of practical importance for computational models of natural language interaction, and since the concept of iterated action is central to planning, the generalisation across iteration and distributives, along with the observations about their nature, have interesting implications for work in this area.</Paragraph>
    <Paragraph position="1"> I. DISTRIBUTIVES First, three points about the body of phenomena called 'distributives'. These are taken to be relatively uncontroversial, and are simply assumed in the rest of this paper.</Paragraph>
    <Paragraph position="2"> (i) Examples (a) and (b) in (I) illustrate the distributive/collective distinction. Essentially, sentences containing at least one plural or universally quantified NP, the denotation of which might be regarded as a set, &amp;quot;can either be read in terms of the individual members of this set (as in la), or given a 'group' reading in terms of the set as a whole (as in Ib).</Paragraph>
    <Paragraph position="3"> (1)a The three girls each had a pizza. (dist) b The three girls shared a pizza. (coll) (ii) It is distributive readings which give rise to the possibility of quantifier scope ambiguities - including interpretations which involve dependency relations between the NPs in the sentence. Dependency interpretations in turn allow 'inferential set construction' Consider example (2).</Paragraph>
    <Paragraph position="4"> (2) Mary gave each boy ~ book a ...and told him to look after it.</Paragraph>
    <Paragraph position="5"> b They took them into the garden to read.</Paragraph>
    <Paragraph position="6"> On the most common reading of the distributive clause Mary gave each boy book, there is a dependency relation between the two object NPs such that book is in the scope of each boy and the interpretation of the former is relative to that of the latter. (2b) illustrates one type of anaphoric relation which distributive clauses may participate in: plural pronouns and definite NPs are used to refer to implicit sets of entities which instantiate variables introduced in distributive clauses by just such singular indefinite NPs in the scope of distributive NPs. So in (2b) the underlined NP they refers to the set of books such that Mary gave each one to some boy.</Paragraph>
    <Paragraph position="7"> As Webber (1979, 1983) has pointed out, this anaphoric possibility represents a practical problem for computational accounts of discourse, since a mechanism 'is required for constructing as a  discourse entity a set with the correct description, on the basis of the semantic representation of the initial distributive sentence containing the singular indefinite NP.</Paragraph>
    <Paragraph position="8"> temporal binding. These support the hypothesised generalisation and tell us something about the temporal or event-theoretical structure of both distributives and iteratives.</Paragraph>
    <Paragraph position="9"> Notice that singular anaphora (as in 2a) is also possible: the singular anaphor indicates the maintenance of a rhetorical mode of 'generalisation through singularisation', which is established by the initial distributive sentence. The pronoun it acts as a placeholder, signifying a representative member of the set of books such that Mary gave each one to some boy, and it has the status of a 'bound variable' Such pronouns cannot be taken to refer and I describe the contrast between them and the plural anaphors as being that the plural ones represent a 'referential' or 'extensional' cashing out of the initial semantic value.</Paragraph>
    <Paragraph position="10"> (iii) Sentence (2b) also indicates the possibility of using a plural pronoun th@y - to refer to some relevant set of boys (in contrast to (2a) where the singular, 'bound variable' pronoun him is used). However, it is not really necessary to propose a second algorithm to construct such sets because the initial, syntactically singular distributive NPs, such as eac h bow, are arguably almost always themselves 'referential' and 'anaphoric', ~ust in the sense that the range of quantification is restricted by context. Here, the quantifier does not range over the set of all boys, but over some otherwise specified subset \['host' or 'witness set' - Barwise &amp; Cooper, 1981\] of boys. It can be paraphrased with the partitive expression: each of the bows. My intention in this paper is to explore a temporal, event-oriented perspective on distributives. The question at issue is: What are the consequences for the temporal or event-theoretical analysis of a clause, of its being 'distributive' in the sense defined? First I indicate similarities between distributives and clauses marked with iterative aspect. I then make certain observations which apply to both distributives and iteratives, concerning two kinds of discourse phenomena: definite NP anaphora to event entities, and</Paragraph>
    <Paragraph position="12"> The observations made in this paper are confined to the past tense and to 'telic' or 'bounded' situation types (Mourelatos, 1981).</Paragraph>
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