DISTRIBUTIVES, QUANTIFIERS AND A MULTIPLICITY OF EVENTS 
Lesley Stifling 
School of Epistemics & Department of Linguistics 
University of Edinburgh 
2 Buccleuch Place 
Edinburgh EH8 9LW, U°K. 
ABSTRACT 
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" 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. 
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. 
(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, "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). 
(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). 
(2) Mary gave each boy ~ book 
a ...and told him to look after 
it. 
b They took them into the garden 
to read. 
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. 
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 
16 
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. 
temporal binding. These support the 
hypothesised generalisation and tell us 
something about the temporal or event- 
theoretical structure of both 
distributives and iteratives. 
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. 
(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 \['host' or 
'witness set' - Barwise & Cooper, 1981\] 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 
one I 
aspectual I 
parameter I 
I 
The observations made in this paper 
are confined to the past tense and to 
'telic' or 'bounded' situation types 
(Mourelatos, 1981). 
2. ITERATIVES 
The following are examples 
iterative clauses in English: 
of 
(3)a Each day Mary wrote a letter 
to her sister. 
b Every time John went abroad 
he bought a souvenir. 
c Vesuvius erupted three 
times. 
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. 
3. GENERALISATION 
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). 
I multiple actions (repetition I 
of a situation) \] 
I 
single action/situation 
iterative 
'distributive 
Figure I. Generalisation over distributives and iteratives. 
17 
There are a number of intuitive 
arguments for the prima facie plausibility 
of such a generalisation, two of which 
will be considered here. 
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. 
(4) EverYtime John went abroad he 
bought A souvenir. 
a Sometimes it was a silver tea- 
spoon, sometimes an antique vase. 
b They just lie around the house, 
cluttering it up. 
(5) Each day, Mary wrote ~ letter 
to her sister. 
a It was usually ten pages long. 
b They were chatty letters. 
The solution to the set construction 
problem should if possible be a general 
one, covering both distributive and 
iterative cases. 
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. 
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). 
(6)a Mary lent each boy the book. 
b John visited each of his 
aunts. 
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. 
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. 
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 in- 
trasentential phenomenon, is used with a 
less restrictive sense in this paper. 
18 
event: --- 
*participant I 
*participant 2 
*participant n 
*spatiotemporal location 
R 
\['daily' in 
interval tr\] 
event: 'writing' 
*participant I 
*participant 2 
'Mary' 
'her sister' 
l'participant 3 'a letter'I 
I I 
l*spatiotemporal location t I 
I vl 
Figure 2. 'Case' specification \[2\] 
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. 
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- 
mar. 
Figure 3. Case specification for 
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. 
The similarities between the informal 
proposal which has just been sketched and 
Lewis°s (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. 
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. 
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 
19 
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. 
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. 
4. ANAPHORIC REFERENCE TO EVENTS 
(8) John visited each of his 
great aunts. 
a The visits were much appreciated 
by the old ladies. 
b These ~ were a source of 
torment to him. 
(9) Everytime John went to Namibia 
he visited an old friend. 
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. 
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. 
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. 
(12) John visited each of his 
aunts. 
a * They were a dismal failure. 
b * He had a good time on all of 
them. 
c * Each of them went well. 
(13) John flew to Paris twice. 
a He enjoyed both trips. 
b the enjoyed both of them. 
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 
20 
5. TEMPORAL BINDING PHENOMENA 
First it is necessary to review some 
claims of theories of temporal reference. 
Consider the following example: 
(14) When John made the cake, he 
broke the oven. 
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> 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. 
With this background, we can consider 
cl&uses which involve iteration, marked by 
temporal quantification, in addition to 
temporal connection of the type just 
described. For example (15). 
(15) When Max left the office, he 
always turned the lights off. 
It seems that such sentences 
said with respect to the phenomena exam- 
ined in this section; this wil~ be dealt 
with in forthcoming work. 
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. 
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. 
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). 
(16) Mary gave each boy a book. 
Sometimes the boy thanked her, but 
more often he did not. 
(17) Harry invited each of his 
relatives to stay. On each occa- 
sion he bought in enough food to 
feed an army. 
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 
21 
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. 
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). 
(18) Please wait until machine is 
completely silent before inserting 
each 5p coin. 
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. 
a Then she marked his name Off 
her list ashaving received it. 
b Then she dismissed them. 
(20) Everytime John went abroad he 
brought back a souvenir. 
a Then he put it in the cupboard 
with the rest of them. 
b Then he stopped going abroad and 
threw them all away. 
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" 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). 
(21) Mary gave each boy a book. 
a On each occasion the boy 
thanked her. 
b On that occasion they were 
grateful to her. 
(22) John visited each of his 
maiden aunts. Each one gave him a 
cup of tea. 
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 narra- 
tive discourse, a denial which is more 
plausibly made of earlier examples, or 
even (19) or (20), than it is of (22). 
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 generalisation- 
through-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. 
6. CONCLUSIONS 
The anaphoric examples in section 4 
show that both distributive and iterative 
clauses enable subsequent reference to 
sets of cases/events using a definite NP. 
This is clearly parallel to the 
possibility of using a plural anaphoric NP 
to make reference to some set of 
individuals (such as books), on the basis 
of an original singular NP introduction. 
It would seem to be desirable to account 
for both kinds in terms of the same 
mechanism of 'set construction'. The 
anaphoric examples also indicate a 
qualitative difference between the 
distribution of definite NP and pronominal 
anaphora, and show that there is discourse 
anaphoric access not just to the subparts 
of the distributed or iterated situation, 
but also to something like the whole 
distributive quantification, which may be 
an entity of a different kind. 
The temporal binding phenomena of 
section 5 give a different type of 
evidence for the explanatory value of 
making a generalisation of the kind 
described. The observations in this 
section also show that, whereas past tense 
clauses describing a single situation have 
a reference time with some specific 
temporal referent, distributive and 
iterative clauses seem to require 'nested 
reference times', with temporal ordering 
relations definable at two levels. The 
Kamp/Hinrichs/Partee account needs to be 
modified before it is able to incorporate 
these phenomena. 
I've said that the set construction 
problem is of practical importance for 
computational models of natural language 
interaction. In addition, the concept of 
iterated action is important to planning, 
so that a generalisation across 
distributives and iteratives plus what has 
been said about their temporal nature 
should have interesting implications in 
this area. If iteration is handled 
computationally by setting up a loop which 
embodies the instruction to repeat an 
action under certain conditions, then 
distributives may be handled the same way. 
Distributive and iterative interpretations 
may hold over stretches of discourse, the 
delimitation of which is relevant to the 
interpretation of temporal connectives, 
and as we saw with examples (19) to (21), 
in some cases anaphoric phenomena may give 
clues about this delimitation, that ,is, 
indicating when to turn off the iterative 
loop. The delimitation of such discourse 
chunks corresponds to the delimitation of 
the extent of influence of the t or 
'witness set', and so anaphor~ in 
following sentences may allow us to close 
off this interval. 
ACKNOWLEDGEMENTS 
This paper results from research 
towards a PhD which has been supported by 
a grant from the Association of 
Commonwealth Universities. The 
development of the ideas presented here 
has benefitted considerably from the 
opportunities for stimulating discussion 
provided by the School'of Epistemics Tense 
and Discourse Workshop. I am particularly 
grateful to the following people for 
helpful comment on earlier versions of the 
paper: Mark Steedman, Marc Moens, Henk 
Zeevat, Ewan Klein, Han Reichgelt, Barry 
Richards, Jim Miller, Jan de Vuyst, David 
McCarty, Jim Hurford. 
23 
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