Generic NPs and Habitual VPs 
Allan Ramsay 
Department of Computer Science 
University College Dublin 
Belfield, DUBLIN 4, Ireland 
ABSTRACT 
We propose a simple, intuitively satisfying 
treatment of the semantics of bare plural 
NPs. This treatment avoids the use of non- 
standard logics, and avoids the need for sys- 
tematic ambiguity of verb semantics. 
1 Background 
Previous work on the semantics of bare plural NPs 
has largely focussed on the contribution they make 
in habitual sentences like 
(1) Mar~ eaiJ peaches. 
and 
(2) John likes driving fast cars. 
Both (1) and (2) seem to express tendencies, general 
rules. If you heard (1) then you would feel confi- 
dent that you could offer Mary a peach for dessert. 
(1) seems to express a general characteristic of Mary, 
namely that if you offer her a peach in a suitable situ- 
ation she will eat it. If you heard (2) then you would 
hide the keys of your Ferrari when John was visiting. 
(2) tells you that if he gets the chance of driving a 
fast car he is likely to take it. 
If we take (1) and (2) as paradigms of the way bare 
plural NPs get used then it is reasonable to suppose 
that they express some hind of general property. The 
NP peaches in (1), for instance, seems to express some 
relationship between Mary and peaches in general, or 
possibly between Mary and the property of being a 
peach. This feeling that bare plural NPs express gen- 
eral relationships has led to some rather desperate 
strategies. One is to suppose that they should be 
treated just as though they were universally quanti- 
fied. The most cursory examination, however, shows 
that this cannot be right. It simply is not true that 
(1) entails that Mary has any relationship to the set 
of all peaches. It is not even true that it entails that 
she will always eat a peach if you offer her one in the 
right circumstances. Whatever bare plural NPs do, 
they do not act like universally quantified NPs. 
A more sophisticated approach treats them as de- 
noting properties. Chierchia and Turner \[1987\], for 
instance, interpret (1) as saying that Mary is in some 
relationship to the property of being a peach. There 
are two problems with this approach. The first is that 
they fail to be very explicit about what this relation- 
ship is, so that the proposal simply does not get us 
very far. The second is that whatever the relationship 
turns out to be we seem to end up with a systematic 
ambiguity in the meanings of simple verbs like eat. In 
(3) Mary is eating a peach. 
it looks as though the verb eat denotes u relation be- 
tween two individuals, namely Mary and some peach. 
In (1), however, it must denote a relationship between 
an individual (Mary) and a property (the property of 
being a peach). Eat, it seems, is polymorphic. And 
so must every other verb which can take either an in- 
definite NP or a bare plural as complement be. Far- 
thermore, there must be some systematic relation be- 
tween the two interpretations of each of these verbs. 
It would surely be better to express this systematic 
relation in the semantics of the bare plural NPs, and 
to leave verbs like eat as relations between individu- 
als. 
Much the same can be said of Carlson's \[1989\] pro- 
posal that bare plurals denote extended individuals 
and indefinite NPs denote stages ofindivlduals. If we 
take this approach then (a) most English verbs must 
be polymorphic, accepting either extended individ- 
uais or stages of individuals as arguments, and (b) 
there must be some systematic relationship between 
these pairs of meanings. It is particularly disappoint- 
ing that Carlson's discussion of this systematic rela- 
tionship consists of the use of a type-raising operator 
Gn which is given no semantics. 
A third approach is to try to capture the feeling 
that bare plurals indicate some sort of "tendency" 
by appealing to non-monotonic logic. Just as with 
the analysis in terms of universals, however, this just 
seems to get the intuitions wrong. What sort of non- 
monotonic paraphrase can we give to (1)? It certainly 
AcIYeS DE COLING-92, NANTES, 23-28 ^ol;r 1992 2 2 6 PROC. OF COLING-92, NANTES, AUG. 23-28, 1992 
v.es~pposi.o~s = {,(g, VH me,,a~r(H, El ,mine(H, job,t) 
A Igl : 0}\] 
This says that there is a singleton set A of "eating 
events"; that for each member of A the agent is E 
(remember, A is a singleton set so there is in fact 
only one such member); that there is a singleton set 
B of peaches which is the object of every member 
of A; that every member of A is extended and took 
place at some past instant; and that the existence 
of a unique singleton set E of items called John is 
presupposed. It is easy to argue with the details of 
this analysis of (7), particularly with the temporal 
element, but the basic outline is familiar. 
We now want an analysis of 
(8) Mary was ealin 9 peaches. 
which fits our intuition that (8) refers to an eating 
event whose agent was Mary and all of whose objects 
were peaches. The following seems suitable: 
\[mtriz =JA instant(A) A A < now 
^ 3B VC member(C, B) 
--. e~t(c) 
A agent(C) D) 
AVE object(C, E) 
-~ peach(E I 
A IBI = 1 
A vg member(F, B) 
--* instantaneous(F) 
^ at(A, F), 
presuppositions = {t(D, VG member(G, D) nan.(G, ~mru) 
^ IDI = 1)}\] 
This says that B is a singleton set of instantaneous 
events; that the sole member of this set took place 
at some past instant A; that its agent is the entity 
described by the presupposition that there is a single 
entity called Mary in the context; and that all its 
objects are peaches. This formal paraphrase seems 
to fit our intuitions about (8) perfectly. How did we 
obtain it? 
3 NP semantics 
We follow the tradition first established by Rus- 
sell, and made concrete by Montague, of treating 
NP semantics as generalised quantificrs, i.e. as ex- 
pressions which provide the qnantificational informa- 
tion required for turning some proposition schema 
into a proposition. Montague, for instance, re- 
gards the meaning of every student as something like 
X(P, YXstudent(X) -~ P.X) (we use the notation 
P.X to denote the application of P to X). Applying 
this to a property such as A(Y, sleep(Y)) will produce 
the sent .... VX,tudent(X) --~ sleep(X). In general, 
the meaning of an NP is treated in this tradition as 
something which will lower the type of an expression 
-- something which will turn a property into a propoo 
sition, or a function from properties to properties into 
a property, or ... 
We make one slight change to this analysis of NP 
semantics. The standard treatment of NPs says that 
they are of type (e --, t) -* t. In other words, 
they take a function which maps individuals (en- 
tities of type e I to truth values (entities of type 
t) and return a truth value. We propose to gen- 
eralise u step further, making NP semantics map 
functions of type (e -4 t) --~ t to truth values 
(i.e. that they arc of type ((e --, t) --4 t) --, t)). 
Thus we propose that the matrix for every stu- 
dent should be A(A, A.A(B, VC\[VD member(D, C) 
student(D)\] ~ B.C)). The embedded expression 
A( B, VU~/ D rnember( D, C) -~ student(D)\] --~ B.C) 
is similar to the generallsed quantifier that standard 
model theoretic semantics provides for every student. 
The only difference is that we are quantifying over 
sets of students (i.e. over sets C satsifying the require- 
ment that VDmember(D,C) -* student(D)) rather 
than over individuals. The meaning of the NP is then 
an expression which is waiting for something which 
will combine with this standard generalised quanti- 
tier. We will refer to such objects as genercllsed ~ 
quantifiers, to emphasise the extra level of abstrac- 
tion. 
We obtain such representations of NP semantics in 
the usual way, by taking the meanings of determin- 
ers to be even higher level objects which get com~ 
bincd with the meanings of nominal groups. Thus 
the meaning of every is A(E, A(A, A.A(B, V C \[ V D 
member(D, C) --, E.D\] --* B.C))). Applying this to 
A(X, student(X)), the meaning of the nominal group 
consisting of the word student, produces A(A, A.A(B, 
V C \[V D ,~,~er(V,C) ~. stude,,t(D)\] ~ B.C)) 
as required. Similarly if the meaning of a is taken 
to be A(E, A(A, 3 B b~ C me,,~r(C, B) -~ E.C\] ^ 
IBI = 1 A A.A(D, D.B))) then the meaning of a peach 
becomes ;t(A, ~ B IV C member(C, B) -. peach(C)l 
A IBI : 1 A A.A(D, D.B)). This is an abstraction 
over the proposition that there is some singleton set 
B all of whose members are peaches which satisfies 
some complex property involving the abstracted vari- 
able, which is again what we require. Note that the 
application of A in this formula is inside the scope of 
the quantifcation over members of B. It is this ex- 
tra control over the relative scope of quantifiers that 
makes us prefer generalised ~ quantifiers to ordinary 
gencralised quantifiers. 
ACRES DE COLING-92, NArCrES, 23-28 Ao(rr 1992 2 2 7 PROC. OF COLING-92, NAICrEs, Au(i. 23-28, 1992 
does not mean that Mary eats most peaches~ in the 
sense that there is some relationship between Mary 
and more than half the peaches there either are now 
or ever have been. It does not mean that it is fre- 
quently, or even usually, the case that she can be 
found eating a peach (it is true, for instance, that I 
eat quails eggs, but it is certainly not true that it hap- 
pens very often). The gut feeling that sentences llke 
(1) and (2) express general tendencies, and that the 
best machinery we have for dealing with tendencies is 
non-monotonic logic, is very understandable. It does 
not, however, seem easy to give convincing formal 
paraphrases of sentences like these in these terms. 
The problems with these suggestions arise from the 
fact (1) and (2) seem to express general tendencies, 
and that this is taken to be due the presence of the 
bare plurals NPs. Suppose we consider instead the 
occurrence of bare plural NPs in non-habitual sen- 
tences: 
(4) Marl/ is eaZingpeaches. 
(5) John is driving fast cars. 
(4) does not express any sort of tendency, any general 
rule. It describes a specific current event. There is 
an individual, Mary, who is doing something. What 
is she doing? She's eating. What is she eating? She 
is eating several things, each of which is a peach. 
(5) does not even seem to make much sense. Why 
not? Because it seems to describe a specific driving 
event with a single agent but with several objects, 
each of which is a fast car. (5) seems odd because 
it seems to say that John is driving several fast cars 
at the same time, and we know that most people can 
only drive one ear at a time. 
We therefore suggest that the feeling that (1) and 
(2) express tendencies arises entirely from the form 
of the verb, and that bate plurals should be thought 
of as delimiting the arguments of the verb. In other 
words, we sugest that (4) should be thought of in 
much the same way as 
(6) Ma~ is house-hunting. 
which says what Mary is doing is hunting for some- 
thing, and that what she is looking for is a house. 
2 Semantic Framework 
The treatment of bare plurals proposed in this paper 
ntJ within the following general framework. 
• Verbs denote events (subdivided into states, ex- 
tended actions and instantaneous actions). 
• There is a finite set of thematic roles, such as 
agent, instrument, target and object. The syn- 
tactic sub-categorisation rules of individual verbs 
allocate sets of items to these roles. These sets of- 
ten turn out to be singletons, but it seems better 
to distinguish between singular and plural NPs 
in terms of the cardinality of some tee of objects 
than to say that singular NPs denote individuals 
and plurals denote sets. 
• Tense and aspect express relations between 
events or sets of events and temporal objects such 
as instants and intervals. 
• Definite reference and anaphora are treated as 
PRESUPPOSITION-INDUCING mechanisms. Pre- 
suppositions are described in terms of formulae 
each of which is required to pick out exactly one 
item in the context of an utterance. The seman- 
tics of any natural language expression consists 
of a set of such presuppositions and a matrix, 
which corresponds to the usual notion of propo- 
sitional content. 
The dements of this framework ate not universally 
accepted, but they do at least all have respectable 
ancestors. The most contentious is the view that 
definite reference and anaphora should be dealt with 
in terms of constraints on the situation of utterance. 
The basic notion here is similar to the use of ANCHORS 
in situation semantics \[Barwise & Perry 1983\], and to 
the treatment ofanaphora in DRT \[Kamp 1984\]. The 
details of our approach are given in \[Ramsay 1990a\]. 
Very little in the present discussion of bare plurals de- 
pends on this treatment of definite reference. Sceptics 
about this part of our framework are invited to sus- 
pend their disbelief while considering the treatment 
of bare plurals. 
The following analysis of 
(7) John a~e a peach. 
should illustrate the crucial aspects of our represen- 
tation: 
\[.~tri~ :3A 3B VC mer.~r(C, B) -4 ~h(C) 
^ IBI = 1 
A VD member(D, A) 
eat(D) 
A agent(D, E) 
^ objed(D, B) 
m IAI = 1 
A VF member(F, A) 
--~ eztended( F) 
A 3G instant(G) 
A G < now 
A at(G, F), 
Acrv.s DE COLING-92, NANTES, 23-28 AO~r 1992 2 2 8 PROC. OF COLING-92, NANTES, AUG. 23-28, 1992 
In order to interpret bare plurM NPs we need the 
following rule: 
\[sV,,taz :\[major : \[cat : u, bar : 2\], 
head : \[agree : \[~hird : \[sing :: no, 
Vl,,ral = yes\]\], •..\]} 
misc = \[slaM, = null, wh : no,.. •\]\], 
semantics : \[matriz := A(I, I.A(J, VK(J.K -. L.K))), 
presuppositions : M\]\] 
\[syntax :\[rtmjtrr : \[cat : u, bar : 1\], 
head : \[agree : \[third : \[sing :: no, 
r~ur-Z : yes\]\], •..\]~ 
•..\], 
semantics : \[matrix : L, 
presuppositions -- M\]\] 
This rule, with quite bit of syntactic detail omitted, 
says that a plural nominal group (something of cat- 
egory u and bar level 1) may be rewritten as an NP 
(something of category n and bar level 2). The matrix 
of the NP consists of a generalised 2 quantifier derived 
from the matrix of the NN, and the presuppositions 
of the NN are inherited by the NP. 
This is exactly the rule we need to obtain 
\[matriz : A(A, A.A(B, VC B.C -~ peach(C))), 
presuppositions = {}\] 
the meaning of the bare plural peaches, and hence 
to obtain the interpretation given above of (8). It is 
worth noting that bare plurals as subject have very 
much the same effect -- that the analysis of 
(9) Wolves were chasing a deer• 
says that there was a past instantaneous chasing event 
whose object was a (singleton set of) deer and all of 
whose agenfs were wolves: 
\[raxdriz =3A instant(A) A A < ,tow 
A 3B VC nvember(C, B) 
-. chase(C) 
A VD agent(C, D) 
• wdf(~) 
A 3E VF member(F, E) 
-4 ~er(~') 
^ IEI : I ^ ob#ct(C, E) 
^ IBI = 1 
h VG member(G, B) 
--* instantaneous(G) 
A at(A, G), 
presuppositions = {}\] 
4 Habituals Revisited 
The analysis giveu above seems to provide a satisfac- 
tory treatment of the contribution of bare plural NPs 
in sentences which report simple events. How do we 
deal with their use in habituM sentences like (1)? 
We take it that (1) somehow expresses a general 
tendency, qb say Mar T eats peaches is to say that on 
suitable occasions she can be found eating peaches. 
The word %uitable n carries a lot weight here• If you 
say Mary cain Beluga caviar, you probably mean that 
she eats it whenever she can get it. If you say Mary 
eats sausages you are more likely to mean that she he~ 
quently eats thent, probably because she's too poor 
to afford caviar very often. Indeed, the ehameteri~tt- 
tion of Usuitable" is likely to change from situation to 
situation eveu for the same sentence. You could say 
She eats sausages lit response to the question Is Mart 
a funny eater?, iu which ease Usuitable" might mean 
something like "if she's offered them and there's no 
other choice". You could also say it in response to 
tile question Does Mary \]tare a health v varied diet ¢. 
Here, %uitable" would be more likely to memt Son 
nearly every occasion when site eats anything at all". 
We suggest that the best way to dam with this h 
to treat habituals as simply saying that events of the 
kind iu question exist. The significance oftmying that 
such events exist will depend on the situation in which 
it is said. Suppose you say that events in which Mary 
eats sausages exist in a situation where your hearer 
wants to know about the existence of events where 
she eats things that some people might not like (i.e. 
in response to Is Mary a fussy eater~.), in such a 
case the fact that there are such events is enough to 
satisfy the heater's curiosity, and there are therefore 
no grounds for them to assume anything about how 
often site eats them. Suppose, on the other hand, that 
you respond to a question about the variety of her diet 
by simply saying that there are occasions when she 
eats sausages. Your hearer is then likely to assume 
that you are implicating that these are MI or most of 
the "Mary eating something" events that you know 
about, since if you knew about other things Mary ate 
then you would know that her diet was reasonably 
varied, lit other words, hnbituaLs simply posit the 
existence of sonic set of events of the specified kind. 
Decisious about whether these events are common, 
about the circumstances in which they occur, can only 
be made on the basis of extra-linguistic contextuM 
facts. 
We theretbre analyse the sentence 
(10) Mary drives a fast car. 
Ks: 
lain/vii =:~IA ~JB VC men~er(C, B) 
ACRES DE COL1NG-92, NANTES, 23-28 hO~r 1992 2 2 9 PROC. OV COI,ING-92, NANTF.S. AUG. 23-28, 1992 
--, fast(C, ~,(D, car(D))) 
^ I~1 = 1 
^ VE member(E, .4) 
--, drive(E) 
^ agent(E, y) 
^ objea(E, n) 
^ IAI > 1, 
~es,.wos..,,,s = {,(e, VG memb,,e(G, e) 
---. ,,.~m~(C, m.,eU) 
^ IFI = 1)}\] 
This says that there is a set A of driving events, where 
A has more than one member; that each member of 
A has Mary as its agent; and that there is some sin- 
gieton set B of fast ears (things which are "fast for 
a cam) which is the object of every member of A. 
How often she drives it, where she drives it, and so 
on are all questions which can only be answered when 
we know more about the context in which (10) was 
uttered. All that (10) actually says is that there is 
such a set of events. 
This analysis of habituals gives a clue as to why 
(11) John eats a peach. 
does not seem to admit a habitual reading. The in- 
terpretation of (11) as 
\[matri~ =3A 3B VC member(C, B) 
-~ push(C) 
^ Inl-- 1 
A VD member(D, A) 
eat(D) 
^ agent(D, E) 
^ objea(D, ~) 
A JA I > 1, 
presuppositions = {t(E, VF member(F, E) 
--..~me(F. john) 
^ IEI = 1)}\] 
says that there is a single peach which is the object 
of several eating events. Since a given peach can only 
be eaten once, this seems most unlikely. 
There are, of course, still open questions concerning 
the interpretation of sentences like: 
(12) John cats a peach for his lunch cver~ day. 
(12) clearly does require a habitual reading, where 
each day he eats a different peach. It seems likely that 
some mechanism such as "Cooper storage n \[Cooper 
1983, Keller 1987\] for delaying decisions about quan- 
tifier scope will be required here. The exact details of 
this mechanism do not concern us here. We simply 
note that something of this kind seems to be nec- 
essary anyway for traditional problems of quantifier 
scope ambiguity. Since we will, for instance, need 
something like this for obtaining the de re/de ditto 
readings of 
(13) John wants to catch a unicorn. 
we will assume that we will be able to rely on it for 
dealing with the relation between (11) and (12) as 
well, We end the current discussion by noting that 
our analyses of bare plurals and habituals do st least 
provide a sensible formal paraphrase of (1): 
\[matriz -=3A V B member(B, A) 
eat(n) 
A agent(B, C) 
^ VD ~bjea(.. D) 
^ IAI > 1, 
was,,m~osit~,,s = {,(C, VE mer,~,-(E, C) .,*me(E, 
nu*rU) 
^ ICI = 1)}\] 
This analysis of (I) says that there are eating events 
whose agent is Mary and all of whose objects are 
peaches. This seems to be about as much as you 
can reasonably expect to get from (1) without some 
extra contextua! information. 
5 Conclusions 
We have argued that the semantics of bare plurals 
can be captured without any extension to the formal 
underpinning of our semantic framework. The essen- 
tial points were that 0) we separated out the effects 
of the habitual aspect and of the bare plural; (it) we 
assume that the fillers for thematic roles are always 
sets of items, with singular NPs denoting singleton 
sets. This enables us to avoid postulating a system- 
atic polymorphism for verb semantics t with one inter- 
pretation in terms of individuals for cases where some 
argument is supplied by a singular NP and another in 
terms of sets of individuals for cases where the same 
argument is supplied by a plural NP; and (iii) we 
used an event-oriented treatment of verb semantics 
(see for instance Davidson \[1980\]). It is worth noting 
that Krit~ \[19901 and Pulman \[1991\] have also devel- 
oped treatments of complex quantificstional phenom- 
ena on the basis of this kind of treatment of verbs. 
The realisation that verbs can denote sets of events 
in the same way that NPs can denote sets of indi- 
viduals, and that you can quantify over these as well 
over the individuals and sets of individuals denoted 
by NPs, seems to provide n great deal of flexibility 
without increasing your ontological commitments. 
The analyses of bare plurals and habituals dis- 
cussed above have been implemented in u version of 
the system described in \[Ramsay 1990a\]. This sys- 
tem includes a left-corner chart parser, lexical en- 
tries containing subcategorisation frames, disjunctive 
unification of the kind described in \[Ramsay 1990b\], 
ACTES DE COLING-92, NANaT.S, 23-28 bOUT 1992 2 3 0 PROC. OF COLING-92, NANTES, AUG. 23-28, 1992 
etc., etc., etc. All of the example semantic anal- 
yses were derived by this system. I would in fact 
say that unless you have a working implementation 
of your grammar and semantics, including automatic 
/f-reduction of applications of A-abntractioas t then 
the sheer complexity of the semantic formulae that 
arise will overwhelm you. Deciding, for instance, 
that using A(A,-~B VC' member(C',B) -4 D.C A 
IBI = 1 A A.A(E,E.B)) for the matrix of a led 
to more satisfactory analyses of indefinite NPs than 
X(A,A.X(E, 3B VC memher(C,B)-~ D.C A IBI= 
1 A (E.B))) would have been a great deal more te- 
dious than it was if I had not had a system which 
would show me the consequences of the two choices 
in n variety of settings. 
AcrEs DE COL1NG-92. NAm'rs. 23-28 Aot~r 1992 2 3 1 PROC. OF COLING-92, NAtCrEs, AUG. 23-28, 1992 

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