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<Paper uid="C92-1037">
  <Title>Generic NPs and Habitual VPs</Title>
  <Section position="3" start_page="0" end_page="0" type="intro">
    <SectionTitle>
3 NP semantics
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    <Paragraph position="0"> We follow the tradition first established by Russell, and made concrete by Montague, of treating NP semantics as generalised quantificrs, i.e. as expressions which provide the qnantificational information required for turning some proposition schema into a proposition. Montague, for instance, regards 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 ...</Paragraph>
    <Paragraph position="1"> 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 (entities of type e I to truth values (entities of type t) and return a truth value. We propose to generalise 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)).</Paragraph>
    <Paragraph position="2"> Thus we propose that the matrix for every student 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.</Paragraph>
    <Paragraph position="3"> The only difference is that we are quantifying over sets of students (i.e. over sets C satsifying the requirement 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 quantitier. We will refer to such objects as genercllsed ~ quantifiers, to emphasise the extra level of abstraction. null We obtain such representations of NP semantics in the usual way, by taking the meanings of determiners 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 variable, 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 extra control over the relative scope of quantifiers that makes us prefer generalised ~ quantifiers to ordinary gencralised quantifiers.</Paragraph>
    <Paragraph position="4"> 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 frequently, 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 happens 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.</Paragraph>
    <Paragraph position="5"> 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 sentences: null  (4) Marl/ is eaZingpeaches.</Paragraph>
    <Paragraph position="6"> (5) John is driving fast cars.</Paragraph>
    <Paragraph position="7"> (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.</Paragraph>
    <Paragraph position="8"> (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.</Paragraph>
    <Paragraph position="9"> 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.</Paragraph>
    <Paragraph position="10"> which says what Mary is doing is hunting for something, and that what she is looking for is a house.</Paragraph>
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