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DP-SEMANTICSARNIM VON STECHOW, WIEN JANUARY 2009

1. Remarks to the Course.........................................................................................................1

2. LF.........................................................................................................................................2

3. DPs.......................................................................................................................................3

4. Definite Article....................................................................................................................5

5. Quantifiers in Object Position – QR!...................................................................................6

6. Other Semantics for Indefinites: Choice Functions.............................................................7

6.1. The (Abusch, 1994) – challenge:..................................................................................8

7. Possessives.........................................................................................................................10

8. Structure of the NP............................................................................................................11

8.1. PRO-subject and Quantifiers in NPs..........................................................................11

8.2. Relative Clauses..........................................................................................................12

9. Plural..................................................................................................................................13

9.1. Mereology as a unified ontology of mass and count nouns........................................13

9.2. Plural Predication........................................................................................................16

9.3. Co-distributive Readings............................................................................................19

9.4. Co-distributive Readings............................................................................................20

9.5. Contextually Restricted Relational Plural...................................................................21

9.6. Distributors as verbal plurals......................................................................................22

9.7. Notes on the literature.................................................................................................23

10. Mass Nouns and Classifiers.............................................................................................23

10.1. Measure Nouns and Classifiers.................................................................................23

10.2. Possessors in Chinese...............................................................................................25

11. Questions to (Keenan, 1996)...........................................................................................27

12. Exercises..........................................................................................................................27

13. Literature..........................................................................................................................28

1. REMARKS TO THE COURSE

The course presupposes (Heim and Kratzer, 1998) [H&K]. It repeats some of the stuff and introduces further material. One particular aim of the course is to give some training in model-theoretical computation.

We will deal with the following topics.Semantics of determiners jeder, ein, kein, der.

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Different treatments of indefinites: choice functions, Skolem functionsIntegration of DPs into the syntax (QR)Logic properties of determiners (papers by Keenan)Plural DPs (lecture notes by Heim)Negative indefinites (Penka)Perhaps: mindestens n, höchstens n, genau nPerhaps: comparative quantifiers (Hackl)

Zeugnis: To get a Zeugnis you have to solve a certain number of the exercises.

2. LFThe language L follows H&K. The only difference is that assignments are total functions here.

The types of L are: e (entities), t (truth-values). The functional types are generated by the following rule: if a and b are types, then (ab) is a type. Outermost brackets are usually omitted.

The syntax of L is based on a lexicon of expressions belonging to some type in the style of the examples already given. Furthermore, we have infinitely many variables for any type (often written as numbers with type indices or as traces with numbers). Finally we have the following syntactic rules:

() Syntax of L1. If is a lexical entry or a variable of type a, them is an expression of type a.

(“Lexicon”)2. If is an expression of type (ab) and is an expression of type a, then [ ] is an

expression of type b. (“functor-argument”)3. If and are expressions of type (at), then [] is an expression of type (at).

(“predicate modification”)4. If is an expression of type a and x is a variable of type b, then [x] is an

expression of type (ba). (“abstraction”)

The interpretation of the language is based on a model M = (E, {0,1}, F), where E is the set of entities, {0,1} is the set of truth-values. F is a function that interprets the lexicon with appropriate meanings. To do this, we need a system of semantic domains D a for each type a. We define: De = E, Dt = {0,1}, and D(ab) = the (possibly partial) functions from Da into Db. A condition for the interpretation of the lexicon is that F() Da if is a lexicon entry of type a.

We now define the function [[ . ]],M,g that interprets each expression of L. The function

depends on the model M and a variable assignment g.

() Interpretation of L

1. a. If is a lexical entry of type a, then [[ ]] M,g = F(). (“Lexicon”)

b. If x is a variable of type a, then [[ x ]] M,g = g(x) (“Variable”)

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2. If is of type ab and is of type a, then [[ [ ]]] M,g = [[ ]] M,g ([[ ]] M,g)(“Functional Application”, FA)

3. If and are of type at, then [[ [] ]] M,g = xa.[[ ]] M,g (x) & [[ ]] M,g (x).(“Predicate Modification”, PM)

4. If x is a variable of type a and a is an expression of type b, then [[ [x] ]] M,g = u Da.[[ ]] M,g[x/u]

.

(“Abstraction”, )

g[x/u] is defined like g with the (possible) exception that g[x/u](x) = u. As a special case of PM we will assume that and are of type t. Then [[ [] ]] M,g = 1 iff [[ ]] M,g = 1 = [[ ]] M,g.

is true in M with respect to the assignment g iff [[ ]] M,g = 1. is false in M with respect to g iff [[ ]] M,g = 0. Formulas that are undefined will denote #.

3. DPS The structure of DPs:

()

(et,t)DP

(et)(et,t)Det

einjederkeinder

etNP

Studentkluger Student

Student aus GrazStudent, den Josefine kennt

NPs denote sets, Dets (determiners) denote relations between sets. DPs are called Generalized Quantifiers.

The first argument of a Det is provided by the NP, the second by the VP.

Standard semantics for ein, jeder, kein.

() F(ein) = Pet.Qet.(x De) P(x) = 1 & Q(x) = 1 (or: P Q ≠ )F(jeder) = Pet.Qet.(x De) P(x) = 1 Q(x) = 1 (or: P Q)F(kein) = Pet.Qet.(x De) P(x) = 1 & Q(x) = 1

This notation is not fully explicit. Recall that in a typed language formulas of type t denote truth values and functions of type et, (e(et)) etc. are schönfinkelized. So determiner meanings have to be written more accurately as:

() F(ein) = Pet.Qet.that t {0,1}:( t = 1, if (x De) P(x) = 1 & Q(x) = 1) & (t = 0, (x De) P(x) = 1 & Q(x) = 1))

The notations in () assume the following convention in (Heim and Kratzer, 1998) [= H&K]:

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() Suppose is of type t. Then [[ xa ]] g = that P Dat:(u Da)[ f(u) = that t {0,1}: (t = 1 , iff [[ ]] g[x/u] = 1) & (t = 0 , iff [[ ]] g[x/u] = 0)

Determiners are logical constants: every model interprets them alike.

() Jeder Student arbeitet.

() Ein Student stöhnt.

() Kein Student schläft.

The following model M makes these sentences true.

M = (E, {0,1}, F)

E = {s1,s2}

F(arbeitetet) = {<s1,1>, <s2,1>} = F(Studentet)

F(stöhnt) = {<s1,1>, <s2,0>}

F(schläft) = {<s1,0>, <s2,0>}

We show that [[ Kein Student schläft ]] M = 1

This is the case

iff [[ Kein Student schläft ]] M = 1

iff [[ Kein Student]] M ([[ schläft ]] M) = 1 FA

iff (([[ Kein ]] ([[ Student]] M)) ([[ schläft ]] M) = 1 FA

iff ([Pet.Qet.(x De) P(x) = 1 & Q(x) = 1] ([[ Student]] M)) ([[ schläft ]] M) = 1 Lexicon

iff Qet.(x De) [[ Student]] M(x) = 1 & Q(x) = 1]([[ schläft ]] M) = 1 -conversion

iff (x De) [[ Student]] M(x) = 1 & [[ schläft ]] M (x) = 1 -conversion

iff (x De) {<s1,1>, <s2,1>}(x) = 1 & {<s1,0>, <s2,0>}(x) = 1 Lexicon 2

Suppose there is an x satisfying the two conjuncts:

Case 1: x = s1

{<s1,1>, <s2,1>}(s1) = 1 FA

i.e. the first conjunct is 1, because 1 = 1 is true

{<s1,0>, <s2,0>}(s1) = 0 FA

i.e. the second conjunct is 0, because 0 = 1 is false

Case 2: x = s2

{<s1,1>, <s2,1>}(s2) = 1 FA

i.e. the first conjunct is 1, because 1 = 1 is true

{<s1,0>, <s2,0>}(s2) = 0 FA

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i.e. the second conjunct is 0, because 0 = 1 is false

For both cases we obtain 0 for the conjunct. Therefore there is no x that makes the two conjuncts true.

Recall the definition of FA, when a function f is a set of ordered pairs:

f(x) = that y such that <x,y> F.

Homework 1 (see below).

4. DEFINITE ARTICLE

There are two analyses of the definite article. One is due to (Russell, 1905). Russell interprets the as a determiner that holds of two sets P and Q iff x[P(x) & Q(x) & y[P(y) x = y]]. The other semantics is attributed to (Frege, 1891). He says that the definite article takes a unit set as argument and gives the individual in that set as value. We assume this semantics. The best article about the definite article that is known to me is (Heim, 1991).

We only treat the singular. The plural is introduced later.

() Definite Articleder,die,das, type (et)eF(der) = Pet: | P | = 1. the unique x such that P(x) = 1.

The condition between : and . is a presupposition. If the condition is not met in a model, the function is undefined. Undefined functions are represented as giving always # as value. | P | is the cardinality of P, i.e. P has exactly one pair whose second component is 1 in its extension.

() Jedes Mädchen lacht.

() #Das Mädchen lacht.

() Der Hund bellt.

Here is a model M that makes () and () true and leaves () undefined.

E = {m1,m2, h}

F(Mädchen) = {<m1,1>,<m2,1>, <h,0>} = F(lacht)

F(Hund) = {<m1,0>,<m2,0>, <h,1>} = F(bellt)

We compute the truth-value of ().

[[ der Hund bellt ]]

= [[ bellt ]] ([[der ]] ([[ Hund ]] )) FA, 2

We now check whether [[der ]] is defined for [[ Hund ]] = {<m1,0>,<m2,0>, <h,1>}. Yes, because there is exactly on individual in this set, viz. h. Therefore,

[Pet: | P | = 1. the unique x such that P(x) = 1]( {<m1,0>,<m2,0>, <h,1>})

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= the unique x such that {<m1,0>,<m2,0>, <h,1>} (x) = 1

= h

Therefore

[[ bellt ]] ([[der ]] ([[ Hund ]] )) = {<m1,0>,<m2,0>, <h,1>}(h)

= 1

() is undefined in M for the following reason. F(Mädchen) contains two girls. Therefore F(das) maps [[ Mädchen ]] to #. We assume that when a function f is applied to #, f(#) = #.

[[ lacht ]] (#) = #, and this counts as undefined.

5. QUANTIFIERS IN OBJECT POSITION – QR!Quantifiers in object positions must be QR-ed for type reasons. This might create scope ambiguities.

( ) Einen Politiker kennt heute jeder. (Nämlich Obama)(x) Politician(x) & (y)[Person(x) knows(y)(x)]

The plausible reading is the one where the object has wide scope with respect to the subject. This is the specific reading.

() Ein Handy hat heute jedermann.a. (x) Cellular(x) & (y)[Person(x) has(y)(x)]b. (y)[Person(x) (x) Cellular(x) & has(y)(x)]

This time the reading in which the object has narrow scope with respect to the subject is the plausible one because not everyone possesses the same cellular.

Derivations:

DS: Jedermann(et)t [ein Handy](et)t hate(et) Type clash!

2 x QR => [ein Handy](et)t y [Jedermann(et)t x [VP tx ty hate(et) ]] LF1

or

=> Jedermann(et)t x [[ein Handy](et)t y [VP tx ty hate(et) ]] LF2

The scope of a DP is its c-command domain. Jedermann has wide scope with respect to ein Handy in LF1, narrow scope with respect to jedermann in LF2.

The following model M makes LF1 false and LF2 true.

E = {p1, p2, h1, h2}

F(Person) = {<p1,1>,<p2,1>,…} =: Person

….. = all the other combinations end in 0

F(Handy) = {<h1,1>, <h2,1>,…} =: Cellular

F(hat) = {<h1, <p1,1>>, <h2, <p2,1>>,…..} =: has6


F(jedermann) = P.(x)[Person(x) = 1 P(x) = 1]

We show that LF1 is false in M:

LF1 is false iff [(x) Cellular(x) = 1 & (y)[Person(x) = 1 has(y)(x) = 1] = 0

Suppose [(x) Cellular(x) = 1 & (y)[Person(x) = 1 has(y)(x) = 1] = 1

Case1: x = h1.

Choose y = p2.

Since <h1,<p2,1>> is not in has, the second conjunct is false for this choice.

Case1: x = h2

Choose y = p1.

Since <h2,<p1,1>> is not in has, the second conjunct is false for this choice.

Therefore the entire condition is 0.

6. OTHER SEMANTICS FOR INDEFINITES: CHOICE FUNCTIONS

Literature : (Engdahl, 1980), (Heim, 1994b), (Reinhart, 1997), (Winter, 1997), (Kratzer, 1994), (von Stechow, 2000).

Choice functions have been used in the literature to get rid of long LF-movement of indefinites. This works only for very special cases. In most other cases we either have to move the indefinite article or an existential quantifier binding the choice function variable contained in the indefinite article.

() Let f be in D(et)e. f is a choice function – ch(f) – iff for every Pet: P(f(P)) = 1.

Here is the formalisation of a simple sentence:

() Ein Hund bellt.

(f)[ch(f) & bellt(f(Hund))]

Let the indefinite article be an existential quantifier over choice function.

() Choice semantics for indefinite article.ein, type ((et)e,t)tF(ein) = P((et)e,t).(f) ch(f) & P(f)

DS: [ein((et)e,t)t Hund] bellt type clash!

QR => ein((et)e,t)t [((et)e,t) f [t[f(et)e Hund]e bellt]] type clash resolved!

We have to move the indefinite article (or to index the article ein with a choice variable f and bind f via an invisible existential quantifier that means the same as ein. This comes to the same:

() Alternative representation:

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((et)e,t)t [((et)e,t) f [t[einf(et)e Hund]e bellt]]

Representing scope ambiguities:

() Ein Handy hat jedermann.a. ein f jedermann f(Handy) hat

(f) ch(f) & (x)[Person(x) has(f(cellular))(x)]= (y) cellular(y) & (x)[Person(x) has(y)(x)]

b. jedermann x ein f [x f(Handy) hat](x)[Person(x) (f) ch(f) & has(f(cellular))(x)]= (x)[Person(x) (y) cellular(y) & has(y)(x)]

If we want to represent scope ambiguities, we cannot leave f free, thus avoiding article movement (or obligatory existential binding of f).

The model M of the last section makes (b) true and (a) false:

E = {p1, p2, h1, h2}

F(Person) = {<p1,1>,<p2,1>,…} = Person

….. = all the other combinations end in 0

F(Handy) = {<h1,1>, <h2,1>,…} = Cellular

F(hat) = {<h1, <p1,1>>, <h2, <p2,1>>,…..} = has

F(jedermann) = P.(x)[Person(x) = 1 P(x) = 1]

Consider the following choice functions:

F = {f1,f2} f1 = {<Cellular,h1>, ….} f2 = {<Cellular,h2>,….}

The …. mean that we are not interested in the values of the choice functions for other predicates.

We show that (20a) is false. If it were true, the following condition were true:

(f F)(x)[Person(x) has(f(Cellular))(x)]

Case 1: f = f1

Choose x = p2.

We calculate: 1 0, and this is false.

Case 2: f = f2

Choose x = p1

This falsifies the second case.

So the condition is falsified.

6.1. The (Abusch, 1994) – challenge:

( ) Every professor rewarded every student who read a book he had recommended.

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a. (x)[[P(x) & (y)[S(y) & (z)[B(z) & x recommends z & y reads z]]] x rewards y]

b. (x)[P(x) & (z)[B(z) & x recommends z & (y)[[S(y) & y reads z] x rewards y]]]

The intermediate reading (b) requires extraction out of a relative clause! Island violation. This is Abusch’s challenge.

() every prof x [a book x recommends] z every stud who reads z y x rewards y

|_____________________|

island violation

Classical restriction for scope of indefinites: Either local scope or widest scope.

Indefinites scope freely?

(Kratzer, 1994): The intermediate reading requires a bound variable in indefinite.

() Every professor rewarded every student who read a book professor K. had recommended.

≠ (x)[P(x) & (z)[B(z) & K recomm z & (y)[[S(y) & y reads z] x reward y]]]

Abusch’s reading (b) would not be interesting if it did entail (a). We could then argue that (b) is a special instance of (a). But (b) is weaker, i.e. (b) can be true while (a) is false.

A model M that makes (b) true and (a) false

E = {p1,p2,s1,s2,b1,b2}

F(professor) = {<p1,1>,<p2,1>,…}

…. : the other combinations end in 0

F(student) = {<s1,1>, <s2,1>,…}

F(book) = {<b1,1>,<b2,1>,…}

F(recommend) = {<b1,<p1,1>>, <b2, <p1,1>>,<b1,<p2,1>>,<b2,<p2,1>>,…}

F(read) = {<b1,<s1,1>>, <b2,<s2,1>>,…..}

F(reward) = {<s1,<p1,1>>, <s2,<p2,1>>}

Kratzer’s solution: choice functions are free variables in the position of an indefinite article. Their value is determined by the assignment (= context).

() every professor x every student who reads af (book x recommends) z x rewards z(x)[P(x) (z)[S(z) & y reads f(book that x recommends) x rewards z]], ch(f)

A potential problem for Kratzer: Not every indefinite article can be a choice function (observation by Yoad Winter):

() Every professor invited a colleague from his university

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≠ a. (x)[P(x) x invite f(colleague from x’s university)]= b. (x)[P(x) (y) y colleague from x’s university & x invite y]= c. (x)[P(x) f [ch(f) & x invite f(colleague from x’s university)]]

Suppose the professors are from the same university, i.e., x = M.I.T. Then f(colleague from x’s university) = f(colleague from M.I.T). This is a particular professor, say Irene Heim. This is the classical wide scope reading for the indefinite. The narrow scope reading requires an existential quantifier in the scope of the universal quantifier.

(Kratzer, 1994): The indefinite article is ambiguous between a free choice function and the classical determiner. We can choose a choice function if the DP contains a pronoun to be bound at LF.

If we don’t accept the analysis in terms of free choice functions, we have to stipulate the following:

() An indefinite DP containing a variable may scope as long as the variable is bound. An indefinite DP without a variable has local scope or widest scope.

7. POSSESSIVES

() Jeder Deutsche liebt sein Auto.= “das Auto von ihm”

() Jeder Italiener liebt seine Mutter.= “die Mutter von ihm”

(We don’t say die Mutter von ihm, but semantically it comes to this.)

() a. Der Martin putzt dem Max sein Auto.b. Der Martin putzt dem Max seiner Mutter ihr Auto.

( ) a. Martin cleaned Mary’s car.b. Martin cleaned Mary’s mother’s car.

The possessive has to distinguish two cases: (a) the modified NP is of type et, (b) the NP is of type e(et).

() Possessive pronounsa. sein, type e(et,e)

F(sein) = x.Pet: | y.P(y) & x possesses y | = 1. the unique y.P(y) & x possesses y

b. sein, type e(e(et),e)F(sein) = x.Re(et): | R(x) | = 1. the unique y.R(x)(y) = 1

The first argument of sein is a variable that can be left free or that can be bound. The first variant of the possessive introduces a possessor as internal object. The second variant knows of no possessor; its role is taken by the object of the relational noun.

() [[ [DP [D sein5 ] Auto] ]] g = ([[ sein ]] g([[ 5 ]] g)) ([[ Auto ]] g)= the unique x.[[ Auto ]] (x) = 1 & g(5) possesses x

( ) [[ seine7 Mutter ]] g = ([[ seine ]] g([[ 7 ]] g)) ([[ Mutter ]] g)

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= the unique x.[[ Mutter ]] (g(7))(x) = 1

Homework: Give the LFs for () and () such that the possive variables are bound.

() [[ [Max seine(et,e)] Auto ]] = ([[ sein ]] ([[ Max ]] )) ([[ Auto ]] )= the unique x.[[ Auto ]] (x) = 1 & Max possesses x

() [[ [[Max seiner] Mutter ihr] Auto ]] =

the unique x.Car(x) & Possess(x)(the unique y.Mother(Max)(y))

It should be noted that the possessive pronoun is not subjected to the binding theory: the pronoun can be bound in a local domain (A-configuration) or it may remain free in that domain:

() a. Jeder5 bewundert sein5 Auto= (x) x admires x’s car

b. Jeder bewundert sein5 Auto= (x) x admires Martin’s car

mein, dein have a deictic interpretation.

() meina. type (et,e)

Fc(mein) = P: | y.P(y) & sc possesses y | = 1. the unique y.P(y) & sc possesses yb. type (e(et),e)

Fc(mein) = Re(et): | R(sc) | = 1. the unique y.R(sc)(y) = 1sc is the speaker at context c.

8. STRUCTURE OF THE NP8.1. PRO-subject and Quantifiers in NPs

The subject argument of an NP is never overt. At D-structure, it may be filled with PRO, a semantically empty pronoun that must be QR-ed for type reasons. This is useful for the analysis of quantifiers in the NP.

() Every owner of a Macintosh hates Windows. (Quantifying into NP)

Note first that the N-object a Macintosh must have narrow scope with respect to the determiner every. If QR gave the quantifier wide scope with respect to every, we would obtain a reading that is at best marginal, viz.

() ? (x)[Mac(x) & (y)[y is an owner of x y hates Windows]]

The reading we are after is:

() (y)[(x)[Mac(x) & y is an owner of x] y hates Windows]

Here is the SS of the subject DP with PRO as the NP subject.

() [DP every [NP PRO [N’ ownere(et) [PP of [DP((et)t) a Mac]]]]] (SS)

Ignoring the intervening preposition of, we encounter the familial type clash between the head noun owner and the object a Mac.

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DP

Det et tevery

NP

NPPRO1

NP

DPet t

a MacNP

2 NPet1

N'

Ne etowner PP

Pof

et 2

The structure is obtained by QR-ing a Mac first. In the next step PRO is QR-ed and has wide scope with respect to a Mac. Both movements leave a trace of type e. The next step consists in applying the Principle of Full Interpretation (FI)1: (a) we delete PRO, leaving its index as 1; (b) we delete the vacuous preposition of; we delete the syntactic categories and project the types according to the syntax rules of L. This gives us a fully interpretable generalised quantifier:

() [every [1[a Mac [2 [t1 [owner t2]]]]]]

I leave it to the reader to add the types. We interpret owner exactly as it were the transitive verb owns. The reader may convince himself that this structure expresses the generalised quantifier Pet.(y)[(x)[Mac(x) & y is an owner of x] P(y)].

Homework 5 (see below)

8.2. Relative ClausesThere is a long tradition among semanticist to interpret moved relative pronouns as -operators that bind a variable in the base position of the pronoun. H&K have proposed a theory that can explain the construction. We assume that relative pronouns, abbreviated as WHl, are semantically vacuous, i.e. they have no meaning and no type. When we move a relative pronoun, it leaves a co-indexed trace of type e. By FI we delete the pronoun at LF and are left with the adjoined index, the wanted -operator. Consider the SS of the relative clause in the following example:

() Bill is a boy [CP WH4 C Mary likes t4]

FI gives us the LF [et 4 [t Marye [et likese(et) t4]]], which expresses the property of being liked by Mary. We combine it with boy by PM. The final LF will involve QR of the object. (is expresses identity). The rule that moves WH, i.e. who, to [Spec,CP] is sometimes called operator movement.1 The Principle is due to Chomsky. It says that the representations at LF contain only

interpretable material (similar for PF).12


The relative clause is combined with the head noun by Predicate Modification.

9. PLURAL

Sentences to be analysed:

() Mädchen küssten Jungen.

() Die Mädchen küssten die Jungen.

() Zwei Mädchen küssten zwei Jungen.

() Die zwei Mädchen küssten die zwei Jungen.

etc. The semantic plural consists of cumulation operators PL for nouns and * for verbs that cumulate predicates and, more generally, n-place relations. For the LF construal it is important to know that plural operators can be inserted in the syntax at the LF branch if the semantics requires that. The construction of LFs that represent so-called co-distributive readings requires the restriction of the *-operator by a cover variable C and the unconventional parallel QR we have known in previous sections.

9.1. Mereology as a unified ontology of mass and count nounsWe follow (Link, 1991) and (Krifka, 1991) in providing a unified treatment of mass terms and plural terms. In order to do that, we have to say something about the ontology of the domain of individuals E: it must be closed under mereological fusion. For count nouns, each such fusion is a plurality of these things. Think of E as made of one biggest thing U and all parts of it. If we write the part-of-relation as ≤ we may define:

() The generalised domain of individualsE = {x : x ≤ U}

U may be thought as Spinoza’s nature. There might be things that have no proper parts, and those would be the absolute atoms. Most treatments of the plural assume atoms, and we seem to need them for the treatment of count nouns. The NP six boys should be true of a plurality x if x are boys and x is a plurality consisting of six atoms. Strictly speaking, this makes no sense, however. If the plurality x that makes up the six boys consisted of atoms, the particular boys should have no parts. But they have innumerably many. Consider the following sentence, for example:

() The boys scratched their noses.

Each boy has a nose as a part, legs, lungs and so on. Each nose is made up of many other parts, and this seems to be true of virtually everything language speaks about. It seems then that the notion of absolute atomicity makes no sense for the semantics of natural language. We need a notion of relative atomicity: x is a boy-atom if no proper part of x is a boy. (The proper part relation will be written as <.) Different pluralities will require different relative atoms. This makes the proper treatment of plurality somewhat tedious and might be the reason why most treatments of the plural are sloppy in this respect.

Let us assume then that there are no absolute atoms. We introduce the following 13


terminology for elements in E.

() a. x and y overlap iff they have some common part:x o y iff z[z ≤ x & z ≤ y]

b. x and y are distinct iff they do not overlap

( )Let M be a subset of E. is the fusion of the elements of M if it has all of them as parts and has no part that is distinct from each of them:

= that x D.(y M)[y ≤ x & (z)[z ≤ x & (u M)[z is distinct from u]]]

If M is the finite set {x1,…,xn}, we write M as x1+…+xn.

() Let P be a one-place predicate. a. x is a P-atom in world w iff P(x) & (y)[y < x & P(w)]b. P is quantized if P is true only of P-atoms, i.e. (x)[P(x) x is a P-atom]c. x is a P-plurality iff x is a fusion of at least two P-atoms, i.e. (M P)[|M| ≥ 2 &

x = M]. If y is a P-atom of x, it is called a member of x, written as y x.

Singular count nouns are quantized: no proper part of a boy is a boy. Mass nouns are not quantized, but divisive, every part of milk (or at least many parts of milk) is milk again. Quantized predicates allow us to form pluralities by means of a Plural Operator for nouns:

() The Plural Operator (for count nouns)[[ PL ]] = P(et). x: P is quantized. x is a P-plurality.

Let us say something on the count/mass noun distinction. We have said that count nouns are quantized and mass nouns are divisive. These properties are no part of the lexical entries. The lexical entries are as before and we assume that we know for each noun meaning whether it is quantized or divisive.

Here is a meaning for the definite article that works for singular and plural count nouns and for mass nouns likewise.

() Definite ArticleF(def(et)e) = Pet:x[P(x) & y[P(y) y ≤ x ].x[P(x) & y[P(y) y ≤ x]

As an illustration we consider the LFs for der Junge, die Jungen and die Milch.

() a. [[ der Junge ]] =: x[boy(x) & y[boy(y) y ≤ x ].x[boy(x) & y[boy(y) y ≤ x]

b. [[ die [PL Jungen] ]] = : x[x is a boy-plurality & y[y is a boy-plurality y ≤ x ].x[x is a boy plurality & y[y is a boy-plurality y ≤ x]

c. [[ die Milch ]] = : x[milk(x) & y[milk(y) y ≤ x ].x[milk(x) & y[milk(y) y ≤ x]

We can form pluralities of things in De by means of non-Boolean and:

() Non-Boolean undF(unde(ee)) = x.y. y+x

Here are some applications:

() a. [[ Anna und [die PL Jungen] ]] = the plurality that consists of Ann and the boys 14


b. [[ [die PL Jungen] [und die PL Mädchen] ]] = the plurality that consists of the boys and the girls

c. [[ die Milch und der Kaffee ]] = the fusion of the milk and the coffee

In a mereology that knows of no absolute atoms we have a problem with counting. Consider the NP sechs Jungen. This should apply to a plurality x if x is the fusion of six boys. The individual x doesn’t give us the information that it is made up of boy atoms. To recover that information, we assume that numerals take a silent classifier as their first argument, where a classifier is simply a quantized predicate. The LF of six boys could then be:

() [[ sechsC [PL Jungen]] ]] = x.x are boys & |{y | y ≤ x & C(y)}| = 6, where C = person

The classifier is a free variable whose value is determined by the context. It should be an appropriate class of individuals, e.g. the persons in the world of evaluation.

Here is the meaning of a numeral:

() A numeral (to be revised)sechs has the type (et)((et)(et)). F(six) = w.Cet.Pet.x: C is quantized & x is a C-plurality. P(x) & | {y | y ≤ x &

C(y)}| = 6

In classifier languages like Chinese or Japanese, a numeral is always accompanied by a classifier, e.g., Chin. qi- zhang- zhuo-zi ‘six flat-thing table’, Jap. inu san-biki ‘dog three animal-thing’.

This analysis is not general enough because it is not clear where the comparative could fit in:

() Mehr Mädchen als Jungen waren im Zimmer.the n s.t. n many girls were in the room > the n s.t. n many boys were in the room

I.e., the number must be an argument of an abstract adjective MANY/VIELE

() VIEL, type (et)(d,et)F(VIEL) = Cet.d.x: quantized(C) & x is a C-plurality.C(x) & | {y | y ≤ x & C(x)}| =

d

Numerals can have their ordinary meaning:

() zwei, type dF(zwei) = 2

( ) die zwei Mädchen[[ die [zwei C VIEL] [Pl Mädchen] ]] g

= the x.x is a human-plurality & |{y | y ≤ x & y is a human being }| = 2 & x is a girl-plurality

& (z)[ (z is a human-plurality & |{y | y ≤ z & y is a human being }| = 2 & z is a girl-plurality) z ≤ x]

g(C) = human being

Viola’s Question :

“Wie macht man die Jungen und Mädchen, oder Jungen und Mädchen ?”15


Here is a proposal.

() DS: [DP die [NP PRO [N’ BE [ PL Jungen unde(et) PL Mädchen] ] ]]

() F(BE) = x.y.y = x

() F((et)(et,t)) = F(ein)

The two plural DPs and PRO have to be QR-ed for type reasons. This gives the following LF:

( ) die Jungen und Mädchen[DP die x PL Jungen y PL Mädchen z [NP xe [N’ BE [ye unde(et) ze] ] ]

= the biggest group x s.t. x is the fusion of a plurality y of boys and a plurality z of girls

() Jungen und Mädchen tanzten mit einander.

The DP has two analyses:

() PL Jungen 1 PL Mädchen 2 [t1 und t2] tanzten mit einander.

Here the two indefinite DPs are QR-ed out of the subject. The other analysis starts from the more complicated DS we have just discussed.

() [DP x PL Ju. y PL Mä. z [NP xe [N’ BE [ye unde(et) ze] ] ] tanzten mit e.a.

9.2. Plural PredicationLet us take up plural predication next. Predicates can be classified according to the following criteria.

1. Purely distributive predicates: if a group has such a predicate, every member of the group has it. Examples: laugh, sneeze, frown.

2. Purely collective predicates: only groups can have them; a single individual cannot have such a predicate. Examples: gather, hate each other.

3. Mixed predicates: an individual can have them, but if the predicate applies to a group, its members cooperate in a particular way. Examples: eat the cake, lift the piano, write a paper.

Here are lexical entries for some of these predicates:

() A purely distributive predicateF(laugh) = x: x is a person. x laughs.

Since “person” is a quantized predicate, laugh is only defined for singular persons. I we want to apply the verb to a plurality like the boys, we have to pluralize the predicate in a way that the plurality laughs if each member of it does. The plural operator * will do the job.

() A purely collective predicateF(gather) = x: x is a plurality of animal-atoms in w. x gathers.“animal” is taken in the general sense of living being.

“the plurality x gather” means that there is a place to which each member of x goes.

() A mixed predicate16


F(eat the cake) = x. Each member of x eats a part of the cake and each part of the cake is eaten be a member of x. (The context has to make clear which the relevant members of x are.)

Given lexical entries of this sort we can analyse the following sentences:

() a. A boy laughed (singular subject, distributive predicate)b. The PL students gathered (plural subject, collective predicate)c. Ede/the PL boys ate the cake (singular or plural subject, mixed predicate)

None of the predicates contains a semantic plural. These examples make clear that the plural of the predicate is not licensed by a Plural Operator modifying the predicate but by one contained in the subject. Hence we assume the following condition:

() The morphological plural of the verb is licensed by a PL-Operator contained in the subject.

We cannot analyse analyze the following sentence yet:

() a. The boys laughed b. The boys and the girls met (separately)c. The boys ate a cake (each)

Each of these sentences has a distributive reading. It would seem then that the semantic plural of the VP is a distributive operator that distributes the predicates over the relevant parts of the subject, the singular boys in the case of sentence (a), the boys and the girls in the case of (b), and the particular boys in the case of (c). Such an approach is taken in (Link, 1991) and (Schwarzschild, 1996). The following cumulation operator is such a distributor.

() The Cumulation Operator *Let be any n-place predicate (of type ent). Then * is of the same type.[[ * ]] is the smallest relation R such that [[ ]] R & (x1,…,xn,y1,…,yn)[R(x1)…(xn)

& R(y1)…(yn) R(x1+y1)…(xn+yn)]

We will assume that * expresses the semantic plural for verbs (a standard assumption) and relational nouns. Note that * is a logical symbol. We could define functors, but we would have to do this for each type of relation separately. (Sternefeld, 1998) introduces the functor * for one-place relations, ** for 2-place relations, and so on. Our star symbol stands for any of these. The type of the modified expression makes it clear which star is used in each particular case.

With the exception of (b) we can now analyse the recalcitrant plural statements just mentioned.

() Die Jungen lachen.[die PL Jungen] *lachen

() [Die PL Jungen und die PL Mädchen] *lachen.

Here is a model M that makes these true:

E = {b1,b2, g1,g2}

I simplify and write the relations as sets. Rewrite these in the Schönfinkel style!

17


F(Junge) = {b1,b2}

F(Mädchen) = {g1,g2}

F(lachen) = {b1,b2,g1,g2}

Here is the proof that () is true in M:

[[ PL Jungen ]] = {b1+b2}

[[ die PL Jungen ]] = b1+b2

[[ *lachen ]] = { b1,b2,g1,g2, b1+b2, b1+g2, b2+g1, b2+g2, b1+b2+g1, b1+b2+g2, b2+g1+g2,…,b1+b2+g1+g2}

Since b1+b2 is in [[ *lachen ]] ., [[[die PL Jungen] lachen ]] is true in M.

Convince yourself that [[ die Jungen und die Mädchen ]] = b1+b2+g1+g2So the LF in () is true in M.

() Die Mädchen küssen die Jungen.die PL Mädchen die PL Jungen **küssen= (x)[girl(x) (y)[boy(y) & kisses(x,y)]]

& (y)[boy(y) (x)[girl(x) & kisses(y,x)]]

The truth condition comes to this! They are very weak. Here is a model M that makes the sentence true:

E = {b1,b2,g1,g2,g3}

F(Junge) = {b1,b2}

F(Mädchen) = {g1,g2,g3}

F(küssen) = {<g1,b1>,<g1,b2>, <g2,b1>, <g3,b1>}

[[ **küssen ]] = F(küssen) {<g1,b1+b2>, <g1+g2,b1>, <g1+g3,b1>, <g2+g3,b1>, <g1+g2+g3,b1>, <g1+g2,b1+b2>, <g1+g2+g3,b1+b2>}

[[die PL Mädchen ]] = g1+g2+g3

[[die PL Jungen ]] = b1 + b2

The pair <g1+g2+g3,b1+b2> is in [[ **küssen ]] . Therefore the LF is true in M.


The following sentence has been brought up by (Scha, 1984). It shows that without the *-operator (or an appropriate distributor) it is hopeless to obtain a compositional semantics that respects the syntax:

() The sides of A are parallel to the sides of B.[the sides of A] [the sides of B] **parallel

Assume that A and B are rectangles. Suppose that sides of A and sides of B denote the sets {a1, a2, a3, a4} and {b1, b2, b3, b4}, respectively; parallel is the set {<a1,b1>,<a1,b3>, <a3,b1>, <a3,b3>, <a2, b2>, <a2, b4>, <a4, b2>, <a4, b4>,…}. Hence *parallel certainly

18


contains the pair <a1+a2+a3+a4, b1+b2+b3+b4> consisting of the sides of A and those of B.

() Mädchen küssten die Jungen. PL Mädchen die PL Jungen **küssen

F(küssen) = {<g1,b1>, <g2,b1>,<g2,b2>}

g3 doesn’t kiss any boy, but the sentence is true.

() Die Jungen küssten Mädchen. PL Mädchen y[die PL Jungen [y **küssen]]

F(küssen) = {<b1,g1>, <b2,g2>}

g3 is not kissed by any boy.

() Die Jungen aßen einen Kucheneinen Kuchen y[die PL Jungen y **essen]

The following model makes the LF true.

E = {b1,b2,k1,k2,p1,p2}

F(Junge) = {b1,b2}

F(Kuchen) = {k1,k2} with k1 = p1+p2 („pieces“)

F(essen) = {<b1,p1>,<b2,p2>}

[[y[die PL Jungen y **essen] ]] = {p1+p2} = {k1}

[[einen Kuchen ]] = P.(x)[x {k1,k2} & x P]

[[ () ]] = 1 iff (x)[x {k1,k2} & x {k1}]

This is true.9.3. Co-distributive Readings

So far the cumulation operator applies to lexical entries. So pluralization might be a lexical operation. In fact this has been claimed; (Kratzer, 2005), (Winter, 2000). The following eamples show that we need cumulation in the syntax.

() Anna und Bert schreiben ein Papier.

() Anna und Bert schreiben zwei Papiere

The two sentences can be used to describe the following scenario:

F(schreiben) = {<a,p1>, <b,p2>}

F(Papier) = {p1,p2}

F(Anna) = a, F(Bert) = b

The following LFs are true in this scenario. They formalise the sentences.

() A und B *x. ein Papier y. x y schreiben19


() zweiC Papiere y [A und B y ** schreiben]

g(C) = {p1,p2}.

Co-distributive Readings)/() requires cumulation in the syntax, i.e., the insertion of * after QR.

[[ x. ein Papier y. x y schreiben ]] = {a,b}

[[ *x. ein Papier y. x y schreiben ]] = {a,b,a+b}

[[ A und B ]] = a+b ({a,b,a+b})

So LF () is true. Next, consider ().

[[ **schreiben ]] = {<a,p1>, <b,p2>, <a+b,p1+p2>}[[y [A und B y ** schreiben] ]] = {p1+p2}[[ zweiC Papiere ]] = P.(x)(x = p1+p2 & P(x)[[ zweiC Papiere y [A und B y ** schreiben] ]] = 1 iff p1+p2 {p1+p2}.

(Schein, 1993) discusses sentence of the following type:

() Die Jungen schenken den Mädchen Blumen.

We have two boys and two girls. b1 gives g1 the rose (f1), b2 gives g2 the carnation (f2). Schein holds the theory that these sentences motivate an event semantics with complicated mechanisms (“essential separation”). Actually, his sentences are much more complicated. We discuss a sentence due to (Beck and Sauerland, 2000), which makes the same point.

() Die Jungen schenken den Mädchen eine Blume.

Following (Beck and Sauerland, 2000), there is an account of these sentence with the cumulation operator, provided we can insert * in the syntax („counter cyclically“), wherever the operator makes sense.

If we allow to insert the *-operator wherever it makes sense, we can generate many LFs for a plural sentence, some of which are equivalent.

() die PL Jungen den PL Mädchen **yx[eine Blume z[x schenken y z]]

There are two unconventional steps in the generation:

1. We first QR the subject and then the object under the subject. This generates the (singular) relation yx[…].

2. We insert the operator ** after QR. This is the countercyclic adjunction of the modifier **.Here is a model that makes the sentence true:

F(Blume) = {f1,f2}

F(Junge) = {b1,b2}

F(Mädchen) = {g1,g2}

F(schenken) = {<b1,g1,f1>, <b2,g2,f2>}

20


[[ yx[eine Blume z[x schenken y z]] ]] = {<b1,g1>, <b2,g2>}

[[ **yx[eine Blume z[x schenken y z]] ]] = {<b1,g1>, <b2,g2> , <b1+b2,g1+g2>}

9.4. Contextually Restricted Relational Plural

() The sides of the bookcase are parallel to the walls. (Heim)

The LF is true in the first scenario but not in the second:

We call the inner walls b1, b2, b3 and the outer walls nearest to them w1, w2, w3.This is so because the cover pairs each side of the bookcase with the wall fronting it. It is obvious that e.g. <b1,w1> is a member of [[ C2 parallel ]] , but <b3, w1> isn’t. For the scenario B, this is required, however. The *-operator makes () true for both scenarios. Intuitively, the sentence is wrong in the second scenario. To get this, we have to restrict the verbal plural operator *. We do this by defining distributors restricted by contextually given covers:

() Cover (mereological version)Let x be a plurality. C E is a cover of x – Cov(C,x) – iff C = x.

The definition can be generalised to n-place covers. As an example I give the definition for a pair-cover:

( ) The predicate Ce(et) covers the pair (of pluralities) (x,y) – Cov(C,x,y) – iff x = {x’ | (y’) C(y’)(x’)} and y = {y’ | (x’) C(y’)(x’)}

() The Cumulation Operator(s) *C (restricted version)Let be any n-place predicate (of type ent) and let C be a cover variable. Then *C is

of the same type.[[ *C ]] g is the smallest relation R such that [[ ]] g(C) R & (x1,…,xn,y1,…,yn)

[R(x1)…(xn) & R(y1)…(yn) R(x1+y1)…(xn+yn)], i = 1,…,n

Here is the analysis of ()

() S [*C parallel] W C = {<b1, w1>, <b2,w2>, <b3, w3>}

The following model + assignment makes scenario 1 true:

E = {b1,b2,b3,w1,w2,w3}

F(S) = b1+b2+b3

F(W) = w1+w2+w3

F(parallel) = {<b1,w1>, <b2,w2>, <b3,w3>,....}

21


... the symmetric and reflexive pairs

g(C) = {<b1,w1>, <b2,w2>, <b3,w3>}

[[ *C parallel ]] = [[ *parallel ]]

For scenario 2:


g(C) = {<b1,w1>, <b2,w2>, <b3,w3>}

[[ *C parallel ]] = **(g(C) F(parallel)) =

Since < b1+b2+b3, w1+w2+w3> is not in this set, the LF is false.

9.5. Distributors as verbal pluralsThe *-operators closes singular VPs under cumulation. In general, the singular VP is a proper subset of the stared VP. There is a method that achieves the same result, namely the distributors by (Schwarzschild, 1996).

() A two-place distributorDISTR = w.Ce(et).Re(et).x.y: Cov(C,x,y) & (x,y) C.(x’)(y’)[x’ ≤ x & y’ ≤ y

& C(y)(x) R(y)(x)]2

(The definition assumes that the fusion operator is defined for relations, an obvious extension of the definition for one place predicates. In fact, C = **C. The restriction “(x,y) C“ is necessary. Otherwise the definition is trivialised because any pair not satisfying the restriction would be in the distributed predicate.)

The LF in () can now be represented as:

() S W DISTRC parallel

We convince ourselves that DISTRC does the same as *C , it is a restricted plural operator.

Look at scenario 1:

F(S) = b1+b2+b3

F(W) = w1+w2+w3


... the symmetric and reflexive pairs

g(C) = {<b1,w1>, <b2,w2>, <b3,w3>}

[[DISTRC parallel ]] g = {<x,y> g(C) | (x’,y’)[x’ ≤ x & y’ ≤ y & <x’,y’> g(C) <x’,y’> F(parallel)]}

This set can contain only things in **g(C). First, all the pairs in g(C) are in this set. And a bit of reflection show that **g(C) [[DISTRC parallel ]] g. So this is the same predicate as **C

parallel.

2

22


For scenario 2:


g(C) = {<b1,w1>, <b2,w2>, <b3,w3>}

[[DISTRC parallel ]] may contain only things in **g(C). Since g(C) F(parallel) = , the predicate is empty as well. This is the same result we had for **C parallel.

Lexical cumulation comes for free and the distributors play the role of our relativized * C

operator.

9.6. Notes on the literatureSchwarzschild’s covers always cover the entire universe, which is not implemented in the rules given here. Schwarzschild can have pluralized predicates as total functions whereas our approach has them defined only for particular arguments. The generalized semantics for the definite article in () traces back to (Sharvy, 1980). The technique of restricting star operators or distributors by means of covers is presumably due to (Heim, 1994a). The cumulation operators are due to (Sternefeld, 1998) The material presented here follows my article (von Stechow, 2008). The best introduction into plural semantics is the unpublished paper (Heim, 1994a). A theoretical foundation of mereology and its relation to set theory is (Lewis, 1991). The first detailed formalization of plural operators and their application to the analysis is found in the work of G. Link, e.g. (Link, 1991). Link introduces a one-place cumulation operator (* and ). He discusses the examples due to (Scha, 1984), but he cannot analyze them, which is due to the fact that his theory contains no n-place cumulation. Link’s ontology assumes atoms, which makes the treatment of count nouns easy but has to assume a multiplicity of part-relations. Link makes use of cumulation in the syntax. (Krifka, 1989a, Krifka, 1989b) gives a unified treatment of mass and count nouns. Krifka introduces n-place cumulation but only at the lexical level. The distinction between count and mass nouns in terms of divisibility is due to (Quine, 1960). (Scha, 1984) has brought the attention to plural sentences with more than one quantifier that have cumulative readings. His solution does not assume a general cumulation operator. He encodes the required quantifiers into the lexical entry. For instance, the adjective parallel would have the semantics x.y.(x’ ≤ x)(y’ ≤ y)[x’ is parallel to y’] & (y’ ≤ y)(x’ ≤ x)[x’ is parallel to y’].

10. MASS NOUNS AND CLASSIFIERS

10.1. Measure Nouns and Classifiers

() a. Martin aß (die) fünf Kilo Fleisch.b. Ede trank (die) fünf Liter Bier.

() Fünf Pullover von Viola sind im Koffer.

() a. Die fünf Pullover von Martin sind im Koffer.b. Martins fünf Pullover sind im Koffer.

() [DP die/ [MP [M’ fünf [M Liter]] NPBier]]]

( ) Measure nouns

23


[[ Litern(et) ]] = n.x:x is a liquid.volume(x) = n liter

Things like ‘five liter’ are degrees of quantities of liquids. “five liter” is an equivalence class. It contains all the quantities of liquids whose volume is the same as a particular amount of water stored in a can in Paris; for the construction of degrees, see (Klein, 1980).

[[ fünf Liter ]] = x:liquid(x).vol(x) = 5 l: x[milk(x) & y[milk(y) y ≤ x ].x[milk(x) & y[milk(y) y ≤ x]

[[ fünf Liter Bier ]] = x:liquid(x).vol(x) = 5 l & beer(x)

Combined by PM.

[[ die fünf Liter Bier ]] =

: x[vol(x) = 5 l & beer(x) & y[vol(y) = 5 l & beer(y) y ≤ x ].x[vol(x) = 5 l & beer(x) & y[vol(y) = 5 l & beer(y) y ≤ x ]

= the unique amount of liquid that consists of 5 liter beer

fünf Liter is like an adjective, and semantically, beer is the head of the construction. Since case, number and gender of the DP are determined by the measure noun Liter, this one is the head in the syntax. The measure noun Liter is the analogon of a classifier.

For plural countable nouns the classifier is a variable Cl of type et that is a contextually determined set of “natural units” of the kind in question. (Krifka, 1989b) speaks of natürliche Einheiten (NE). For the noun Pullover Cl would be the set of individual sweaters.

() [[ 5 Clet ]] g = x:x is countable. card{y | y ≤ x & g(Cl)(y) = 1} = 5

To get this, we need a special composition rule or our abstract adjective VIEL/MANY:

() F(VIEL) = Cet.n.x:x is a C-plurality. card{y | y ≤ x & C(y) = 1} = 5

[[ [5 Cl VIEL] PL Pullover ]] g = x:x is a g(Cl)-plurality. | {y | y ≤ x & g(Cl)} = 5 & x is the fusion of at least 2 individual sweaters.

Here is an answer to Sarah’s question: “How do you treat Pullover von Martin?”, i.e. what is the analysis of post-nominal possessors.

() Possessive von, type e(et)F(von) = x.y.x possesses y

[[ Pullover von Martin ]] = y.sweater(y) & possess(y)(Martin)

Pullover is combined with von Martin via PM.

We pluralize the NP in the syntax!

[[ PL [Pullover von Martin] ]] = y.y is the fusion of at least two sweaters possessed by Martin

[[ [5 Cl VIEL] PL [Pullover von Martin] ]] g = y:y is a g(Cl)-plurality. | {x | x ≤ y & g(Cl)} = 5 & x is the fusion of at least 2 individual sweaters possessed by Martin

[[ die [5 Cl VIEL] PL [Pullover von Martin] ]] g = the unique y that is a fusion of five 24


individual sweaters each possessed by Martin

If the head noun is relational, we need a second meaning rule (in analogy to possessive pronouns):

() Possessive von, type e((e(et)),et)F(von) = x.Re(et).y.R(x)(y)

[[ Mutter von Martin ]] = y.mother(Martin)(y)

This time we cannot work with PM. von Martin is a genuine modifier in this construction.Here is the analysis of the possessive DP Martins 5 Pullover.

() Possessor s, type e(et,e)F(s) = x.Pet.| y.P(y) & x possesses y | = 1.the unique y. P(y) & x possesses y

() [D Martin s] [5 Cl VIEL PL Pullover]= :|{x is the fusion of 5 individual sweaters possessed by Martin}| = 1.the unique x. x

is the fusion of 5 individual sweaters possessed by Martin


10.2. Possessors in ChineseI take up Sarah’s question concerning Partee’s report on Chinese possessors; (Partee, ?). The following semantics assumes CL to be a variable of type et.

( ) Bare NounZhangsan de maoxianyiZh DE sweater‘Zhangsan’s sweater(s)’

Definite DP

( ) Possessor DE + [Numeral + CL + N]Zhansan de [san jian maoxianyi]Zh DE three CL sweater‘Zhangsan’s three sweaters’

Definite!

( ) Possessor DE + [Dem + (Numeral) + Cl + N]Zh. de [na (san) jian miaoxianyi]‘lit. Zh’s those three sweaters’

Sort of definite.

( ) [CL + [Possessor DE] + N]you [jian [Zh de] maoxianyi] zai jiaoshi lihave CL Zh DE sweaters in at classroom in‘There is one of Zh’s sweaters…’

Indefinite, „partitive“

25


( ) Numeral + CL + [Possessor DE] + Nyou san jian Zh de maoxhianyi zai zhou shanghas three CL Zh DE sweater at table top

Indefinite

( ) Dem + CL + Possessor DE + Nna jian Zh DE maoxhianyi hen piaoliangthat CL Zh DE sweater very pretty

Sort of definite, partitive

( ) Dem + Numeral + CL + Possessor DE + Nna san jan Zh de maoxhianyi shi meiguo zhi dethat three CL Zh DE sweater BE America make‘Those three sweater’s of Zhangsan’s are made in the US’

Sort of definite, partitive.

Partee observes that definites in Chinese don’t have a uniqueness presupposition, similar to „There is this pub behind the town hall“. She discusses that use but gives no interpretation for this use. We ignore this feature and treat definites as if they had the English meaning.

( ) [DP def [NP [PP Zhangsan DE] sweater] ]= the x. sweater(x) & possess(Zh,x)

DE means the same as possessive von.

( ) Zhansan de [san jian maoxianyi]def [[Zh DE] [[three CL MANY] sweater]] the of Zhangsan 3 many sweaters= that x. possess(Zh,x) & sweater(x) & |{y | y ≤ x & CL(y)}| = 3

( ) Possessor DE + [Dem + (Numeral) + Cl + N]

Zh. de [na (san) jian miaoxianyi]def [[Zh DE] [[three CL MANY] sweater]] the of Zhangsan 3 many sweaters= that x. possess(Zh,x) & sweater(x) & |{y | y ≤ x & CL(y)}| = 3

The demonstrative na is not where we see it. Perhaps the possessor PP [Zh DE] has been moved [to Spec,DP].

( ) [CL + [Possessor DE] + N]you [jian [Zh de] maoxianyi] zai jiaoshi lihave CL Zh DE sweaters in at classroom in [ONE CL many] [Zh DE] sweater

ONE is not expressed.

‘There is one of Zh’s sweaters…’

( ) Numeral + CL + [Possessor DE] + N

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you san jian Zh de maoxhianyi zai zhou shanghas three CL Zh DE sweater at table top [[3 Cl many] [[Zh DE] sweater]]

So the main difference from English is the covertness of the determiners. The interpretation follows from the semantics already introduced.

11. QUESTIONS TO (KEENAN, 1996)

Homework:1. Write down the definitions for the following properties of GQs.(a) increasing(b) decreasingGive examples.2. Write down the definitions for the following properties of determiners(a) intersective(b) co-intersective(c) proportional(d) cardinal(e) co-cardinal(f) conservativeProvide an example for each definition.

12. EXERCISES

To obtain a certificate, you have to make at least the following exercises: 2b (with the model given in the text), 5, 6-1 (with the model given in the text), 7.Homework 1 (for section 3)

1. Show that the sentences () and () are true in M. 2. Make a model that makes () false, () true and () false.

Homework 2 (for section 5): Use the model given and prove either (a) or (b) for an arbitrary assignment g:

a. [[[ein Handy](et)t y[Jedermann(et)t x [VP tx ty hate(et) ]] ]] M, g = 1 (LF1)

iff (x) Cellular(x) = 1 & (y)[Person(x) = 1 has(y)(x) = 1]

b. [[Jedermann(et)t x [[ein Handy](et)t y [VP tx ty hate(et) ]] ]] M, g = 1 (LF2)iff (y)[Person(x) = 1 (x) Cellular(x) = 1 & has(y)(x) = 1]

Homework 3 (for section 5). Show that LF1 Homework 2 is true in M.

Homework 4 (for section 6). Show that the model M indicated in the section makes (b) true.

Homework 5 (for section 8.1). Give an analysis of the sentence

() Ein Ei in jeder Schachtel ist faul.27


The reading intended is (y)[box(y) (x)[egg(x) & in(x,y) & rotten(x)]]. Ignore the copula and assume that the adjective is analysed as it were an intransitive verb. Give deep structure and LF.

Homework 6 (for section 9.2)

1. Modify F(küssen) such that the sentence is false.

2. Rewrite the model in the correct schönfinkelized version and show by a computation that the LF is true (or false, if you take your modified model).

Homework 7 (for section 10.1): Give a lexical entry for s that accounts for Ulis drei Kinder. Give the eplicit LF for this term.

Homework 8: Questions on Keenan

13. LITERATURE

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Engdahl, E. 1980. The Syntax and Semantics of Questions in Swedish, University of Massachusetts, Amherst: doctoral dissertation.

Frege, Gottlob. 1891. Funktion und Begriff. Jena: H. Pohle.

Heim, Irene. 1991. Artikel und Definitheit. In Semantik – Ein internationales Handbuch zeitgenössischer Forschung, eds. Arnim von Stechow and Dieter Wunderlich, 487-534. Berlin/New York: Walter der Gruyter.

Heim, Irene. 1994a. Plurals. Ms. Cambridge, Massachusetts.

Heim, Irene. 1994b. Questions: MIT, Lecture notes.

Heim, Irene, and Kratzer, Angelika. 1998. Semantics in Generative Grammar: Blackwell Textbooks in Linguistics. Oxford/Malden, MA: Blackwell.

Keenan, Edward L. 1996. The Semantics of Determiners. In The Handbook of Contemporary Semantic Theory, ed. Shalom Lappin: Blackwell.

Klein, Ewan. 1980. A semantics for positive and comparative adjectives. Linguistics and Philosophy 4.1:1-45.

Kratzer, Angelika. 1994. Scope or Pseudescope? Are there Wide-Scope Indefinites?

Kratzer, Angelika. 2005. On the plurality of verbs: Semantics Archive.

Krifka, Manfred. 1989a. Nominal Reference, Temporal Constitution and Quantification in Event Semantics. In Semantics and Contextual Expression, eds. R. Bartsch, J. van Benthem and van Emde Boas, 75-115. Dordrecht: Foris.

Krifka, Manfred. 1989b. Nominalreferenz und Zeitkonstitution: Studien zur Theoretischen Linguistik. München: Wilhelm Fink.

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Krifka, Manfred. 1991. Massennomina. In Semantik. Ein internationales Handbuch zeitgenössischer Forschung., eds. Arnim von Stechow and Dieter Wunderlich, 399-417. Berlin/New York: Walter de Gruyter.

Lewis, David. 1991. Parts of Classes. Oxford: Basil Blackwell.

Link, Godehard. 1991. Plural. In Semantik. Ein internationales Handbuch zeitgenössischer Forschung, eds. Arnim von Stechow and Dieter Wunderlich, 418-440. Berlin/New York: Walter de Gruyter.

Partee, Barbara. ? A Note on Mandarin Possessives, Demonstratives, and Definiteness. Ms.

Quine, Williard van Orman. 1960. Word and Object: Studies in Communication. New York/London: The Technology Press of The Massachusetts Institute of Technology/John Wiley & Sons.

Reinhart, Tanya. 1997. Quantifier Scope: How Labor is Divided between QR and Choice Functions. Linguistics and Philosophy 20:335-397.

Russell, B. 1905. On Denoting. Mind 14:479-493.

Scha, Remko. 1984. Distributive, Collective and Cumulative Quantification. In Truth, Interpretation and Information, eds. Jeroen Groenendijk and et al., 131-158. Dordrecht.

Schein, B. 1993. Plurals and Events. Cambridge, Massachusetts: MIT Press.

Schwarzschild, R. 1996. Pluralities: Studies in Linguistics and Philosophy. Dordrecht: Kluwer.

Sharvy, R. 1980. A More General Theory of Definite Descriptions. The Philosophical Review 89.4:607-624.

Sternefeld, Wolfgang. 1998. Reciprocity and Cumulative Predication. Natural Language Semantics:303-337.

von Stechow, Arnim. 2000. Some Remarks on Choice Functions and LF-Movement. In Reference and Anaphoric Relations, eds. Klaus von Heusinger and Urs Egli, 193-228. Dordrecht/Boston/London: Kluwer.

von Stechow, Arnim. 2008. Syntax and Semantics. Ms. Tübingen University.

Winter, Yoad. 1997. Choice Functions and the Scopal Semantics of Indefinites. Linguistics and Philosophy 20:399-467.

Winter, Yoad. 2000. Distributivity and Dependency. Natural Language Semantics 8:27-69.

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