WEAK NOUN PHRASES: SEMANTICS AND SYNTAX

Barbara H. Partee

University of Massachusetts, Amherst

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Acknowledgements

Thanks to many students in classes at RGGU and MGU for data, suggestions, and ideas about weak NPs in Russian.

Thanks to Vladimir Borschev, Elena Paducheva, Ekaterina Rakhilina, and Yakov Testelets for ongoing discussion of the Russian Genitive of Negation.

This material is based upon work supported in part by the National Science Foundation under Grant No. BCS-0418311 to B.H. Partee and V. Borschev.

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Outline

NPs as Generalized Quantifers <<e,t>,t> Determiners as functions Weak NPs and existential sentences Property-type interpretations of NPs Intensional contexts Genitive of negation hypothesis, conjecture

for future research.

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Introduction: NPs as Generalized Quantifiers

Montague: Noun Phrases denote sets of properties.

Semantic type for NPs:

(e t) t

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Some NP interpretations

John λP[P(j)] type (e t) t

(the set of all of John’s properties)

John walks λP[P(j)] (walk) walk (j)

(function-argument application)

j: type e P, walk: type e t

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NP interpretations, continued

every student type (e t) t λPx[student(x) P(x)]

(the set of properties that every student has)

every student walks

λPx[student(x) P(x)] (walk)

(function-argument application)

x[student(x) walk (x)]

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NP interpretations, continued

a student: λPx[student(x) & P(x)] (the set of properties at least one student has)

the king :

λP [x[king(x) & y ( king(y) y = x) & P(x))]

(the set of properties the one and only king has)

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Syntactic structure

S 2

NP VP 2 walk DET CN

every student

Semantics: CN(P) (Common Noun (phrase)): type e t VP: type e t

Note: It is more common now to have DP where I have NP, and NP where I have CN(P).

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Semantics of DET

DET: interpreted as a function of type (e t) ((e t) t)

it applies to CN meaning, type (e t), to give a a generalized quantifier, a function

of type (e t) t, which in turn applies to a VP meaning to give truth value.

NP: type (e t) t

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Semantic structure

truth-value

2function(arg1) (arg2)

2 walks

function (arg1)

every student

||every|| (||student|| ) (||walks|| )

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Determiners as functions

||Every||(A) = {B| x ( x A x B)}.

Equivalently: ||Every|| = Q[P[x ( Q(x) P(x) )]].

Some, a: takes as argument a set A and gives as result {B| A B }.

|| a || = Q[P[x ( Q(x) & P(x) )]]

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So Determiner Properties Project through Whole Sentence

2

(arg2) 2 function (arg1)

DET

Determiners can license Negative Polarity Items inside NP and/or in “arg2”, the “rest of the sentence”.

Weak vs. strong determiners: crucial for “existential sentences”

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“Weak” determiners and existential sentences.

Data: OK, normal: There is a new problem. There are three semantics textbooks. There are many unstable governments.

Anomalous: #There is every linguistics student. #There are most democratic governments. #There is the solution. (# with “existential” there)

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Semantic explanation – Milsark, Barwise and Cooper, Keenan

Definition (Keenan 1987): A determiner D is a basic existential determiner if for all models M and all A,B E,

D(A)(B) = D(AB)(E).

English test: “Det CN VP” is true iff “Det CN which VP exist(s)” is true.

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Examples

(i) Three is an existential determiner: Three cats are in the tree iff three cats which are in the tree exist.

(ii) Every is not existential: Suppose there are 5 cats, and 3 are in the

tree. Then: “Every cat is in the tree” is false but “Every cat which is in the tree exists” is true.

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Existential = Symmetric

Basic existential determiners = symmetric determiners. One can prove, given that all determiners are conservative

(Barwise and Cooper 1981), that Keenan’s basic

existential determiners are exactly the symmetric

determiners.

Symmetry: A determiner D is symmetric iff for all A, B, D(A)(B) ≡ D(B)(A).

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Testing symmetry

Weak (symmetric): Three cats are in the kitchen ≡ Three things in the kitchen are cats.

More than 5 students are women ≡ More than 5 women are students.

Strong (non-symmetric): Every Zhiguli is a Russian car Every Russian car is a Zhiguli.

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Test symmetry in Russian

Три черные кошки на кухне ≡ Три вещи на кухне черные кошки

три is weak

Все черные кошки на кухне Все вещи на кухне черные кошки

все is strong

See abstract for more discussion of Russian

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Further related topics

Partee (1991) suggests a systematic connection between weak-strong, Heimian tripartite structures, and topic-focus structure, which is further explored in Hajicová, Partee and Sgall (1998) .

See also Partee (1989) on the weak-strong ambiguity of English many, few and Babko-Malaya (1998) on the focus-sensitivity of English many and the distinction between weak много and strong многие in Russian.

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CNP and NP types

Prototypical case: NPs are type e (proper names, pronouns, referring terms)

or type <<e,t>,t> (quantifier phrases). CNPs are type <e,t> (predicates).

Sometimes NPs shift to <e,t> type (predicate nominals: John is a student.)

Sometimes bare CNPs shift to e type (Russian singular count nouns in e-type argument positions: Молодой лингвист кончил свой доклад во-время.)

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Property-type NP interpretations

NP types:

e: entity type

<e,t> : (extensional) predicate type

<s,<e,t>>: (intensional) property type

<<e,t>,t>: generalized quantifiers: Montague’s NP type, and the agreed-on type for essentially quantificational NPs

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Property-type NP interpretations, continued

Where do predicate-type and property-type NPs appear?

Predicate-type <e,t>:

(i) predicate nominals: John is a student.

(ii) Some say also: There is a cat on the mat. (McNally, Landman, Kamp)

Property-type: recent proposals, to be discussed next.

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Property-type NP interpretations, continued

Zimmermann 1993: argues against Montague’s analysis of “intensional transitive verbs” like seek

Montague: object is intensional generalized quantifier, type <s,<s,<e,t>>,t>.

Zimmermann: object is property-type, type <s,<e,t>>.

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Fundamental properties of intensional contexts(11) Caroline found a unicorn.

(extensional, unambiguous)(12) Caroline sought a unicorn.

(intensional, ambiguous) Sentences with seek are ambiguous between

a specific and a non-specific reading (or transparent vs. opaque reading). (11) is unambiguous, (12) is ambiguous.

On the opaque reading of (12), the existence of a unicorn is not entailed.

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Fundamental properties of intensional contexts, continued

Substitution of extensionally equivalent expressions in an intensional context does not always preserve truth-value.

Caroline is looking for a unicorn The set of unicorns = the set of 13-leaf

clovers Not entailed: Caroline is looking for a 13-

leaf clover

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The classical analysis

Everyone agrees since Frege: the complement of seek must be intensional, not extensional.

Quine (1960) argued that seek should be decomposed into try to find. He argued that intensionality is (in general) the result of embedding a proposition under an intensional operator, such as the verb try.

Within Caroline try [Caroline find x] , there are then two places a quantifier phrase could take its scope:

the higher clause, giving the transparent reading the lower clause, giving the opaque reading.

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The classical analysis, continued

Montague (1973) argued that the same semantic effect can be achieved with a simpler syntax: seek + NP, if NPs like a unicorn express Generalized Quantifiers.

The argument of an intensional verb gets an intensional operator “^” applied to it.

So Montague treats a verb like seek1 as denoting a relation between an individual and an intensional generalized quantifier.

The transparent reading results from “quantifying in” to an e-type argument position of seek2, a relation between two individuals.

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The classical analysis, continued

For Montague, the relation between seek and try to find is captured not by decomposition but by a meaning postulate.

Meaning postulate:

seek’ (x, ^Q) try’ (x, ^[Q(y find’ (x,y))]).

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Problems with the classical analysis

But there are problems with Quine’s and Montague’s classical analyses.

Among other problems, (Zimmermann 1993) points out an overgeneration problem:

True quantifier phrases like every doctor are normally unambiguously “transparent” after intensional transitive verbs like compare, seek, although they are ambiguous in constructions like try to find, so Montague and Quine predict ambiguity.

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Problems with the classical analysis, continued. Simple indefinites with a, on the other hand, are

indeed ambiguous with intensional verbs. Compare: (a) Alain is seeking a comic book.

(ambiguous) (b) Alain is seeking each comic book.

(unambiguous; lacks ambiguity of (c)) (c) Alain is trying to find each comic book.

(ambiguous)

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Zimmermann’s alternative account

Zimmermann: we can capture the relevant generalizations if we treat definite and indefinite arguments of intensional verbs, (but not generalized quantifiers) as properties, type <s,<e,t>>.

Zimmermann’s proposal is that a verb like seek1 denotes a relation between an individual and a property.

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Zimmermann’s alternative account, continued

Zimmermann: seek a unicorn: seek’(^unicorn’)

( ^ is Montague’s ‘intension operator’) This is a case of NP type-shifting by coercion: seek

demands a property-type argument. We know that indefinite NPs easily shift into <s,<e,t>>

readings, as was shown for predicate nominals in (Partee 1986).

transparent, or de re, reading: “quantify in” to e-type argument position of seek2.

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Russian Genitive of Negation

Hypothesis: Wherever we see Nom/Gen and Acc/Gen alternation (both under negation and under intensional verbs), Nom or Acc represents an ordinary e-type argument position (‘referential’; and may be quantified), whereas a Gen NP is always interpreted as property-type: <e,t>, or <s,<e,t>>.

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Russian Genitive of Negation, continued. In the case of intensional verbs like ждать,

this agrees with Zimmermann’s analysis. There is a similar connection to the work of

van Geenhoven, who treats ‘weak’ object NPs in West Greenlandic as “incorporated to the verb”: they are not fully independent objects, but get an existential quantifier from the verb.

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Russian Genitive of Negation, continued.

In the case of Genitive of Negation, the construction is not intensional.

But Russian linguists from Jakobson to Paducheva have argued that Genitive-marked NPs have reduced “referential status”, and Western linguists have generally claimed that they must be “indefinite”.

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Russian Genitive of Negation, continued.

A shift of NP-meanings to property-type under Negation could capture those insights and intuitions.

But negation is not really intensional; there seem to be different kinds of ‘reduced referentiality’.

We have a few facts in favor, but also some doubts.

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Russian Genitive of Negation, continued.

Evidence in favor:(a) Петя нашел ответ.

(b) Петя не нашел ответ.

(c) Петя не нашел ответа. Competing analyses of case (c):

Standard analysis: definite vs. indefinite -- (c) has an indefinite (weak) NP under the scope of Neg.

Suggested analysis: (c) has a property-type NP under the scope of Neg.

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Russian Genitive of Negation, continued.

Evidence casting doubt on property analysis:(a) Я не видела Машу.

(b) Я не видела Маши.

The (b) case causes problems for all “quantificational” approaches to the Genitive of Negation, unless we suggest a meaning like “any trace of Masha”.

(c) Ваня не решил все задачи.

(d) Ваня не решил всех задач.

Exs. (c-d) may differ in scope, but not in intensionality.

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Russian Genitive of Negation, continued.

For examples with negated indefinites, the property-type analysis for Gen Neg examples looks good.

For examples with proper names or strong quantifiers, the property-type analysis does not look good.

But no uniform semantic approach looks good for all cases (yet).

This issue is still under exploration – more coming in future years.

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Спасибо за внимание.