Transcript WEAK NOUN PHRASES: SEMANTICS AND SYNTAX

WEAK NOUN PHRASES:
SEMANTICS AND SYNTAX
Barbara H. Partee
University of Massachusetts, Amherst
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
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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
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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
λPx[student(x)  P(x)]
(the set of properties that every student has)


every student walks
λPx[student(x)  P(x)] (walk)
(function-argument application)
 x[student(x)  walk (x)]
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NP interpretations, continued

a student:
λPx[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
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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
2
function(arg1) (arg2)
2 walks
function
every

(arg1)
student
||every|| (||student|| ) (||walks|| )
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Determiners as functions
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||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
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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.
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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
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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(AB)(E).
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English test: “Det CN VP” is true iff “Det CN
which VP exist(s)” is true.
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Examples
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(i) Three is an existential determiner: Three
cats are in the tree iff three cats which are in
the tree exist.
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(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
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Basic existential determiners = symmetric
determiners.
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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
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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
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Три черные кошки на кухне
≡
Три вещи на кухне черные кошки
три is weak
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Все черные кошки на кухне

Все вещи на кухне черные кошки
все is strong
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See abstract for more discussion of Russian
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Further related topics
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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) .
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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:
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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 вовремя.)
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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
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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)

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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
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Substitution of extensionally equivalent
expressions in an intensional context does
not always preserve truth-value.
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Caroline is looking for a unicorn
The set of unicorns = the set of 13-leaf
clovers
Not entailed: Caroline is looking for a 13leaf clover
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The classical analysis
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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
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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.
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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
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For Montague, the relation between seek and
try to find is captured not by decomposition
but by a meaning postulate.
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Meaning postulate:
seek’ (x, ^Q)  try’ (x, ^[Q(y find’ (x,y))]).
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Problems with the classical analysis
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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.
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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
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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.
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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.
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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.
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In the case of Genitive of Negation, the
construction is not intensional.
But Russian linguists from Jakobson to
Paducheva have argued that Genitivemarked 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.
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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.

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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.
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