P-2

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Nandini Bhattacharya 16.01.2014

M.Phil in Linguistics. Sem –I

P-2 Term Paper

Semantics of Quantification in Bangla :-

Abstract: Quantifications over individuals or objects are sometimes explicit or implicit

in Natural languages. The question of how the quantification is encoded in various

languages has been widely debated in formal semantics. The traditional view in Generalized

Quantifier Theory is that the Noun Phrases in Natural Languages behave like quantified

expressions and the quantifiers act like determiners. The existing literature mostly probes

into the English data and there is a lot more need for cross-linguistic data to validate the

Theory and examine some language specific phenomena concerning NP quantification. This

paper, proposes a uniform survey of the existing literature highlighting the key points. The

Paper also provides an adequate description of the quantifiers in Bangla. Together with that,

this paper presents some analysis regarding the formalizations of some of the non-logical

and partitive quantification in Bangla. Moreover, the last section of the paper examines the

scopal interaction of quantificational NPs with Negation in Bangla. The analysis focuses on

the semantics of the Noun Phrase quantification following Generalized Quantifier Theory,

and sheds light on the language specific features of quantification in Bangla.

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1. Introduction :-

There are many semantic theories that propose methods for

the proper interpretation of quantified Noun Phrases in natural language. The Generalized

quantifier theory has been an influential sub-field of semantic theory of all. David Lewis

(1970) , first proposes that noun phrases should be interpreted as properties of properties

rather than as in first order predicate logic. His idea was based on the set theoretic notion of

set-subset and set membership and treated Noun Phrases as Generalized quatifiers. After

Lewis, the Generalized Quantifier theory (abbre. GQ Theory), has been developed by

Barwise and Cooper (1981), to the level of Universals. They suggest that all noun phrases

denote generalized quantifiers. They theorizes that the Quantifier Phrase (QP) is formed by

Quantifier determiners combined with Nominal arguments of type <e,t> . They also

proposed weak-strong distinctions of quantifiers. Carlson’s papers (1980) focus on the issue

of the treatment of the English bare plurals and how they interact with quantification.

Partee (2004) applies the semantic type theory and type-shifting principles to reconcile the

Generalized Quantifier Theory with the ‘non-uniform’ NP semantics proposed by Heim and

Kratzer (1998). This tradition has been further put forward by another notable semanticist

such as, Anna Szabolsci (2010).

There is a different between the accounts of the Syntax

and Semantics of quantification. The syntax of quantification has been proposed by kennedy

(1997) and Szabolcsi (1999/2001, 2010). The semantics of quantification is proposed by

Heim and Kratzer (1998) ,Chierchia Gennaro and Sally McConnell-Ginet ( 2000) and

Anastasia Giannakidou and Monika Rathert (2009). By emphasizing, the significance of the

GQ theory, Anastasia Giannakidou and Monika Rathert (2009) state that, the Generalized

Quantifier Theory has motivated an extensive and fruitful research agenda, since 1980s to

the current time. They point out that the framework of GQ Theory has featured in

“extensive studies of quantificational structures, with attention to the constituents of QPs,

and their scopal properties.” They have emphasized on the cross-linguistic study of

quantification in natural languages. There have also been notable researches in the syntax-

semantics interface of quantification as well.

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2. Overview of Literature :-

Modern quantifiers were first introduced by Montague

(1973). Thereafter, the treatment of quantification has been a most discussed area of

Formal semantics. Following are the overviews of some of the eminent existing literature of

Generalized Quantifier theory in natural language semantics.

2.1. Barwise and Cooper (1981/2002):-

According to Barwise and Cooper, the quantifiers of first order

logic are not adequate to properly treat the quantification in Natural languages. There are

natural language sentences that can’t be symbolized using Restricted quantification.

Barwise and Cooper argues that the syntactic structure of quantified sentences in predicate

calculus is different from the syntactic structure of the quantified sentences in natural

language. In the article, Barwise and Cooper, discusses the notion of Generalized

Quantification and formalizes it. They propose a detailed analysis of the possible

implications of Generalized Quantifier theory of natural language. They attest their theory

with appropriate examples from English language data. In the article, Barwise and Cooper,

cites some English quantified NPs, such as ‘more than half’, ‘most of’, ‘no one’, ‘only one’

etc, and reasons why these quantifiers can’t be treated appropriately using traditional first

order logic. They argues that, if ‘E’ is an arbitrary non-empty set of things , first order logic

only allows quantification over objects in E, it doesn’t permit the quantification over the

arbitrary sets of things. So, Generalized quantifier theory in Model-theoretic Semantics,

provides a way to treat and formalize the determiners like ‘most’, ‘many’, ‘few’ etc.

Barwise and Cooper suggests, that in a sentence like “More

than half *emphasis mine+ of John’s arrows hit the target”, ‘more than half’ doesn’t behave

like a quantifier but like a determiner. This determiner combines with a set expression (i.e.

set of John’s arrows) to produce a quantifier. Barwise and Cooper argues that this structure

of the logical quantifiers, such as ‘more than half’, ‘most’ etc, corresponds in a similar way

to the structure of English NPs. The determiner combines with the set of things in a

quantified NP and the whole NP is the quantifier, for example, “most people”, “more than

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half of John’s arrows’ etc. Barwise and Cooper terms these kinds of quantifiers as “non-

logical quantifiers”. They also argues that the truth value of these quantified sentences will

not depend upon ‘a priori’ logic but will depend on the ‘underlying measure of infinite sets

that is one is using’, which at the same time needs to be included in the Model.

Barwise and Cooper argues that there should be a fixed set of

contexts that determines the meaning of the basic expressions in the quantified sentences.

They propose this assumption as “fixed context assumption”. So the interpretation of the

non logical quantifiers, like ‘most’, ‘may’, ‘more than half’, ‘few’ etc will depend on the

Model and will vary from model to model. According to Barwise and Cooper that the

interpretation of the logical quantifier ‘Every’ (∀ ) remains same in every model (M).

According to Barwise and Cooper, the quantifiers are used to denote the property of a set,

for example, the Existential quantifier (∃) asserts that the set of individuals (x) have the

property which contains at least one member. The Universal quantifier (∀ ) asserts that the

set contains all the individual. Barwise and Cooper argues that a quantifier divides up the

family of sets provided by the model (M). When the quantifiers are combined with some

sets it will produce the truth value (T) and with combing with other sets will produce the

truth value (F). Barwise and Cooper argues that the denotation II Q II, of a quantifier symbol

Q, can be formalized as follows,

II ∃ II = { X ⊆ E I X ≠ ∅ } [ E = set of entities provided by M]

II ∀ II = { ∃ }

II Finite II = { X ⊆ E I X is finite }

II More than half of N II = { X ⊆ E I X contains more than half of the Ns }

II Most N II = { X ⊆ E I X contains most Ns }

Therefore, the quantifiers functions from set of things/individuals to the property of a non-

empty set.

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According to Barwise and Cooper, the predicate calculus

can’t adequately translate the subject NPs with non logical quantifiers. So they propose a

simple formalization. For example, they cites the sentence, “Most babies sneeze”, and

formalizes it as , (Most babies)(sneeze). The sentence will have the truth value T, if the set

of sneezers contains most babies. Barwise and Cooper argues that proper names within a

NP also acts as a quantifier. The NP, with a proper name represents a family of sets,

containing that particular individual denoted by the proper name. Barwise and Cooper

proposes that the semantics of L(GQ) or Generalized quantifier logic, will be defined so that

‘thing’ always denotes the set E of things in the Model (i.e. the set of individuals or objects).

They also proposes the syntactic formation rules for L(GQ) using the logical symbols.

Barwise and Cooper, proposes the semantic analysis of

L(GQ) by using the set theoretic notions. They formalizes some of the English quantifiers,

such as, ‘some’, ‘every’, ‘no’, ‘both’, etc. According to Barwise and Cooper,‘ II some II is the

function which assigns to each A ⊆ E the family, II some II (A) = { X ⊆ E I X ∩ A ≠ 0 - ‘. They

explains their formalism as, for each of the determiner D, II D II (A) is a family of sets Q with

the property that X ∈ Q iff (X ∩ A) ∈ Q. They describe this property of II D II by proposing

that the quantifier II D II (A) lives on A. They proposes the universal semantic feature of the

determiners that they have the ability to assign to any set A a quantifier, that is the family of

sets, which ‘lives on A.’ To give evidence of this, Barwise and Cooper provides examples of

the applications of the logic of the GQ Theory to the fragments of English syntax.

Barwise and Cooper proposes some Semantic

Universals, relating to the Generalized Quantifier Theory. They proposes that, “ Every

natural language has syntactic constituents (called noun-phrases) whose semantic function

is to express generalized quantifiers over the domain of discourse.” They argues that, apart

from that it is the whole NP who participate into scope relationships in a proposition. They

proposes another Semantic Universal, “If a language allows phrases to occur in a dislocated

position associated with a rule of variable binding, then at least NPs (i.e. the syntactic

category corresponding to quantifiers over the domain of discourse) will occur in this

position.” After that, Barwise and Cooper proposes the Determiner Universal and states

that ,”Every natural language contains basic expressions, (called determiners) whose

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semantic function is to assign to common count noun denotations (i.e. , sets) A quantifier

that lives on A. They cites the example, ‘Many men run ↔ Many men are men who run.’

Here, the quantifier ‘many’ lives on the set of ‘men’.

Barwise and Cooper draws the distinction between the

‘weak’ and ‘strong’ quantifiers. According to them, the weak quantifiers are the followings:-

‘a’, ‘some’ , ‘one/two/three etc’, ‘many’, ‘a few’, ‘few’, ‘no’ , and the strong quantifiers are

the followings :- ‘both’, ‘all’, ‘every’, ’each’, ‘most’, ‘neither’ etc. They also proposes the

‘Monotone increasing’ and ‘Monotone decreasing’ quantifiers and formalizes the

‘Monotonicity correspondence Universal’ and ‘Monotonicity Constraints’. They attests their

arguments with English data. Barwise and Cooper concludes by critiquing Montague’s

(1974) Quantifier Theory. So, therefore, Barwise and Cooper paved the pathways for a

greater grounding of The Generalized Quantifier Theory.

2.2. Carlson (1980) :-

According to Carlson, the different meanings of the

English bare plural arise because of the manner in which the context of the sentence

interacts with the bare plural NPs. Similarly we can argue that, the set readings of the

quantifiers such as, ‘some’, ‘many’, ‘most’, ‘few’, ‘all’ etc in English, differs. These

differences arise because of the way in which the context or presupposition set of the

sentence interacts with the quantified expressions and the set NPs. Carlson argues that the

interactions of quantified NPs with negation and bare plurals depends on their relative

scope properties. Carlson proposes that the NPs, such as, ‘Any dog’, ‘All dogs’, ‘Every Dog’

and ‘Each dog’ , all can be formalized as , (∀x) (Dog (x) ) , using the first order logic. He

argues that though these quantifiers are quite distinct from each other, it is plausible to

represent all of them in a unified manner. He suggests that a bare plural is also nothing but

the singular form addition to the quantifier ‘every’, which can also be represented as a

quantified NP. According to Carlson a ‘generic’ and ‘existential’ quantifier can be used to

formalize a bare plural. Later in his thesis, Carlson examines the interaction between the

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determiner with the bare plurals and also studies some set-theoretic approaches to analyse

the bare plurals in English.

2.3. Partee (2004):-

In her article, ‘Many Quatifiers’, Partee analyses the treatment

of ‘many’ and ‘few’ in Formal semantics. According to Barbara Partee, the quantifier ‘ many’

and ‘few’, are ambiguous. She argues that these quantifiers are vague between their

‘cardinal’ and ‘proportional’ readings. Partee critiques Montague’s treatment of ‘many’ and

‘few’ as context-dependent quantifiers only and also highlights other proposals in the

literature in relation to the quantifiers ‘many’ and ‘few’. Partee argues that ‘many’ is like

‘every’ and ‘most’ on the proportional readings. She suggests that the quantificational cases

are almost paraphrasable by partitives. The only difference between them can be that the

restrictor clause of the quantifiers is open-ended set and the partitives involve a definite set.

Partee analyses the behaviour of ‘many’ and ‘few’ by formalizing their cardinal, proportional

and generic readings and sheds lights on some potential research issues in this area.

2.4. Chierchia Gennaro and Sally McConnell-Ginet ( 2000) :-

According to Chierchia and McConnell-Ginet, the

quantificational expressions introduce the power to convey generalizations into natural

languages. The quantifiers express the quantity of the individuals in a given domain (F1)

have a given property. They analyses the quantifier logic in the truth-conditional semantic

theory framework. Chierchia and McConnell-Ginet cites an example, “Everyone likes Loren.”

and states that the sentence is uttered many times, each time pointing at a different

individual until each individual in that domain has been pointed at. They argues that,

relative to that “pointing”, each of the sentences can be assigned the truth value of whether

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they are true or false. If any single individual in that particular domain doesn’t like ‘Loren’

then the proposition yields the truth value F.

According to Chierchia and McConnell-Ginet, the

quantified expressions denote how many different values of the set of entities we have to

consider. They argue that the quantified expressions are the generalizing component. They

propose that the quantifier sentences are built out of sentences that contain different

variable set. Chierchia and McConnell-Ginet, argues that quantification has two

components, one contains the ordinary attribution of properties to referents/entities, and

another contains an instructions of how many such referents should have those properties.

They proposes a formulae, ∃x3Q ( x3 ), in which, the variable x3 is bound. Chierchia and

McConnell-Ginet, proposes that “an occurrence of a variable xn is syntactically bound iff it is

c-commanded by a quantifier coindexed with it.”, the ‘coindexed’ quantifier here refers to

∃xn and ∀xn etc.

Chierchia and McConnell-Ginet hypothesize a syntactic

account of the quantification in relation to c-command and scope interaction. They propose

that an occurrence of xn is syntactically bound by a quantifier, such as, Qn iff Qn is the lowest

quantifier which c-commands xn . They also provide with a semantic account of the

quantification. They suggests that it is part of the semantics of the Pronouns that they can

refer to any individual at all time in a given set , and also can be used with quantifiers to

denote something general about such a set. Chierchia and McConnell-Ginet also presents an

interpretation of the predicate calculus by using independent ‘value’ assignment functions.

They argues that the Models for the predicate calculus are made up of two things, first is a

specification of the sets or the domain of discourse and second a specifications of the

extensions of the language constants. They propose the structure of the Model for the

predicate calculus in semantics.

According to Chierchia and McConnell-Ginet, the

quantification in predicate calculus and the quantification in natural language are

connected. They applies the predicate calculus model to English quantificational NPs. They

argues that in care of English quantificational NPs, there is a presupposition set that

determines the truth-conditionality of the proposition. They also argues that in English, the

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quantifying expressions such as , ‘every’, ‘some’ are always accompanied by some nominal

expressions, that restricts the universe of discourse to a specific set of individuals. Chierchia

and McConnell-Ginet proposes a grammar of English F2 and illustrates its association with a

certain class of English quantified sentences, for example ‘every man is hungry’ etc. They

analyses the scope taking and binding phenomena in the syntactic structure of the QP

which parallels the compositionality of the semantic representation of the natural language

Quantification. Chierchia and McConnell-Ginet concludes by formalizing the interaction

between the predicate calculus and the logical operator ‘if’ in the LF representation. .

Chierchia and McConnell-Ginet also highlight the significance of the Generalized Quantifier

approach (sets of sets). They argues that GQ Theory provides a compositional semantics for

NPs, it allows to bring out the cross-categorical nature of the logical words, such as, ‘and’,

‘or’ etc, it provides a precise criteria for NPs that characterize the distribution of Negative

Polarity Items and it gives an explanation for a substantial universal characteristics of

natural language determiners.

2.5. Szabolsci (2010) :-

According to Szabolcsi, the quantified expressions of the logical

language are different from the quantification in natural language. The syntax of logical

language specifies how the quantifier operator combines with expressions to yield new

expressions, and the semantics specifies their effects. Szabolcsi argues that the scope of an

operator in logic results from the constituent that it is attached to. But in natural language

one has to distinguish between semantic scope and syntactic domain. Szabolcsi argues that

the scope of a quantifier A is the property that is asserted to be an element of A on a given

derivation of sentences. If the property A incorporates another property B, such as,

quantifier, negation, model, then A automatically takes scope over B. Szabolcsi argues that

natural language quantifies over times and worlds in a syntactically explicit manner.

Szabolcsi addresses some issues in Generalized Quantifier Theory that poses problem of

analysis. However, Szabolcsi, argues that those problems arise due to the absence of fully

articulated compositional analysis. Szabocsi states that, “ GQ theory can accommodate so-

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called referential indefinites, non distributive readings of plurals and conjunctions, and

type multiplicity, and it could adopt the stipulation that the “topics sets” of all GQs are

presupposed to be non-empty.” Szabolcsi analyses the scope interaction and the behaviours

of quantified NPs cross-linguistically.

2.6. Syntax of Quantification :-

Anna Szabolcsi (2001), analyses the Theory of Quantifier

Scope in this article. Szabolcsi suggests that the scope of an operator such as, a quantifier, is

the domain within which the operator has the potentiality to affect the interpretation of

other expressions. For example, ‘every boy’ affects the interpretation of the predicte by

inducing referential variation. She argues that the notion of scope is similar in both logic and

logical syntax. Szabolcsi argues that the surface structure S, directly determines the scope

interactions between different operators, such as, quantifiers, pronouns, negative polarity

items etc. She presents an analysis of the scope interactions of the quantifier phrases in

natural languages. According to Szabolcsi, “if QE/1 is in the domain of QE/2 but not vise

versa, QE/1 must take wide scope. If both are in the domain of the other, the structure is

potentially ambiguous. If neither QE is in the domain of the other, they must be interpreted

independently.” (here, QE stands for Quantified Expressions).

Szabolcsi reviews Montague (1974) in order to analyse the

rules of quantification in abstract syntax. Szabolcsi also reviews the ‘Quantifier Raising

‘phenomena in natural languages and tries to draw an affinity between these two

approaches. She reviews the syntactic theories of scope reading from 1980s to the 1990s

Minimalism approach. She critiques those theories by stating that those theories only deal

with the syntax of quantifiers, such as ‘every’ and ‘some’. Szabolcsi proposes that the

varying scope of indefinite quantifiers need to be attributed to unselective binding. She

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argues that the indefinites should be treated as variables. Szabolcsi concludes by critiquing

whether the spell-out syntax is sufficient to capture the scope relationship of indefinite

quantifiers and whether the cross linguistic data uniformly supports such interpretations.

Christopher Kennedy (1997), proposes an account of

Antecedent –contained deletion principle and analyses its relation to the syntactic theory of

Quantifier Raising. Kennedy argues that the matrix reading of the embedded ACD is present

in the Quantifier Raising account only if we assume that QR can move quantified DPs out of

non-finite clauses. He states that the wide scope interpretations of embedded quantifiers

are parallel to the matrix readings of embedded ACD. Kennedy suggests that the principles

that force the LF movements of lexical materials also force the PF movement, that is

interpreted at the interface level. According to him, quantifiers impose two requirements on

the sentence structure, firstly, a quantifier must bind a variable and secondly, nominal

quantification in natural language is restricted. Kennedy argues that the ACD, which show

that the Quantifier Raising selects both a quantificational determiner and its restriction,

gives evidence of the presence of this relationship at LF, as a relation between a head and

its complement. Kennedy argues that both the ACD analysis and Quantifier Raising Theory is

compatible with each other and presents the syntactic representation of the Quantifier in

the framework of the Quantifier Raising Theory..The syntactic representation of the

Quantification, that Kennedy proposes, is restricted quantification unlike the claims of

unrestricted quantification in natural language.

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3. Survey of Bangla Quantifiers :-

Following is a description of the quantified expressions in Bangla, and

the Structure and behaviour of the Quantificational Phrases in Bangla. The various nominal

quantifiers and some adjectival and adverbial quantifiers are discussed.

3.1. Nominal Quantifiers :-

There are many quantifiers in Bangla. The Universal quantifier in

Bangla are the followings:- /sɔb/ (every), /sɔbai/ ( everyone), /sɔb kɪchu/ (everything). In

Bangla sentences, /sɔb/ quantifies over both animate and inanimate, (± count) NPs. In

Bangla, the meaning of / kɪchu / is ‘some’, which when occurs after / sɔb / denotes

inanimate object N. Followings example sentences show the occurrence of /sɔb/ in various

contexts:-

i. sɔb chele -ra boi porche

every boy -plu.ani. Book read.Pres.con.

“Every boy is reading”.

ii. sɔb pʰul -gulo lal

every flower -plu.inani. red.

“ Every flower is red.”

In the above sentences the set of entities/objects quantified by the Universal quantifier, /

sɔb / is restricted by the contexts.

The quantifiers in Bangla can be classified into + count

quantifiers, - count quantifiers, and (± count) quantifiers. The + count quantifiers in Bangla,

are, /protek / (each one ), /proti̪ti/ (each thing), /ɔnek gulo / (many), / ɔnek/ (many),

/kɔekta/ (some of these) etc. The –count quantifiers in Bangla, are, /ɔlpo/ (some/a little),

/ektu/ (little), / ɔnekta/ (much) etc. The (± count) quantifiers in Bangla, are, /kɔto̪/ ( so

many), /kichu/ (some) etc. There are also distinctions between animate and inanimate

quantifiers in Bangla.

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In Bangla, the partitive quantifiers for( –count) Nouns are the

followings, /ɔrdh ek/ (half) , / ɔrdh ek-er kichu besi/ (more than half), / ɔrdh ek-er kichu kɔm/

(less than half), / ɔrdh ek-er ektu besi/ ( a littile more than half), /ɔrdh ek-er ektu kɔm/ ( a

little less than half). Sometimes the classifier / ʈa/ suffixes with / ɔrdh ek/ to denote

definiteness. For example :-

iii. Ram ɔrdh ek - ʈa aam kheche.

Ram half -clas. Mango eat.pres.perf.

“Ram have had half of the mango.”

3.2. Reduplicated Quantifiers :-

Another feature of the Bangla quantifiers are the reduplicated

quantifiers in Bangla. Some quantifiers are reduplicated in Bangla sentences to convey a

partitive reading. Moreover, some question particles are also reduplicated to express a

partitive quantification. For example, /kono kono/ (a few people /a few things, ± animate),

/keu keu/ (a few people/some people, + human), / ɔlpo ɔlpo/ (little), / ekʈu ekʈu/ (a little)

etc. Following sentences shows the occurance of these reduplicated quantifiers in Bangla :-

i. kichu kichu boi bhalo

some some book good

“ Some of the books are good.”

ii. kono kono lok bhalo

Some some people good

“ Some of the people are good.”

iii. Keu keu mela –te esechilo

Some some fair -loc. come.perf.

“ Some of the people have come to the fair.”

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3.3. Adverbial and Adjectival Oquantifiers :-

The quantifiers in Bangla, sometimes occurs as an adjective or

adverbial modifiers. For example,

i. ekʈu jɔl

little water

ii. ɔlpo chini

some sugar

The example sentences shows the – count quantifiers occurring as

an adjective modifier. The same quantifiers combined with a verb functions as an adverbial

modifiers. For example ,

iii. ekʈu hɑ̃ʈa

little walk/walking.

iv. ɔlpo hɑ̃ʈa

some walk/walking.

In Bangla, the classifier, such as ‘-ʈa ‘combines with the

quantifiers and takes on the function of a determiner and specifier. For example, /eto̪ʈa /

(this much), /eto̪kʰani / (this many), /eto̪gulo/ ( this many ) etc.

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3.4. Composite Quantifiers :-

There are some composite quantifiers in Bangla too. For

example, / ɔlpo kichu/ (some/few, ± count), /ekʈu kʰani / (some, -count), / ekʈu besi/ (little

much) etc. These composite or complex quantifiers occur to denote the Partitive readings in

Bangla NPs. The composite quantifier / ekʈu besi/ also occurs as an adverbial modifier. The

following sentences exemplifies the occurrence of these composite quantifiers in Bangla :-

i. mela –te ɔlpo kichu lok -i eshechilo

fair -loc. few people -emp. come.past.perf.

“Few people had come to the fair.”

ii. ami ekʈu kʰani jɔl kʰabo

I little water drink.fut.

“I’ll drink a little water.”

iii. ami eʈo ʈuku –i jɔl kʰabo.

I this much -emp. water drink.fut.

“I’ll drink only this much water.”

In the above examples, the interaction of the composite quantifiers with the emphatic

markers occurs due to the shift of emphasis on the partitives. This phenomena requires

further research.

3.5. Implicit Quantification :-

The implicit quantification occurs in Bangla, by reduplicating a NP.

In sentences, where there is no overt quantifier present, the implicit quantifiers denote

plurality by reduplicating a singular set of individuals or objects. The following sentences

exemplify this phenomenon:-

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i. “amar pɔt ̪he pɔt ̪he pat ̪hor chɔrano”

my road road stone scatter.pres.

“ There are many stones in my roads.”

ii. “ghɔre ghɔre sei barta̪ roti -gelo krome.”

House house that news spread -asp. Slowly

“Slowly that news has spread in every house.”

iii. “goli -te goli -te baje sanai”

alley –loc. alley -loc. play.pres. shehnai

“Shehnai is being played in every alley.”

iv. kɔt ̪haye kɔt ̪haye ɔnek d̪eri hoe gelo

word word much late happen.perf.

“ It has got much late by talking (to you).”

The examples shows that, by reduplicating the NPs with their case markers, the NP set is

doubled in the proposition and it denotes plurality. The reduplicated Noun Phrases in those

sentences behaves like an implicit quantifier,that quantifies over the set of entities/objects.

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4. Analysis :-

The applications of the Generalized Quantifier Theory to the

Bangla language data has been analysed in the following sections.

4..1. Formalization :-

The Bangla quantifiers can be formalized following the framework of

the Generalized Quantifier theory. Quantifier is an operator that operates on the Nominal.

For example, ‘∀x (x : Boy)’ denotes that every x is such that x is a boy. In Bangla, there is a

distinction between ‘every’ and ‘each.’ Following examples describes the distinction :-

i. sɔb chele -ra kh elche.

Every boy - plu play.pres.con.

“Every boy is playing”.

ii. protek chele kh elche.

Each boy play.pres.con.

“Each boy is playing.”

So, we can formalize, both the quantifiers using the ‘∀x (x : Boy)’ formulae. However, the

NP, ‘protek chele’ denotes a specific and definite reading. The quantifier / protek/ quantifies over

a specific set of entities, i.e. ‘boys’ , within a given context. Whereas, / sɔb/ quantifies over to a more

general set of individuals/boys within a larger context.

The partitive readings of the Bangla quantifiers can be formalized

using the set theoretic notions. For example :- the reduplicated quantifier /kono kono/ in

the sentence, ‘kono kono lok bhalo’ can be formalized as, ,P: Person’ ⊆x} . For example, if

Ram includes the property set of being /bhalo/ (good), i.e. (R : p ∈ happy’), and iff (R ⊆ P) ,

then the proposition yields the truth value T.

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4.2. Scope Interaction :-

The quantifier /kauke/ in Bangla is a + count and + human

quantifier. The following sentences shows the scope interaction between the negative

phrase (Neg.P.) and noun phrase (NP) in Bangla. For example :-

i. ami kauke cini na

I no one know neg.

“I know no one./ I don’t know anyone.”

ii. ami kauke kauke cini na

I some some know.pres. neg.

“ I don’t know some people.”

The quantifier /kauke/ in the example (iii) expresses that, everyone is such that I don’t know

anyone. In this sentence the Neg takes scope over the NP. This can be formalized in first

order predicate calculus , as,

¬ ( ∀ : Person x) (∃ : Person y) [know(x,y)]

In the (iv) example, the NP takes wide scope over the Neg. This sentence expresses that,

there is some people such that I don’t know him/her. This can be translated in the first

order logic, as,

(∃ : Person y) ¬ (∃ : Person x) [know (x,y)]

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5. Conclusion :-

In , this paper, the focus has been on the Semantics of

the Noun Phrases in general with special attention to the Quantificational Noun Phrases. I

have discussed the different approaches to quantification in Formal semantics and given an

overview of the literature. However, the main objective was to draw an uniform survey of

the different quantifiers in Bangla and propose some analysis following the Generalized

Quantifier Theory. Some of the quantifiers could have been captured using the formalism

and some of them have showed more ambiguity and complexity. Nonetheless, more in

depth further research is needed to resolved the unsolved issues in the semantics of

quantificational noun phrases in Bangla.

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Readings’. Oxford/Malden, MA : Blackwell Publishing.

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8) Giannakidou, Anastasia. and Rathert, Monika.(eds). 2009. ‘Quantification,

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9) Carlson, Gregory.N. 1980 . ‘Reference to kinds in English’. In ‘Outstanding

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10) Kennedy, Christopher. 1997. ‘ Antecedent- Contained Deletion and the Syntax of

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