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Quantifier Raising in a Top-Down Grammar. Valentina Bianchi & Cristiano Chesi University of Siena XVII Colloquium on Generative Grammar Girona, June 13, 2007. The initial assimilation. QR is another instance of Move (1) a. Mary see who  Who did Mary see t ?

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quantifier raising in a top down grammar

Quantifier Raisingin a Top-Down Grammar

Valentina Bianchi & Cristiano Chesi

University of Siena

XVII Colloquium on Generative Grammar

Girona, June 13, 2007

the initial assimilation
The initial assimilation
  • QR is another instance of Move

(1) a. Mary see whoWho did Mary see t?

b. Mary saw nobodyNobody Mary saw t.

  • Motivation for LF-covert syntax
  • Similar locality constraints (Cecchetto 2004)

(2) a. A technician will complain [if you damage every plane]. (>, *>)

b. *What will a technician complain [if you damage t]?

(3) a.Which movie did you see t?

a'. *Which movie did you see t and appreciate ‘‘The House of Mirth’’?

b. A (different) student likes every professor. (>,>)

b'. A (#different) student likes every professor and hates the dean. (>, *>)

Bianchi & Chesi – QR in a Top-Down Grammar

move as of june 2007
Move, as of June 2007
  • Agree as a sub-operation of Move  Move is feature-driven
  • Phase Impenetrability Condition  Move is successive-cyclic
  • The “strong” topmost occurrence is spelled out Move is overt and (generally) leftward

Bianchi & Chesi – QR in a Top-Down Grammar

qr as of june 2007
QR, as of June 2007
  • Standard QR is not feature-driven and doesn’t target a specific position: free adjunction
  • QR = A-movement (Hornstein, 1995)
  • QR targets fixed positions (Beghelli & Stowell, 1997)
  • Exception: negative and focussed phrases (Longobardi 1991, Kayne 1981)

Bianchi & Chesi – QR in a Top-Down Grammar

qr as of june 20075
QR, as of June 2007

b) Standard QR is not successive-cyclic; it is clause-bound (tensed clause boundary).

(4) Someone expected [CP that every Republican would win].

(>; *>)

(Exception: indefinites, Reinhart 1997)

≠ Cecchetto (2004): QR obeys the PIC. “Cyclic” steps are possible if they are semantically motivated.

Bianchi & Chesi – QR in a Top-Down Grammar

qr as of june 20076
QR, as of June 2007

c1) Standard QR is covert (but see Szabolsci 1997, Kayne 1998). With cyclic Transfer, this no longer follows from the architecture of the grammar.

c2) Fox & Nissenbaum (1999), Fox (2002): QR must be rightward.

(5) a. We [[saw a painting] yesterday]

b. We[[[saw a painting] yesterday] <a painting>]

c. We [[[saw a painting] yesterday] <a painting> by John]

Bianchi & Chesi – QR in a Top-Down Grammar

tacking stock
Tacking stock
  • QR is not a well-behaved instance of Move(e.g. Beghelli & Stowell: feature-driven, but not cyclic; Cecchetto: PIC-compliant, but not feature-driven).
  • The covert nature of QR no longer follows from the architecture of the grammar.

Bianchi & Chesi – QR in a Top-Down Grammar

reversing the perspective
Reversing the perspective

Main claim:

The exceptional properties of QR follow if we assume a top-down, left-to-right computation divided in phases

(Phillips 1996, Chesi 2004, Bianchi & Chesi 2006)

In a nutshell:

  • remove the QP since not LF-interpretable
  • re-merge it in a position when it can take an adequate argument/nuclear scope

Bianchi & Chesi – QR in a Top-Down Grammar

slide9

Formalizing a minimalist grammar

  • Feature Structures(lexicon + parameterization)
  • Universals(structural constraints + economy conditions)
  • Structure Building Operations(merge, move, phase)

Bianchi & Chesi – QR in a Top-Down Grammar

slide10

1 – Feature Structures

base = {N, V}

select = {base licensors}

Only TWO main categories: Nouns and Verbs

(e.g. [V give])

Lexical selection

(e.g. [=DP =DP =PPVgive])

Ordered sets of functional features

(e.g. [=DP =DP =PP ... +Mood ... +T ... Vgive];

DP  [ +D N ];PP  [ +K +D N ] )

Bianchi & Chesi – QR in a Top-Down Grammar

slide11

2 – Universals

B

dominance:

B > A

B > C

B

A

B

C

precedence:

<A, B, C>

Linearization Principle(inspired by LCA, Kayne 1994) if A dominates B, then either a. A precedes B if B is a complement of A (that is, A selects B), or b. B precedes A if B is in a functional projectionof A

+ time

Bianchi & Chesi – QR in a Top-Down Grammar

slide12

3 - Structure Building Operations

V

Vgives

NJohn

  • a. MERGE (merge right, Phillips 1996)
  • Lexicon: {[=DP =PP V gives], [+K (N) to], [+D N John], [+D N children], [+D N candies]}
  • merge ([=DP =DP=PP Vgives], [+D NJohn])
slide13

3 - Structure Building Operations

V

Vgives

V

V<gives>

NJohn

  • a. MERGE (merge right, Phillips 1996)
  • Lexicon: {[=DP =PP V gives], [+K (N) to], [+D N John], [+D N children], [+D N candies]}
  • merge ([=DP =DP=PP Vgives], [+D NJohn])
slide14

3 - Structure Building Operations

  • a. MERGE (merge right, Phillips 1996)
  • Lexicon: {[=DP =PP V gives], [+K (N) to], [+D N John], [+D N children], [+D N candies]}
  • merge ([=DP =DP=PP Vgives], [+D NJohn])
  • merge ([=DP =DP=PP Vgives], [+D Ncandies])

V

Vgives

V

NJohn

V

V<gives>

V

V<gives>

Ncandies

slide15

3 - Structure Building Operations

  • a. MERGE (merge right, Phillips 1996)
  • Lexicon: {[=DP =PP V gives], [+K (N) to], [+D N John], [+D N children], [+D N candies]}
  • merge ([=DP =DP=PP Vgives], [+D NJohn])
  • merge ([=DP =DP=PP Vgives], [+D Ncandies])
  • merge ([=DP=DP =PPV gives], [+K +D N to children])

V

Vgives

V

NJohn

V

V<gives>

V

V

Ncandies

V<gives>

N

to children

slide16

3 - Structure Building Operations

V

Force ...

(left periphery)

V

V

V

Mood

V

...

Functional

Sequence

(licensor features)

Asp

V

V

head

Selected Phase(s)

(select features)

M(ove)-Buffer

c. MOVE

Linearization Principle (inspired by Kayne’s LCA) if A immediately dominates B, then either a. <A, B> if A selects B as an argument, or b. <B, A> if B is in a functional specification of A

e.g. “the boy kissed the girl”

Success condition: M-buffer(s) must be empty at the end of the computation

b. PHASE (PROJECTION)

Phase selection requirement: phases must be properly (licensed/)selected

[+T kiss]

[=s =o kiss]

the boy

[=s =o kiss]

kissed

[=okiss]

V

<the boy>

the girl

the boy

M-Buffer

slide17

Successive Cyclic A'-movement

Who

do

Lic.

you

Sel.

who= 1st Nested Phase (DP)

you= 2nd Nested Phase (DP)

Matrix Phase (CP)

that= Selected Phase (CP)

believe

you

<you>

who

<who>

that

who

M(ove)-Buffer

(Matrix Phase, CP)

John

admires

<who>

(6) Whoi do you believe [twhothat John admires twho]?

Bianchi & Chesi – QR in a Top-Down Grammar

slide18

To summarize

  • Every computation is a top-down process divided in phases. Each lexical phase head licenses a left-hand functional domain and some right-hand selected positions.
  • A phase n gets closed when all the functional and selectional specifications of its head are satisfied. Any internal constituent will be a computationally nestedphase.
  • The Move operation stores an unselected element found before (i.e. on the left of) the head position in the local M-buffer of the current phase, and discharges it in a selected position if possible; if not, when the phase is closed the content of the memory buffer is inherited by that of the lowest selected phase (the sequential phase, Chesi 2004).

Bianchi & Chesi – QR in a Top-Down Grammar

a fundamental asymmetry

M1

4

2

P2

P3

1

3

What did John buy tP3

<P2>

What

John

<P3>

P3

P4

P2

P1

P5

A fundamental asymmetry

Overt movement: the system first computes the displaced occurrence in a functionally licensed (criterial) position, stores the element in a M(ove)-memory buffer, and then looks for a selected position where the element can be re-merged.

Bianchi & Chesi – QR in a Top-Down Grammar

a fundamental asymmetry20

M1

Q1

P4

P2

2

4

1

3

every book

Mary gave

<P4>

Mary

tP2

to Sue

P4

P5

P2

P3

P1

P6

A fundamental asymmetry

Quantifier Raising: the system computes the QP in an argument position which is PF-interpretable but not LF-interpretable, stores the QP in a Q(uantifier)-memory buffer, and re-merges it at the point where it can be properly interpreted (i.e., at the end of the phase).

Bianchi & Chesi – QR in a Top-Down Grammar

an implementation of qr
An implementation of QR
  • Compute a QP and spell it out in the selected (or functionally licensed) position within phase n.
  • Insert the QP in the Q-buffer of phase n with index i (QPi)
  • Insert a variable with index i in the selected position.
  • At the end of the computation of phase n, retrieve QPi from the Q-buffer of n and attach it to the structure built in phase n.
  • Success Condition: at the end of any phase n, the Q-buffer of n must be empty.

Bianchi & Chesi – QR in a Top-Down Grammar

slide22

QR – sample derivation

<every booki>

Fuctional

projections

(7) Mary gave every book to Sue

Mary

VP

shells

gave

V

<Mary>

xi

every book

Mary

to John

M(ove)-Buffer

every booki

Q(uantifier)-Buffer

Bianchi & Chesi – QR in a Top-Down Grammar

main consequences
Main Consequences
  • The re-merge position is (as usually) covert
  • The re-merge position of QR follows the computation of the selected position: “rightward” movement.
  • The clause-boundedness of QR is a “right roof” effect, corresponding to a final phase boundary.

Bianchi & Chesi – QR in a Top-Down Grammar

1 covertness

3

4

M1

Q1

1

P2

P4

2

Mary saw

<P4>

We

tP2

a painting

yesterday

P5

P2

P3

P4

P1

by John

P6

1. Covertness
  • The position computed first is “PF-interpretable” (criterial or argumental position) and the QP phase is spelled out there, before storage in the Q-buffer
  • Remerge positions are generally unpronounced (Chesi 2004)
  • It is possible to implement Late Merge à la Fox & Nissenbaum (1999)

Bianchi & Chesi – QR in a Top-Down Grammar

2 rightward orientation
2. Rightward orientation
  • The first position of the QP dependency is selected or functionally licensed.
  • “Rightward” movement: the re-merge position of QR follows the computation of the selected position.
  • The remerge position implements inverse selection: the structure previously computed in the current phase is the argument of the QP function.

Bianchi & Chesi – QR in a Top-Down Grammar

3 clause boundedness
3. Clause-boundedness

(8) a. What did a technician say [t''that John t'inspected t] ?

b. A technician said [that John inspected every plane]

(∃>∀; *∀>∃)

c.* [every plane] a technician said [t''that John t'inspected t]

(cf. Cecchetto 2004:345 )

  • QR is not successive cyclic:
  • Why no attraction by the edge feature EF?
  • Why no one-step Form Chain?

Bianchi & Chesi – QR in a Top-Down Grammar

3 clause boundedness27
3. Clause-boundedness

The clause-boundedness of QR is a right roof effect.

The QP is stored in the Q-buffer of the current phase n:

  • It takes scope over all the phases nested in n, by rightward attachment;
  • It cannot take scope over any superordinate phase, because this would require either non-local retrieval, or super- copying from the Q-buffer of the current phase into the Q-buffer of a superordinate phase.

Bianchi & Chesi – QR in a Top-Down Grammar

3 clause boundedness28

super-copying

non-local retrieval

3. Clause-boundedness

M1

Q1

5

P2

P2

A technician said that J. inspected every plane

P1

<P2>i

Q4

1

4

P5

2

3

P2

P3

A techniciani

tP2

that J. inspected every plane

P4

<P5>k

P5

every planek

Bianchi & Chesi – QR in a Top-Down Grammar

further consequences
Further Consequences
  • Scope ambiguities Surface Scope Preference
  • Pronominal Binding Leftness Condition

Bianchi & Chesi – QR in a Top-Down Grammar

slide30

1. Scope ambiguities

<every boy1>

<two girls2>

Default derivation:

Surface Scope

x1

invited

Every boy

x2

two girls

two girls2

Q-Buffer

every boy1

(9) Every boy invited two girls

two girls (x2.x1 T invited x2)

every boy (x1.two girls (x2.x1 T invited x2))

slide31

1. Scope ambiguities

<two girls2>

<every boy1>

Reordering in Q-buffer:

Inverse Scope

x1

invited

Every boy

x2

two girls

two girls2

Q-Buffer

every boy1

(9) Every boy invited two girls

 every boy  (x1.x1 T invited x2)

two girls (x2.every boy (x1.x1 T invited x2))

slide32

1. Scope ambiguities

<two girls2>

<every boy1>

Reordering in Q-buffer:

Inverse Scope

x1

invited

Every boy

x2

two girls

DQPs

G/CQPs

every boy1

two girls2

Q-Buffer

two girls (x2.every boy (x1.x1 T invited x2))

2 pronominal binding

M1

R1

P2

P2

4

P1

John loves

2

R4

1

P2

3

5

John

<P2>

his-1 wife

P2

P3

P4

2. Pronominal Binding

Implementation of A-binding (Bianchi 2007a, based on Schlenker 2005):

  • When an R-expression is processed, its referent is stored (step 2) in a phase-local R(eferential)-buffer(≠ M-buffer &Q-buffer: no discharge/remerge);
  • Nested and selected phases inherit the R-buffer of the containing phase (step 4)
  • The bound pronoun retrieves the referent (via a negative index) from within the R-buffer (step 5, and moves it to the last position of the R-buffer, where it is used to evaluate the truth conditions)

Bianchi & Chesi – QR in a Top-Down Grammar

2 pronominal binding34
2. Pronominal Binding

When the pronoun is bound by a QP:

  • After QR (step 1), the bound variable is stored in the local R-buffer (step 3);
  • The pronoun retrieves the variable from the R-buffer in the usual way (step 6)

7

M1

Q1

R1

P2

xi

xi

5

P1

2

<every mani>

Every man loves

1

R4

xi

3

4

6

Every man

xi

his-1 wife

P2

P3

P4

Bianchi & Chesi – QR in a Top-Down Grammar

2 pronominal binding35
2. Pronominal Binding

This mechanism immediately derives the Leftness Condition:

(10) *His wife loves every man.

  • The pronoun can retrieve the Q-bound variable from the R-buffer only after the QP has been processed and the variable has been inserted by the QR operation.
  • Therefore, the processing of the QP must precede the processing of the bound pronoun. (Cf. Schlenker 2005, Shan & Barker 2006).

Q1

R1

P1

Every man loves ...

His wife

P2

Bianchi & Chesi – QR in a Top-Down Grammar

conclusions
Conclusions

Advantages of a top-down derivation:

  • Covertness and rightward orientation of QR
  • Rightward attachment as inverse selection
  • Right roof constraint (i.e., limitation to the immediately containing phase)
  • Preference for surface scope (last in, first out retrieval strategy)
  • Leftness Condition on Q-binding of pronouns

What remains of the initial assimilation of QR to overt instances of Move?

  • Storage mechanism, with phase-local stores (but Q-buffer instead of M-buffer)
  • Emptiness condition (the stored elements must be “discharged” from the store by the end of the phase computation)

Bianchi & Chesi – QR in a Top-Down Grammar

further consequences in progress
Further consequences (in progress)
  • Inverse Linking
  • Lower Scope (vP scope) w.r.t. negation and modals
  • Economy of Scope (Fox 2000)
  • Wh-/QP Scope interactions (Chierchia 1993, Beghelli & Stowell 1997)
  • Cyclic QR (Cecchetto 2004)
  • Semantic Nesting

Bianchi & Chesi – QR in a Top-Down Grammar

1 inverse linking
1. Inverse Linking

(11) [cQPOne apple in [iQPevery basket]] is rotten

How to obtain wide scope of the i(nternal)QP over the c(ontaining)QP?

  • Extraction of iQP from cQP (cf. Sauerland 2005)
  • Adjunction of iQP to cQP (cf. Büring 2004)

3

Q1

4

P2

Q2

P1

2

<P2j>

One apple is rotten

P3

1

One apple

<P3i>

in every basket

P3

P2

Bianchi & Chesi – QR in a Top-Down Grammar

1 inverse linking39
1. Inverse Linking

A pronoun in the matrix phase apparently bound by the iQP must be an E-type pronoun, à la Büring (2004):

(12) [cQPSomebody from [iQPevery city]k ]i hates itsk climate

Somebody from every city hates [the city they are from]’s climate

Problem: how to obtain internal scope of the iQP? (Cf. Heim & Kratzer 1998, 221 ff.) This may follow if the PP can be an independent phase with its own Q-buffer (i.e., akin to a reduced relative).

Bianchi & Chesi – QR in a Top-Down Grammar

2 vp scope
2. VP-scope

(13) Al didn’t attend more than two meetings (Heim & Kratzer 1998:218)

(  QP)  (QP > ):

  • (  QP) the maximum number of meetings that Al attended is two
  • (QP > ) There are more that two meetings such that Al did not attend them

Our top-down system doesn’t have a vP phase with a Q-buffer lying in the scope of negation (cp. Fox’s vP scope). The matrix phase Q-buffer will have scope over negation.

Assume that negation too is stored in the Q-buffer, so that it can take either relative scope w.r.t. the QP. This assumption is also required to account for Quantifier Lowering of a subject QP into the scope of negation (cp. Fox’s lowering to the vP-trace position):

(14) Every arrow didn’t hit the target

Bianchi & Chesi – QR in a Top-Down Grammar

3 economy of scope fox 2000
3. Economy of scope (Fox 2000)

(14) a. A boy admires every teacher. (>), (>)

b. A boy admires every teacher. Mary does, too. (* >), (>)

  • In order to have scope reversal in the first conjunct of (b), the QPs in the Q-buffer must be rearranged
  • No rearrangement of the Q-buffer is required in the second conjunct, because the subject is non-quantificational
  • therefore, the two conjuncts are not semantically parallel.

Does the linear position of the scopally uninformative conjunct matter? Probably not:

(14) c. Yesterday, a guard stood in front of this church,

and a policeman did, in front of every mosque.

(#>),(*>)

Bianchi & Chesi – QR in a Top-Down Grammar

selected references
Selected references

Beghelli, Filippo and Tim Stowell. 1997. Distributivity and negation. In Ways of scope taking, ed. Anna Szabolcsi, 77-109. Dordrecht: Kluwer.

Bianchi, Valentina. 2001. Antisymmetry and the Leftness Condition: Leftness as anti-c-command. Studia Linguistica 55, 1-38.

Bianchi, Valentina. 2007. Non-redundancy and backward anaphora. XXX Glow Colloquium, Tromsoe.

Bianchi, Valentina. & Cristiano Chesi. 2006. Phases, left branch islands, and computational nesting. U.Penn Working Papers in Linguistics 12.1, 15-28.

Büring, Daniel. 2004. Crossover situations. Natural Language Semantics 12, 23-62.

Cecchetto, Carlo. 2004. Explaining the locality conditions of QR: Consequences for the theory of phases. Natural Language Semantics 12, 345-397.

Chesi, Cristiano. 2004. Phases and Cartography in Linguistic Computation. Doct diss., University of Siena.

Fox, Danny. 2000. Economy and semantic interpretation. Cambridge, Mass.: MIT Press.

Fox , Danny & Nissenbaum, Jon. 1999. Extraposition and scope: A case for overt QR. Proceedings of WCCFL 18, 132-144.

Kayne, Richard S. 1998. Overt vs. covert movement. Syntax 1: 128-191.

Reinhart, Tanya. 1983. Anaphora and Semantic Interpretation. Chicago: The University of Chicago Press.

Reinhart, Tanya. 1997. Quantifier scope: how labor is divided between QR and choice functions. Linguistics and Philosophy 20, 335-397.

Sauerland, Uli. 2005. DP is not a scope island. Linguistic Inquiry 36, 303-314.

Schlenker, Philippe. 2005. Non-redundancy: towards a semantic reinterpret-ation of binding theory. Natural Language Semantics 13, 1-92.

Shan, C. & Chris Barker. 2006. Explaining crossover and superiority as left-to-right evaluation. Linguistics and Philosophy 29, 91-134.

Bianchi & Chesi – QR in a Top-Down Grammar