Long-distance dependencies
in continuation grammar
Cara Su-Yi Leong & Michael Yoshitaka Erlewine
mitcho@nus.edu.sg
cara@u.nus.edu
National University of Singapore
PACLIC 33
Future University Hakodate, September 2019

Introduction
Barker & Shan (B&S) develop a Combinatory Categorial Grammar whichuses the notion of continuations for semantic scope-taking. One hallmark
of B&S is their explanatory account of crossover effects (Shan andBarker 2006).
Today: We critically evaluate the B&S framework, based on the behaviorof long-distance dependencies.
• Data from quantifier scope-taking and long-distance dependencies
motivate some refinements to the B&S theory...
• ...but these necessary refinements then result in undoing theirpositive predictions for crossover effects.
 Quantifiers, pronouns, and gaps all “take scope” in the same way for
B&S, but their scope-taking behavior is empirically different. We
show that the B&S framework has fundamental difficulties modelingsuch behavior.
2Introduction
Barker & Shan (B&S) develop a Combinatory Categorial Grammar whichuses the notion of continuations for semantic scope-taking. One hallmark
of B&S is their explanatory account of crossover effects (Shan andBarker 2006).
Today: We critically evaluate the B&S framework, based on the behaviorof long-distance dependencies.
• Data from quantifier scope-taking and long-distance dependencies
motivate some refinements to the B&S theory...
• ...but these necessary refinements then result in undoing theirpositive predictions for crossover effects.
 Quantifiers, pronouns, and gaps all “take scope” in the same way for
B&S, but their scope-taking behavior is empirically different. We
show that the B&S framework has fundamental difficulties modelingsuch behavior.
2Introduction
Barker & Shan (B&S) develop a Combinatory Categorial Grammar whichuses the notion of continuations for semantic scope-taking. One hallmark
of B&S is their explanatory account of crossover effects (Shan andBarker 2006).
Today: We critically evaluate the B&S framework, based on the behaviorof long-distance dependencies.
• Data from quantifier scope-taking and long-distance dependencies
motivate some refinements to the B&S theory...
• ...but these necessary refinements then result in undoing theirpositive predictions for crossover effects.
 Quantifiers, pronouns, and gaps all “take scope” in the same way for
B&S, but their scope-taking behavior is empirically different. We
show that the B&S framework has fundamental difficulties modelingsuch behavior.
2§2 Background: Barker &Shan’s continuationbased grammar

3

B&S: CCG with continuations

Barker and Shan (Barker 2002; Shan 2004, 2007; Shan and Barker 2006;
Barker and Shan 2006, 2008, 2014) develop a CCG using continuations.
We refer to these works collectively as B&S.

DP (DP\ S) / DP
Mary
likes
m
likes

DP
S
← syntactic typeJohn = John likes Mary ← surface formjlikes j m
← denotation

4

B&S: CCG with continuations

Barker and Shan (Barker 2002; Shan 2004, 2007; Shan and Barker 2006;
Barker and Shan 2006, 2008, 2014) develop a CCG using continuations.
We refer to these works collectively as B&S.

DP (DP\ S) / DP
Mary
likes
m
likes

← syntactic typeDP
SJohn = John likes Mary ← surface form
← denotationjlikes j m

4

Continuations

Continuations refer to the “computational future of an expression” (Shanand Barker 2006: 95), i.e. the procedures that will later apply to theexpression. B&S use continuation-passing to implement semantic scope.
In addition to common \ and / type constructors for left and rightcomposition, B&S introduce ) and( for continuation-passing.
Informally, following B&S (2014: 6):• A ) B would be a B if we could add an A inside it;• C( D would be a C if we could add a surrounding D.

5

Continuations

Continuations refer to the “computational future of an expression” (Shanand Barker 2006: 95), i.e. the procedures that will later apply to theexpression. B&S use continuation-passing to implement semantic scope.
In addition to common \ and / type constructors for left and rightcomposition, B&S introduce ) and( for continuation-passing.
Informally, following B&S (2014: 6):• A ) B would be a B if we could add an A inside it;• C( D would be a C if we could add a surrounding D.

5

Multi-level towers

B&S introduce multi-level towers with the interpretation in (??), where
higher levels of the towers represent continuation-passing.
(1)

C

B

C( (A ) B)
A
expression := expression
λκ . f (κ (a))
f[ ]
a

6

Composition of towers

Composing two expressions:
(2)

C

D
A
left-exp
g[ ]
x

D E
A\ B
right-exp
h[ ]
f

C

E
B
= left-exp right-exp
g(h[ ])
f(x)Notice that adjacent types on the higher levels have to match.

7

Composition of towers

Composing two expressions:
(2)

C

D
A
left-exp
g[ ]
x

D E
A\ B
right-exp
h[ ]
f

C

E
B
= left-exp right-exp
g(h[ ])
f(x)Notice that adjacent types on the higher levels have to match.

7

Scope-taking and type-shifters

Scope-taking expressions like quantifiers have two-level denotations.

S S
DP
someone∃x . [ ]x(DP \ S) / DP
likes
likes

S S
DP
everyone∀y . [ ]y8Scope-taking and type-shifters

Scope-taking expressions like quantifiers have two-level denotations.

S S
DP
someone∃x . [ ]x

S S(DP \ S) / DP
likes
[]
likes

S S
DP
everyone∀y . [ ]yWe use lift (??) to match non-scope-taking expressions forcomposition.

8

Scope-taking and type-shifters

Scope-taking expressions like quantifiers have two-level denotations.

S S
DP
someone∃x . [ ]x

S S(DP \ S) / DP
likes
[]
likes

S S
DP
everyone∀y . [ ]ySSS= someone likes everyone∃x . ∀y . [ ]likes y x

8Scope-taking and type-shifters

Scope-taking expressions like quantifiers have two-level denotations.

S S
DP
someone∃x . [ ]x

S S(DP \ S) / DP
likes
[]
likes

S S
DP
everyone∀y . [ ]ySSS= someone likes everyone∃x . ∀y . [ ]likes y xS↓⇒
= someone likes everyone∃x . ∀y . likes y x

We then lower (??) the expression at the end.
8

Scope-taking and type-shifters

We can also derive inverse scope using multi-level towers.
S S
S S
DP
someone[]∃x . [ ]x

S S
S S(DP \ S) / DP
likes
[]
[]
likes

S S
S S
DP
everyone∀y . [ ][]yWe use “internal lift” to raise ∀ to a higher level.

9Scope-taking and type-shifters

We can also derive inverse scope using multi-level towers.
S S
S S
DP
someone[]∃x . [ ]x

S S
S S(DP \ S) / DP
likes
[]
[]
likes

S S
S S
DP
everyone∀y . [ ]
[]
y

S
S

S
S

S
= someone likes everyone∀y . [ ]∃x . [ ]likes y x

9Scope-taking and type-shifters

We can also derive inverse scope using multi-level towers.
S S
S S
DP
someone[]∃x . [ ]x

S S
S S(DP \ S) / DP
likes
[]
[]
likes

S S
S S
DP
everyone∀y . [ ]
[]
y

S
S

S
S

S
= someone likes everyone∀y . [ ]∃x . [ ]likes y x
S↓↓==⇒ someone likes everyone∀y . ∃x . likes y x

9Pronouns

The syntactic category A ▷ B represents a B that contains an unboundpronoun of category A, for example:
DP ▷ S S
DP
heλx . [ ]xPronouns are represented as inherently multi-level towers, meaning thatthey are also scope-taking expressions.

10Pronouns
The DP ▷ S type propagates to the left, denoting an open pronoun exists
in the expression until it is bound (hypothetically).

DP ▷ S DP ▷ S
DP
John
[]
j

DP ▷ S DP ▷ S(DP\ S) / S
said
[]
said

DP ▷ S S
DP
heλx . [ ]xS SDP / S
cried
[]
cried

We apply bind (??) to John for it to bind the pronoun to its right.

11

Pronouns
The DP ▷ S type propagates to the left, denoting an open pronoun exists
in the expression until it is bound (hypothetically).

S

DP ▷ S
DP
John
[ ]j
j

DP ▷ S DP ▷ S(DP\ S) / S
said
[]
said

DP ▷ S S
DP
heλx . [ ]xS SDP / S
cried
[]
cried

We apply bind (??) to John for it to bind the pronoun to its right.

11Movement

Continuation-passing provides an in-situ account of movement
dependencies using gaps.
Gaps introduce a variable and λ binder like pronouns:
DP ) SDPS

λx . [ ]xSimilarly, DP ) S propagates to the left to get bound.

12

Crossover

One advertised feature of B&S’s proposal is its explanation for crossover
effects (Postal 1971) using linear evaluation.
(??) a. Which girli did John introduce

to heri second cousin?

b. ?? Which girli did John introduce heri second cousin to(??) a. ✓whi ...

?

i ... pro ib. * whi ... pro i ...

i13

Crossover

One advertised feature of B&S’s proposal is its explanation for crossover
effects (Postal 1971) using linear evaluation.
(??) a. Which girli did John introduce

to heri second cousin?

b. ?? Which girli did John introduce heri second cousin to(??) a. ✓whi ...

?

i ... pro ib. * whi ... pro i ...

i13

Explaining crossover effects
For B&S, in grammatical wh-pro-binding configurations (??/??a), thegap binds the pronoun to its right.

S/(DP ) S)...
which girlλκ . wh(girl y ∧ κ(y))

DP ) SDP
λx . [ ]xSDP ▷ S S
PP... to her second cousin
λc . [ ]second cousin cbind (??) cannot apply to the fronted wh-phrase itself.
Therefore, the binding is grammatical in (??a), but in (??b) there is nopreceding gap that can bind the pronoun, leading to ungrammaticality.
This explains the crossover asymmetry.
14

Explaining crossover effects
For B&S, in grammatical wh-pro-binding configurations (??/??a), thegap binds the pronoun to its right.

S/(DP ) S)...
which girlλκ . wh(girl y ∧ κ(y))

DP ) S DP ▷ S
DP
λx . [ ] xxDP ▷ S S
PP... to her second cousin
λc . [ ]second cousin cbind (??) cannot apply to the fronted wh-phrase itself.
Therefore, the binding is grammatical in (??a), but in (??b) there is nopreceding gap that can bind the pronoun, leading to ungrammaticality.
This explains the crossover asymmetry.
14

Explaining crossover effects
For B&S, in grammatical wh-pro-binding configurations (??/??a), thegap binds the pronoun to its right.

S/(DP ) S)...
which girlλκ . wh(girl y ∧ κ(y))

DP ) S DP ▷ S
DP
λx . [ ] xxDP ▷ S S
PP... to her second cousin
λc . [ ]second cousin cbind (??) cannot apply to the fronted wh-phrase itself.
Therefore, the binding is grammatical in (??a), but in (??b) there is nopreceding gap that can bind the pronoun, leading to ungrammaticality.
This explains the crossover asymmetry.
14

Explaining crossover effects
For B&S, in grammatical wh-pro-binding configurations (??/??a), thegap binds the pronoun to its right.

S/(DP ) S)...
which girlλκ . wh(girl y ∧ κ(y))

DP ) S DP ▷ S
DP
λx . [ ] xxDP ▷ S S
PP... to her second cousin
λc . [ ]second cousin cbind (??) cannot apply to the fronted wh-phrase itself.
Therefore, the binding is grammatical in (??a), but in (??b) there is nopreceding gap that can bind the pronoun, leading to ungrammaticality.
This explains the crossover asymmetry.
14

Preview§3 B&S does not restrict quantifier scope-taking...
 We formalize a suggested fixAA .

complicates the binding of embedded gaps and pronouns...
 We propose minimal modifications
such examples together with A .

B

so that we can model§4 A and B together lead to incorrect predictions for crossover,undoing a key advantage of the B&S framework.
§5 Discussion

15

Preview§3 B&S does not restrict quantifier scope-taking...
 We formalize a suggested fixAA .

complicates the binding of embedded gaps and pronouns...
 We propose minimal modifications
such examples together with A .

B

so that we can model§4 A and B together lead to incorrect predictions for crossover,undoing a key advantage of the B&S framework.
§5 Discussion

15

Preview§3 B&S does not restrict quantifier scope-taking...
 We formalize a suggested fixAA .

complicates the binding of embedded gaps and pronouns...
 We propose minimal modifications
such examples together with A .

B

so that we can model§4 A and B together lead to incorrect predictions for crossover,undoing a key advantage of the B&S framework.
§5 Discussion

15

Preview§3 B&S does not restrict quantifier scope-taking...
 We formalize a suggested fixAA .

complicates the binding of embedded gaps and pronouns...
 We propose minimal modifications
such examples together with A .

B

so that we can model§4 A and B together lead to incorrect predictions for crossover,undoing a key advantage of the B&S framework.
§5 Discussion15

§3 Scope-taking acrossclause boundaries

16

Scope(??) # Someone said [everyone is married to Sue].

✓∃ > ∀, *∀ > ∃17

B&S overgenerates
B&S overgenerates the unattested inverse-scope reading of Someone said
everyone is married to Sue (??):
S S
S S
DP
someone[]∃x . [ ]x

S S
S S(DP \ S) / S
said
[]
[]
said
S
S

S S
S S
DP
everyone∀y . [ ]
[]
y

S S
S S
DP \ S
is married to Sue[][]married to s

S
S

S
S
↓↓
= sm. said ev. is married to Sue ==⇒ sm. said ev. is married to Sue∀y . ∃x . said (married to s y) x
∀y . [ ]∃x . [ ]said (married to s y) x

18

B&S overgenerates
B&S overgenerates the unattested inverse-scope reading of Someone said
everyone is married to Sue (??):
S S
S S
DP
someone[]∃x . [ ]x

S S
S S(DP \ S) / S
said
[]
[]
said
S
S

S S
S S
DP
everyone∀y . [ ]
[]
y

S S
S S
DP \ S
is married to Sue[][]married to s

S
S

S
S
↓↓
= sm. said ev. is married to Sue ==⇒ sm. said ev. is married to Sue∀y . ∃x . said (married to s y) x
∀y . [ ]∃x . [ ]said (married to s y) x

18

B&S overgenerates
B&S overgenerates the unattested inverse-scope reading of Someone said
everyone is married to Sue (??):
S S
S S
DP
someone[]∃x . [ ]x

S S
S S(DP \ S) / S
said
[]
[]
said
S
S

S S
S S
DP
everyone∀y . [ ]
[]
y

S S
S S
DP \ S
is married to Sue[][]married to s

S
S

S
S
↓↓
= sm. said ev. is married to Sue ==⇒ sm. said ev. is married to Sue∀y . ∃x . said (married to s y) x
∀y . [ ]∃x . [ ]said (married to s y) x

18

Scope Island Evaluation

B&S note this problem. Charlow (2014: 65) suggests that scope islands
must be evaluated by “collapsing it into a single level.”
We codify this requirement as follows:(??) Scope Island Evaluation
If the expression is a scope island, apply lower as many times as
possible (↓*).

Embedded tensed clauses are scope islands.

19

Scope Island Evaluation

B&S note this problem. Charlow (2014: 65) suggests that scope islands
must be evaluated by “collapsing it into a single level.”
We codify this requirement as follows:(??) Scope Island Evaluation
If the expression is a scope island, apply lower as many times as
possible (↓*).

Embedded tensed clauses are scope islands.

19

Scope Island Evaluation

B&S note this problem. Charlow (2014: 65) suggests that scope islands
must be evaluated by “collapsing it into a single level.”
We codify this requirement as follows:(??) Scope Island Evaluation
If the expression is a scope island, apply lower as many times as
possible (↓*).

Embedded tensed clauses are scope islands.

19

Scope Island Evaluation

S S
S S
DP
someone[]∃x . [ ]x

S S
S S(DP \ S) / S
said
[]
[]
said

S S
S S
S S
S S
DP
DP\ S
everyone is married to Sue∀y . [ ][][][]ymarried to s

20

Scope Island Evaluation

S S
S S
DP
someone[]∃x . [ ]x

S S
S S(DP \ S) / S
said
[]
[]
said

S
S

S
S

S
everyone is married to Sue∀y . [ ][]married to s y20Scope Island Evaluation

S S
S S
DP
someone[]∃x . [ ]x

S S
S S(DP \ S) / S
said
[]
[]
said

S
everyone is married to Sue∀y . married to s y20Scope Island Evaluation

S S
S S
DP
someone[]∃x . [ ]x

S S
S S(DP \ S) / S
said
[]
[]
said

S
S

S
S

S
everyone is married to Sue[][]∀y . married to s y20Scope Island Evaluation

S S
S S
DP
someone[]∃x . [ ]
x
↓↓

==⇒

S S
S S
(DP \ S) / S
said
[]
[]
said

S
S

S
S

S
everyone is married to Sue[][]∀y . married to s ySsm. said ev. is married to Sue∃x . ∀y . said (married to s y) x

20

Problems with embedded gaps and pronouns

Recall that pronouns and gaps are “scope-taking” in B&S: they posit a λbinder on a higher level, to be bound from the left.
(??) a.

✓Which girli did you say [Mary sawb.

✓Every girli said [Mary saw heri ].

i ]?

 Scope Island Evaluation blocks the binding of gaps (10a) andpronouns (10b) in embedded tensed clauses, contrary to fact.

21

Problems with embedded gaps and pronouns

Recall that pronouns and gaps are “scope-taking” in B&S: they posit a λbinder on a higher level, to be bound from the left.
(??) a.

✓Which girli did you say [Mary sawb.

✓Every girli said [Mary saw heri ].

i ]?

 Scope Island Evaluation blocks the binding of gaps (10a) andpronouns (10b) in embedded tensed clauses, contrary to fact.

21

Problems with embedded gaps and pronouns

Recall that pronouns and gaps are “scope-taking” in B&S: they posit a λbinder on a higher level, to be bound from the left.
(??) a.

✓Which girli did you say [Mary sawb.

✓Every girli said [Mary saw heri ].

i ]?

 Scope Island Evaluation blocks the binding of gaps (10a) andpronouns (10b) in embedded tensed clauses, contrary to fact.

21

Embedded gaps
Clauses with DP gaps that undergo Scope Island Evaluation will be ofcategory DP \ S, the category of a clause missing a DP to its left.
DP ) S DP ) S
DP
Mary
[]
m

DP ) S DP ) S(DP\ S) / DP
saw
[]
saw

DP ) SDP
λx . [ ]xSDP ) S S
S= Mary saw
λx . [ ]saw x m• The syntactic category of the expression cannot compose as a S.
• The λ binder for the gap is on the lowest level and ceases topropagate as a scope-taking expression.

22

Embedded gaps
Clauses with DP gaps that undergo Scope Island Evaluation will be ofcategory DP \ S, the category of a clause missing a DP to its left.
DP ) S DP ) S
DP
Mary
[]
m

DP ) S DP ) S(DP\ S) / DP
saw
[]
saw

DP ) SDP
λx . [ ]xS
DP \ S= Mary saw
λx . saw x m• The syntactic category of the expression cannot compose as a S.
• The λ binder for the gap is on the lowest level and ceases topropagate as a scope-taking expression.

22

Embedded gaps: Intermediate gaps

We resolve this problem by positing intermediate gaps at the left edge of
gapped clauses after they undergo Scope Island Evaluation.
(??)

DP ) SDP
λy . [ ]yS
DP\ SMary saw
λx . saw x m=DP ) S SSMary saw
λy . [ ]saw y mAdding the intermediate gap results in the same meaning as theembedded clause prior to Scope Island Evaluation.

23

Embedded gaps: Intermediate gaps

We resolve this problem by positing intermediate gaps at the left edge of
gapped clauses after they undergo Scope Island Evaluation.
(??)

DP ) SDP
λy . [ ]yS
DP\ SMary saw
λx . saw x m=DP ) S SSMary saw
λy . [ ]saw y mAdding the intermediate gap results in the same meaning as theembedded clause prior to Scope Island Evaluation.

23

Embedded gaps: Intermediate gaps

We resolve this problem by positing intermediate gaps at the left edge of
gapped clauses after they undergo Scope Island Evaluation.
(??)

DP ) SDP
λy . [ ]
y

S

S S
DP\ S
Mary saw[]
λx . saw x m=DP ) S SSMary saw
λy . [ ]saw y mAdding the intermediate gap results in the same meaning as theembedded clause prior to Scope Island Evaluation.

23

Embedded gaps: Intermediate gaps

We resolve this problem by positing intermediate gaps at the left edge of
gapped clauses after they undergo Scope Island Evaluation.
(??)

DP ) SDP
λy . [ ]
y

S

S S
DP\ S
Mary saw[]
λx . saw x m=DP ) S SSMary saw
λy . [ ]saw y mAdding the intermediate gap results in the same meaning as theembedded clause prior to Scope Island Evaluation.

23

Embedded gaps: Intermediate gaps

We resolve this problem by positing intermediate gaps at the left edge of
gapped clauses after they undergo Scope Island Evaluation.
(??)

DP ) SDP
λy . [ ]
y

S

S S
DP\ S
Mary saw[]
λx . saw x m=DP ) S SSMary saw
λy . [ ]saw y mAdding the intermediate gap results in the same meaning as theembedded clause prior to Scope Island Evaluation.

23

Embedded pronouns
We encounter a similar problem with embedded bound pronouns:
DP ▷ S DP ▷ S
DP
Mary
[]
m

DP ▷ S DP ▷ S(DP\ S) / DP
saw
[]
saw

DP ▷ S S
DP
her
λx . [ ]x=DP ▷ S SSMary saw her
λx . [ ]saw x m• The resulting expression after Scope Island Evaluation is of category
DP ▷ S and cannot combine with an S-selecting verb.
• An additional problem: no existing expressions combine withexpressions of category DP ▷ S on the lowest level.

24

Embedded pronouns
We encounter a similar problem with embedded bound pronouns:
DP ▷ S DP ▷ S
DP
Mary
[]
m

DP ▷ S DP ▷ S(DP\ S) / DP
saw
[]
saw

DP ▷ S S
DP
her
λx . [ ]xDP ▷ S= Mary saw her
λx . saw x m• The resulting expression after Scope Island Evaluation is of category
DP ▷ S and cannot combine with an S-selecting verb.
• An additional problem: no existing expressions combine withexpressions of category DP ▷ S on the lowest level.

24

Embedded pronouns: prolift
We propose a new type-shifter:
(??)

B C
DP ▷ A
proliftexpression ======⇒f[ ]λx . g(x)DP ▷ B C
A
expression
λx . f [ ]g(x)prolift returns the pronoun’s λ binder and corresponding
DP ▷-category to a higher level from which it can propagate leftward.

25

Embedded pronouns: prolift
We propose a new type-shifter:
(??)

B C
DP ▷ A
proliftexpression ======⇒f[ ]λx . g(x)DP ▷ B C
A
expression
λx . f [ ]g(x)prolift returns the pronoun’s λ binder and corresponding
DP ▷-category to a higher level from which it can propagate leftward.

DP ▷ S
Mary saw her
λx . saw x m
25

Embedded pronouns: prolift
We propose a new type-shifter:
(??)

B C
DP ▷ A
proliftexpression ======⇒f[ ]λx . g(x)DP ▷ B C
A
expression
λx . f [ ]g(x)prolift returns the pronoun’s λ binder and corresponding
DP ▷-category to a higher level from which it can propagate leftward.
S S
DP ▷ S
Mary saw her[]
λx . saw x m
25

Embedded pronouns: prolift
We propose a new type-shifter:
(??)

B C
DP ▷ A
proliftexpression ======⇒f[ ]λx . g(x)DP ▷ B C
A
expression
λx . f [ ]g(x)prolift returns the pronoun’s λ binder and corresponding
DP ▷-category to a higher level from which it can propagate leftward.
DP ▷ S SSMary saw her
λx . [ ]saw x m25

Summary• To accurately model restrictions on quantifier scope-taking, we
codified a suggestion by Charlow (2014) as Scope Island Evaluation.
• To model the grammatical binding of embedded gaps and pronouns
and maintain Scope Island Evaluation, we proposed intermediate
gaps and prolift.

26

Summary• To accurately model restrictions on quantifier scope-taking, we
codified a suggestion by Charlow (2014) as Scope Island Evaluation.
• To model the grammatical binding of embedded gaps and pronouns
and maintain Scope Island Evaluation, we proposed intermediate
gaps and prolift.

26§4 Crossover in long-distanceconfigurations

27

Consequences for crossover

These three amendments to the theory — Scope Island Evaluation,intermediate gaps, and prolift, all necessary to account for the behavior of quantifier scope-taking as well as long-distance dependencies— together lead to incorrect predictions for crossover effects.

28

Crossover with embedded clauses
Recall that the derivation and explanation of crossover asymmetries (??)
were claimed to be an advantage of the B&S framework.
(??) a. ✓whi ...

i ... pro ib. * whi ... pro i ...

i The revised B&S framework predicts the crossover violation in (??b)
to be grammatical, contrary to fact.
(??) a.
b.

Which girli do you think [??

loves heri mother]?

Which girli do you think [heri mother loves]?

For grammatical embedded gap binding, we hypothesize an intermediate
gap. This gap precedes the pronoun and can bind it!
29

Crossover with embedded clauses
Recall that the derivation and explanation of crossover asymmetries (??)
were claimed to be an advantage of the B&S framework.
(??) a. ✓whi ...

i ... pro ib. * whi ... pro i ...

i The revised B&S framework predicts the crossover violation in (??b)
to be grammatical, contrary to fact.
(??) a.
b.

Which girli do you think [??

loves heri mother]?

Which girli do you think [heri mother loves]?

For grammatical embedded gap binding, we hypothesize an intermediate
gap. This gap precedes the pronoun and can bind it!
29

Crossover with embedded clauses
Recall that the derivation and explanation of crossover asymmetries (??)
were claimed to be an advantage of the B&S framework.
(??) a. ✓whi ...

i ... pro ib. * whi ... pro i ...

i The revised B&S framework predicts the crossover violation in (??b)
to be grammatical, contrary to fact.
(??) a.
b.

Which girli do you think [??

Which girli do you thinkloves heri mother]?
i [heri mother loves]?

For grammatical embedded gap binding, we hypothesize an intermediate
gap. This gap precedes the pronoun and can bind it!
29

Crossover with embedded clauses
Recall that the derivation and explanation of crossover asymmetries (??)
were claimed to be an advantage of the B&S framework.
(??) a. ✓whi ...

i ... pro ib. * whi ... pro i ...

i The revised B&S framework predicts the crossover violation in (??b)
to be grammatical, contrary to fact.
(??) a.
b.

Which girli do you think [??

Which girli do you thinkloves heri mother]?
i [heri mother loves]?

For grammatical embedded gap binding, we hypothesize an intermediate
gap. This gap precedes the pronoun and can bind it!
29??

Which girli do you think [heri mother loves

DP ) S DP ) S(DP \ S) / DP
loves
[]
loves

DP ▷ (DP ) S) DP ) SDP
her mother
λd . [ ]mother d=

DP ▷ (DP ) S) SS
her mother loves
λd . λx . [ ]loves x (mother d)

↓∗

==⇒

DP ) SDP]?

S

λx . [ ]xDP ▷ (DP ) S)
lift, prolift===========⇒
her mother loves
λd . λx . loves x (mother d)

30

??

Which girli do you think [heri mother loves

DP ) S DP ) S(DP \ S) / DP
loves
[]
loves

DP ▷ (DP ) S) DP ) SDP
her mother
λd . [ ]mother d=

DP ▷ (DP ) S) SS
her mother loves
λd . λx . [ ]loves x (mother d)

↓∗

==⇒

DP ) SDP]?

S

λx . [ ]xDP ▷ (DP ) S)
lift, prolift===========⇒
her mother loves
λd . λx . loves x (mother d)

30

??

Which girli do you think [heri mother loves

DP ) S DP ) S
DP
you
[]
you

DP ) S DP ) S(DP \ S) / S
think
[]
think

DP ) S S
S
her mother loves= you think
λy . [ ]loves y (mother y)

DP ) S DP ▷ S
DPλy . [ ] yy]?

DP ▷ S S
DP \ S
her mother loves
λd . [ ]λx . loves x (mother d)DP ) S↓∗
her mother loves==⇒ you think
λy . loves y (mother y)

31

??

Which girli do you think [heri mother loves

DP ) S DP ) S
DP
you
[]
you

DP ) S DP ) S(DP \ S) / S
think
[]
think

DP ) S S
S
her mother loves= you think
λy . [ ]loves y (mother y)

DP ) S DP ▷ S
DPλy . [ ] yy]?

DP ▷ S S
DP \ S
her mother loves
λd . [ ]λx . loves x (mother d)DP ) S↓∗
her mother loves==⇒ you think
λy . loves y (mother y)

31

??

Which girli do you think [heri mother loves]?

S/(DP ) S)
DP ) S
which girl
you thinkher mother loves
λκ . wh(λg . girl g ∧ κ (g))λy . loves y (mother y)S= which girl do you think
her mother loves
wh(λg . girl g ∧ loves g (mother g))

32

Summary

Scope Island Evaluation, intermediate gaps, and prolift — all necessary to model both quantifier scope-taking and long-distance binding— together overgenerates long-distance crossover configurations suchas (??b) as acceptable.

33§5 Discussion

34

Summary

B&S develop a CCG where continuations are passed linearly to model
scope-taking and binding.
A claimed advantage of this framework (Shan and Barker 2006) is its
explanation for crossover effects (Postal 1971).

35

Summary

B&S develop a CCG where continuations are passed linearly to model
scope-taking and binding.
A claimed advantage of this framework (Shan and Barker 2006) is its
explanation for crossover effects (Postal 1971).

35

Summary
Today, we discussed the behavior of quantifiers, pronouns, and gaps in
embedded clauses, which have not been seriously discussed previously inthis literature.
• Limitations on quantifier scope-taking motivate Scope Island
Evaluation, a requirement that all scope islands (including embedded
tensed clauses) be fully lower-ed.
• The availability of long-distance movement and binding
dependencies motivated further refinements to the theory.
• The revised B&S theory correctly accounts for limitations on
quantifier scope, while allowing for long-distance movement andbinding, but makes incorrect predictions for crossover effects.

36Summary
Today, we discussed the behavior of quantifiers, pronouns, and gaps in
embedded clauses, which have not been seriously discussed previously inthis literature.
• Limitations on quantifier scope-taking motivate Scope Island
Evaluation, a requirement that all scope islands (including embedded
tensed clauses) be fully lower-ed.
• The availability of long-distance movement and binding
dependencies motivated further refinements to the theory.
• The revised B&S theory correctly accounts for limitations on
quantifier scope, while allowing for long-distance movement andbinding, but makes incorrect predictions for crossover effects.

36Summary
Today, we discussed the behavior of quantifiers, pronouns, and gaps in
embedded clauses, which have not been seriously discussed previously inthis literature.
• Limitations on quantifier scope-taking motivate Scope Island
Evaluation, a requirement that all scope islands (including embedded
tensed clauses) be fully lower-ed.
• The availability of long-distance movement and binding
dependencies motivated further refinements to the theory.
• The revised B&S theory correctly accounts for limitations on
quantifier scope, while allowing for long-distance movement andbinding, but makes incorrect predictions for crossover effects.

36Choose two:37

Choose two:37

The problem
At issue is B&S’s uniform treatment of quantifier scope-taking,pronominal binding, and filler-gap (movement) dependencies.
But these dependencies are sensitive to different locality restrictions:• Quantifiers generally resist scoping out of tensed clauses, although
there is some speaker variation (Wurmbrand 2018).
• Movement dependencies can cross tensed clauses, but are sensitive
to syntactic islands (Ross 1967).
• Pronominal binding is insensitive to both tensed clause boundaries
and syntactic islands.
 Our demonstration here challenges a unified approach to these
phenomena, in turn challenging the B&S program itself.
38

The problem
At issue is B&S’s uniform treatment of quantifier scope-taking,pronominal binding, and filler-gap (movement) dependencies.
But these dependencies are sensitive to different locality restrictions:• Quantifiers generally resist scoping out of tensed clauses, although
there is some speaker variation (Wurmbrand 2018).
• Movement dependencies can cross tensed clauses, but are sensitive
to syntactic islands (Ross 1967).
• Pronominal binding is insensitive to both tensed clause boundaries
and syntactic islands.
 Our demonstration here challenges a unified approach to these
phenomena, in turn challenging the B&S program itself.
38

The problem
At issue is B&S’s uniform treatment of quantifier scope-taking,pronominal binding, and filler-gap (movement) dependencies.
But these dependencies are sensitive to different locality restrictions:• Quantifiers generally resist scoping out of tensed clauses, although
there is some speaker variation (Wurmbrand 2018).
• Movement dependencies can cross tensed clauses, but are sensitive
to syntactic islands (Ross 1967).
• Pronominal binding is insensitive to both tensed clause boundaries
and syntactic islands.
 Our demonstration here challenges a unified approach to these
phenomena, in turn challenging the B&S program itself.
38

Thank you!

We thank Chris Barker for helpful correspondence and encouraging
discussion and Kenyon Branan for comments on this presentation.

Questions?

39

References I
Barker, Chris. 2002. Continuations and the Nature of Quantification. Natural
Language Semantics 10:211–242.
Barker, Chris, and Chung-Chieh Shan. 2006. Types as Graphs: Continuations
in Type Logical Grammar. Journal of Logic, Language and Information
15:331–370.
Barker, Chris, and Chung-Chieh Shan. 2008. Donkey anaphora is in-scopebinding. Semantics and Pragmatics 1:1–46.
Barker, Chris, and Chung-Chieh Shan. 2014. Continuations and Natural
Language. Oxford University Press.
Charlow, Simon. 2014. On the semantics of exceptional scope. Doctoral
Dissertation, New York University.
Postal, Paul M. 1971. Cross-over Phenomena. Holt, Rinehart and Winston.
Ross, John Robert. 1967. Constraints on variables in syntax. Doctoral
Dissertation, Massachusetts Institute of Technology, Cambridge, MA.

40

References II

Shan, Chung-Chieh. 2004. Delimited continuations in natural language. In
Proceedings of the Fourth ACM SIGPLAN Continuations Workshop.
Shan, Chung-Chieh. 2007. Linguistic side effects. In Direct compositionality,
ed. Chris Barker and Pauline Jacobson, 132–163. Oxford: Oxford University
Press.
Shan, Chung-Chieh, and Chris Barker. 2006. Explaining Crossover andSuperiority as Left-to-right Evaluation. Linguistics and Philosophy
29:91–134.
Wurmbrand, Susanne. 2018. The cost of raising quantifiers. Glossa 3:1–40.

41