Exploring Multidominance in Tree Adjoining Grammar

Joan Chen-Main

joan@cogsci.jhu.edu

Department of Cognitive Science

Johns Hopkins University

In Two Places at Once

• Some constructions seem like they have an element in two places at once:

Joe bakes ___ and Sam eats cookies.

What did Emmy eat ___?

What

DPi

did

Cj

Emmy

DP

t

Tj

eat

V

t

DPi

VP

T'

TP

C'

CP

Standard Treatment: Trees

• Movement or ellipsis

• Unique node immediately dominating each node

Joe

DP

bakes

V

cookies

DP

V'

VP1

and

B

Sam

DP

decorates

V

cookies

DP

V'

VP2

BP

VP1

What

DP did

T Emmy

DP

eat

V

VP

T'

TP

C'

CP

Alternative Treatment: Graphs

• One element in one place

• Mulitidominance

Joe

DP

bakes

V

V'

VP1

and

B

Sam

DP

decorates

V

cookies

DP

V'

VP2

BP

VP1

Gärtner, Wilder, Abels, Goodall, and others

How are such graphs generated?

What introduces multidominance into the system?

Sarkar and Joshi (1996)

• Some nodes are marked for contraction

DP

eats

V DP

V'

VP1

cookies

DP

drinks

V DP

V'

VP2

tea

V'

and

Sarkar and Joshi (1996)

• Node contraction results in multidominance

DP

eats

V DP

V'

VP1

cookies

Joe

drinks

V DP

V'

VP2

tea

V'

and

Example: Conjoined VPs

Elementary trees

NP

eats

V NP

V'

VP1

NP

drinks

V NP

V'

VP2

Joe

NP

cookies

NP

tea

NP

VP

VP

BP

VP

B

and

Example: Conjoined VPs

• VP coordination tree adjoined into eats tree

• drinks tree substituted into coordination tree

NP

eats

V NP

V'

VP1

and

B

drinks

V NP

V'

VP2

BP

VP1

NP

Joe

NP

cookies

NP

tea

NP

Example: Conjoined VPs

NP nodes contract

NP

eats

V NP

V'

VP1

and

B

drinks

V NP

V'

VP2

BP

VP1

Joe

NP

cookies

NP

tea

NP

Joe

NP

eats

V

cookies

NP

V'

VP1

and

B

drinks

V

tea

NP

V'

VP2

BP

VP1

Example: Conjoined VPs

Joe eats cookies and drinks tea.

Pushing the Proposal

Instead of being restricted to coordination . . .

Suppose node contraction is a general mechanism in the TAG system.

Where else might we see multidominance?

Overview• What such a system can do

– Coordination

– “Movement”

– Interleaving

– Factoring out recursion

• Appropriate Restrictions– Island Constraints

– Part of Coordinate Structure Constraint

• Current Concerns– Linearization, Gapping, other part of CSC

Multidomination in “Movement”

PROPOSAL:

Node contraction can replace elementary tree internal movement.

Example: Wh-Question

Did-eat tree substitutes into wh-question tree

DP

did

T

eat

V DP

VP

T'

TP

DP

T TP

QC'

QCP

Example: Wh-Question

DPs substitutes in to yield

What did Emmy eat?

DP

did

T

DP

eat

V

VP

T'

TP

QC'

QCP

Emmy

What

The Interleaving Problem

Does Sam seem to like pizza?

Allowing Interleaving

Elementary trees marked for node contraction

DP

to

T

like

V DP

VP

T'

TP

Sam

DP

pizza

DP

does

T

seem

V T'

VP

T'

X TP

QCP

Allowing Interleaving

The does seem tree adjoins into the to like tree

Sam

DP

pizza

DP

DP

does

T

seem

V

to

T

like

V DP

VP

T'

VP

T'

TP

X TP

QCP

Allowing InterleavingThe to like tree substitutes into the yes-no

question tree

Sam

DP

pizza

DP

DP

does

T

seem

V

to

T

like

V DP

VP

T'

VP

T'

TP

QCP

Final Structure

Sam

DP

does

T seem

V

to

T

like

V

pizza

DP

VP

T'

VP

T'

TP

QCP

• Hegarty (1993): Smaller trees allow further “Factoring out” of recursive structure– V, I, and some C’s not distinguished by the

combinatory operations

Small Trees and Recursion

that

C VP

CP

DP

eat

V DP

V'

VP

did

T V'

V'

• Head Movement in Hegarty’s system requires “hiccup,” two V positions.

• With node contraction, we can maintain parallel between Eng and French.– Schematic for V to I movement

Small Trees and Node Contraction

DP

vuole

T DP

V'

V'

VP

DP

vuole

V DP

V'

VP

T V'

V' yields

Island Constraints

• Certain syntactic configurations block movement. (Ross 1967) – embedded questions– wh-relative clauses– subject islands– complex NPs

• Coordinate Structure Constraint– Part A: No conjunct can be a gap– Part B: No element of a conjunct can be a gap if

its filler is outside the conjunct

A Graph To Ban

which party

DP

did

T Alice

DP

ask

V

who

DP

you

DP

had

T

invited

V

VP

to

P

PP

VP

T'

TP

QCP

VP

T'

TP

QC'

QCP

A Graph To Ban

which party

DP

did

T Alice

DP

ask

V

who

DP

you

DP

had

T

invited

V

VP

to

P

PP

VP

T'

TP

QCP

VP

T'

TP

QC'

QCP

Deriving Island Effects

• Impose a restriction on node contraction:

After substitution, every node marked for contraction must have been contracted.

• No such restriction following adjoining• Imposes some locality on node contraction• Intuition: pieces of structure combined via

substitution are somehow more distinct than pieces of structure combined via adjunction.

Locality on Node Contraction

A

B

C

X

*

Schematic Derivation Trees

OK not OK

X

Tree B

Tree C

Tree A

X

Tree B

Tree C

Tree A

Example: Embedded Question Islands

• Elementary trees marked for contraction:

* Which party did Alice ask who you had invited to?

DP

T TP

QC'

QCP

X TP

QCP

Alice

DP

you

DP

who

DP

which party

DP

DP

did

T

ask

V QCP

VP

T'

TP

DP

had

T

invited

V DP

VP

T'

TP

VP

to DP

PP

VP

Example: Embedded Question Islands

• Problematic to combine these trees:

* Which party did Alice ask who you had invited to?

DP

T TP

QC'

QCP

X TP

QCP

Alice

DP

you

DP

who

DP

which party

DP

DP

did

T

ask

V QCP

VP

T'

TP

DP

had

T

invited

V DP

VP

T'

TP

VP

to DP

PP

VP

The Unavoidable Problem

• In the best case scenario . . .– The to-tree adjoins into

the had invited tree.– Following adjoining,

nodes waiting to be contraction are allowed.

X TP

QCP

DP

had

T

invited

V DP

VP

to DP

PP

VP

T'

TP

The Unavoidable Problem

– Next, the had invited tree substitutes into the question tree.

– Following substitution, no contraction nodes are allowed to be “leftover.”

• no way for all the nodes marked for contraction to do so.

QCP

DP

had

T

invited

V DP

VP

to DP

PP

VP

T'

TP

Failed Derivation* Which party did Alice ask who you had invited to?

‘who' tree

'which party' tree

'had invited' tree

‘to’-tree

emb-question tree

‘you’ tree

'Alice' tree

'did-ask' tree

wh-question tree

*

Additional Island Effects

• This restriction blocks extraction from:– embedded questions– wh-relative clauses– subject islands– complex NPs

Coordinated DPs and the CSC

‘and' tree

'Stevie Wonder' tree ‘a TV show’ tree

‘about’-tree

‘a movie’ tree

‘bridges’ tree

'Joe' tree

'watched' tree

‘about’-tree

Joe watched a movie about Stevie Wonder and a TV show about bridges.

Coordinated DPs and the CSC

‘and' tree

‘who’ tree ‘a TV show’ tree

‘about’-tree

‘a movie’ tree

‘bridges’ tree

'Joe' tree

'watched' tree

wh-question tree

‘about’-tree

*

*Who did Joe watch a movie about ___ and a TV show about bridges?

Coordinated DPs and the CSC

‘and' tree

'Stevie Wonder' tree ‘what’ tree

‘about’-tree

‘a movie’ tree 'Joe' tree

'watched' tree

wh-question tree

*

What did Joe watch a movie about Stevie Wonder and ___?

Conclusions

Allowing general node contraction in TAG:

• Provides a unified mechanism for coordination and movement (sans traces)

• Allows derivation of constructions with interleaved elements

• Allows further factoring out of recursion

• Can be restricted to derive island effects

Current Concerns

• LinearizationHow do we pronounce these graphs?

• GappingHow do we generate two argument

structures from one verb?

• Coordinated TPs and the Coordinate Structure Constraint

Linearization: elementary trees

• Elementary trees are indeed trees (and not graphs!).

• The primitive relations are immediate dominance and sister precedence.

• Sister precedence is not sensitive to segment/category distinction. – E.g. the lower segment of

XP1 sister precedes BP XP1

XP2

BP

XP1

B

Linearization: derived trees

• Each elementary tree contributes immediate dominance and sister precedence information about the derived tree.

• In the finished graph, – Dominance relation: the transitive closure of

available dominance information– Precedence relation: derived from a modified

non-tangling condition which uses notion of full dominance.

Linearization: derived trees

• Full-dominance “non-tangling” condition:

If α sister-precedes β, then everything α fully dominates precedes everything β fully dominates.

• Full-dominance:

α fully dominates γ iff every path from γ to the root of the sentence includes α.

(Wilder 2001)

Simple Case: Shared Subject

Joe eats cookies and ___ drinks tea.* ___ eats cookies and Joe drinks tea.

Joe

DPs

eats

V

cookies

DP1

V'

VP1

and

B

drinks

V

tea

DP2

V'

VP2

BP

VP1 SP’s affecting the contracted node:

DPS SP V1` Joe >> eats, cookies

DPS SP V2` Joe >> drinks, tea

Simple Case: Shared Subject

Joe eats cookies and ___ drinks tea.* ___ eats cookies and Joe drinks tea.

Joe

DPs

eats

V

cookies

DP1

V'

VP1

and

B

drinks

V

tea

DP2

V'

VP2

BP

VP1 Other SP’s will order remaining items:

VP1 SP BP eats, cookies >> and, drinks, teaB SP VP2 and >> drinks, tea (VP2 ¬fully dominate Joe.)V1 SP DP1 eats >> cookiesV2 SP DP2 drinks >> tea

Simple Case: Right Node Raising

Joe bakes ____ and Sam decorates cookies.* Joe bakes cookies and Sam decorates

____.SP’s affecting the contracted node:

V1 SP DPO bakes >> cookies

V2 SP DPO decorates >> cookies

Joe

DP

bakes

V

V'

VP1

and

B

Sam

DP

decorates

V

cookies

DPo

V'

VP2

BP

VP1

Contrasts with Pronounce-in-Highest-Position strategy

Simple Case: Shared Subj & Obj

Joe bakes ____ and ___ decorates cookies.* Joe bakes cookies and ___ decorates ___.* ___ bakes ___ and Joe decorates cookies.* ___ bakes cookies and Joe decorates ___.

Joe

DPs

bakes

V

V'

VP1

and

B

decorates

V

cookies

DPo

V'

VP2

BP

VP1

Simple Case: Shared Subj & Obj

SP’s affecting the contracted nodes:

DPS SP V1' Joe >> bakesDPS SP V2' Joe >> decoratesV1 SP DPO bakes >> cookiesV2 SP DPO decorates >> cookies

Joe

DPs

bakes

V

V'

VP1

and

B

decorates

V

cookies

DPo

V'

VP2

BP

VP1

SP’s ordering remaining items: VP1 SP BP bakes >> andB SP VP2 and >> decorates

Contrasts with Wilder’s full-dominance LCA

Kayne’s (1994) LCA

• If a syntactic structure cannot provide the information needed to linearize its terminals, the structure is ill-formed.

• Two kinds of violation– Antisymmetry– Totality

Antisymmetry Violations

What did Emmy ___ eat ___?

DP

did

T

DP

eat

V

VP

T'

TP

QC'

QCP

Emmy

What

Symmetrical Pair:

DPO SP QC' what >> eat, did, Emmy

V SP DPO eat >> what

Avoiding Symmetry

• Dominance provides a partial order on SP pairs

• Give priority to information from the SP pair ordered earliest.– If a contradiction arises later, ignore it. – i.e. If you can’t preserve order, pronounce as

high as you can.

Avoiding Symmetry

What did Emmy ___ eat ___?

Symmetrical Pair:

DPO SP QC' what >> eat, did, Emmy

V SP DPO eat >> what

DP

did

T

DP

eat

V

VP

T'

TP

QC'

QCP

Emmy

What

Totality Violations

John and Mary ate cookies.

John, Mary, and and are all unordered wrt ate and cookies.

John

DP V'

VP1

and

B

Mary

DP

ate

V

cookies

DP

V'

VP2

BP

VP1

Coordinated Subjects

John and Mary ate cookies.

John

DP1

and

B

Mary

DP2

BP

DP1

ate

V

cookies

DP

V'

VP

Need such a structure for sentences like: John and Mary met in the park.

Contraction of V', V, & DP

John and Mary ate cookies.

Could allow contraction of X' nodes.Would need a way to delete one of the anchor verbs.

John

DP

VP1

and

B

Mary

DP

ate

V

cookies

DP

V'

VP2

BP

VP1

Contraction of DP, V', & V

Joe eats cookies and ice cream.

Allowing contraction of X' won’t help: Neither VP1 nor VP2 fully dominate anything. And remains unordered.

Joe

DPs

eats

V

cookies

DP1

V'

VP1

and

B

ice cream

DP2

VP2

BP

VP1

Coordinated Objects

Joe eats cookies and ice cream.

Joe

DP

eats

V

cookies

DP

and

B

ice cream

DP

BP

DP1

V'

VP

When Linearization Chooses

• Coordinated Subjects– Conjoined DPs, no node contraction – If Conjoined TPs, then requires X' contraction

• Coordinated Objects– Conjoined DPs, no node contraction – Even with X' contraction, NOT Conjoined TPs

Gapping

Sam likes beans and Joe ___ rice.

• Linearization *Sam ___ beans and Joe likes rice.

• *Gapping & RNR

*Sam likes ___ and Joe ___ rice.

• *Gapping & ATB movement

*What does Sam like ___ and Joe ___ ___?

A pro-Verb Story for Gapping

• pro-V is the lexical anchor for an elementary tree

Sam

DP

likes

V DP

V'

VP1

and

B

Joe

DP

e

V

rice

DP

V'

VP2

BP

VP1

beans

A pro-Verb Story for Gapping

• Like its anchor, the pro-V tree is defective– Cannot have contraction nodes

*Gapping & RNR, *Gapping & ATB movement

– Depends on a bona fide verb for its interpretation (in some as yet unspecified structural relation)Linearization, Restriction to coordination

Coordinated TPs and the CSC

‘and' tree ‘cookies’ tree

‘drinks’ tree

‘Joe’-tree

‘eats’ tree

‘tea’ tree ‘Sam’-tree

Joe eats cookies and Sam drinks tea.

Coordinated TPs and the CSC

‘and' tree ‘cookies’ tree

‘drinks’ tree

‘who’-tree

‘eats’ tree

‘tea’ tree ‘Sam’-tree

‘question’ tree

*Who eats cookies and Sam drinks tea?What rules out this derivation?

Coordinated TPs and the CSC

‘and' tree ‘cookies’ tree

‘drinks’ tree

‘Joe’-tree

‘eats’ tree

‘tea’ tree ‘Sam’-tree

‘question’ tree

*What (does) Joe eats cookies and?What rules out this derivation?

Concluding Remarks

• Linearization . . .– Requires a means to suppress conflicting

information– Requires computation on the global structure– May choose between alternate analyses

• Gapping is postulated to . . .– Involve a pro-V and an anaphoric dependency

• CSC for coordinated TPs . . . ???

Acknowledgements

• Bob Frank is gratefully acknowledged for his encouragement and guidance.

• Thanks also to the Hopkins LingLab and Paul Smolensky for helpful feedback.

• This work is supported by an NSF IGERT grant.

Thank you

Relating Coordination and Movement

COORDINATION MOVEMENT

John read a book about Nixon on Monday and (about) Reagan on Tuesday.

Who did John read a book about __ ?

* Mary read Sue’s book about Nixon on Monday and (about) Reagan on Tuesday.

* Who did Mary read Sue’s book about __ ?

* John destroyed a book about Nixon on Monday and (about) Reagan on Tuesday.

*Who did Mary destroy a/Sue’s book about __ ?

A parallel between elements that can be extracted and elements that can be coordinated (Dowty 1988).

Gapping

• Tight match between antecedent and gap (cf) ellipsis. – * identifying an active and passive VPEllipsis:Botanist: That can all be explained.

Mr. Spock: Please do ____.Gapping: *The budget cuts might be defended

publicly by the chancellor, and the president might defend publicly her labor policies.

(Johnson 2003)

Gapping

• Tight match between antecedent and gap (cf) ellipsis.– * identifying an active and passive VP

– * an antecedent fashioned out of two VPs

Ellipsis: Wendy is eager to sail around the world and Bruce is eager to climb Killimanjaro, but neither of them can ____ because money is too tight.

Gapping: * Wendy should sail the English Channel and Bruce climb Whitney, and their partners should sail and climb the Pacific or Killminjaro.

Gapping

• Tight match between antecedent and gap (cf) ellipsis.– * identifying an active and passive VP– * an antecedent fashioned out of two VPs– * an antecedent from inside a DPEllipsis: ?Sal is a talented forger, but Holly can’t ___ at all.

Gapping: *Sal may be a forger of passports and Holly may forge paintings.

Gapping

• Tight match between antecedent and gap (cf) ellipsis.– * identifying an active and passive VP– * an antecedent fashioned out of two VPs– * an antecedent from inside a DP

• Restricted to coordination