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Exploring Multidominance in Tree Adjoining Grammar
Joan Chen-Main
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
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
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
• 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.
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.