Exploring Multidominance in Tree Adjoining Grammar

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Exploring Multidominance in Tree Adjoining Grammar

• Joan Chen-Main
• joan_at_cogsci.jhu.edu
• Department of Cognitive Science
• Johns Hopkins University

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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 ___?

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Standard Treatment Trees

• Movement or ellipsis
• Unique node immediately dominating each node

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Alternative Treatment Graphs
Gärtner, Wilder, Abels, Goodall, and others

• One element in one place
• Mulitidominance

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How are such graphs generated?

• What introduces multidominance into the system?

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Sarkar and Joshi (1996)

• Some nodes are marked for contraction

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Sarkar and Joshi (1996)

• Node contraction results in multidominance

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Example Conjoined VPs

• Elementary trees

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Example Conjoined VPs

• VP coordination tree adjoined into eats tree
• drinks tree substituted into coordination tree

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Example Conjoined VPs

• NP nodes contract

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Example Conjoined VPs

• Joe eats cookies and drinks tea.

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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?

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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

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Multidomination in Movement

• PROPOSAL
• Node contraction can replace elementary tree
  internal movement.

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Example Wh-Question

• Did-eat tree substitutes into wh-question tree

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Example Wh-Question

• DPs substitutes in to yield
• What did Emmy eat?

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The Interleaving Problem

• Does Sam seem to like pizza?

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Allowing Interleaving

• Elementary trees marked for node contraction

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Allowing Interleaving

• The does seem tree adjoins into the to like tree

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Allowing Interleaving

• The to like tree substitutes into the yes-no
  question tree

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Final Structure
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Small Trees and Recursion

• Hegarty (1993) Smaller trees allow further
  Factoring out of recursive structure
• V, I, and some Cs not distinguished by the
  combinatory operations

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Small Trees and Node Contraction

• Head Movement in Hegartys system requires
  hiccup, two V positions.
• With node contraction, we can maintain parallel
  between Eng and French.
• Schematic for V to I movement

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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

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A Graph To Ban
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A Graph To Ban
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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.

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Locality on Node Contraction
Schematic
Derivation Trees OK not OK
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Example Embedded Question Islands
Which party did Alice ask who you had invited
to?

• Elementary trees marked for contraction

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Example Embedded Question Islands
Which party did Alice ask who you had invited
to?

• Problematic to combine these trees

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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.

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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.

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Failed Derivation
Which party did Alice ask who you had invited
to?
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Additional Island Effects

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

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Coordinated DPs and the CSC
Joe watched a movie about Stevie Wonder and a TV
show about bridges.
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Coordinated DPs and the CSC
Who did Joe watch a movie about ___ and a TV
show about bridges?

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Coordinated DPs and the CSC
What did Joe watch a movie about Stevie Wonder
and ___?

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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

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Current Concerns

• Linearization How do we pronounce these graphs?
• Gapping How do we generate two argument
  structures from one verb?
• Coordinated TPs and the Coordinate Structure
  Constraint

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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

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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.

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Linearization derived trees

• Full-dominance non-tangling condition
• If a sister-precedes ß, then everything a fully
  dominates precedes everything ß fully dominates.
• Full-dominance
• a fully dominates ? iff every path from ? to the
  root of the sentence includes a.
• (Wilder 2001)

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Simple Case Shared Subject

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

SPs affecting the contracted node DPS SP V1 ?
Joe gtgt eats, cookies DPS SP V2 ? Joe
gtgt drinks, tea
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Simple Case Shared Subject

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

Other SPs will order remaining items VP1 SP BP
? eats, cookies gtgt and, drinks, tea B SP VP2 ?
and gtgt drinks, tea (VP2 fully dominate
Joe.) V1 SP DP1 ? eats gtgt cookies V2 SP DP2 ?
drinks gtgt tea
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Simple Case Right Node Raising

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

SPs affecting the contracted node V1 SP DPO ?
bakes gtgt cookies V2 SP DPO ? decorates gtgt
cookies
Contrasts with Pronounce-in-Highest-Position
strategy
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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 ___.

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Simple Case Shared Subj Obj
SPs affecting the contracted nodes DPS SP V1'
? Joe gtgt bakes DPS SP V2' ? Joe gtgt
decorates V1 SP DPO ? bakes gtgt cookies V2 SP
DPO ? decorates gtgt cookies
SPs ordering remaining items VP1 SP BP ?
bakes gtgt and B SP VP2 ? and gtgt decorates
Contrasts with Wilders full-dominance LCA
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Kaynes (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

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Antisymmetry Violations

• What did Emmy ___ eat ___?

Symmetrical Pair DPO SP QC' ? what gtgt eat,
did, Emmy V SP DPO ? eat gtgt what
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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 cant preserve order, pronounce as
  high as you can.

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Avoiding Symmetry

• What did Emmy ___ eat ___?

Symmetrical Pair DPO SP QC' ? what gtgt eat,
did, Emmy V SP DPO ? eat gtgt what
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Totality Violations
John and Mary ate cookies.
John, Mary, and and are all unordered wrt ate and
cookies.
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Coordinated Subjects

• John and Mary ate cookies.

Need such a structure for sentences like John
and Mary met in the park.
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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.
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Contraction of DP, V', V
Joe eats cookies and ice cream.
Allowing contraction of X' wont help Neither
VP1 nor VP2 fully dominate anything. And remains
unordered.
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Coordinated Objects
Joe eats cookies and ice cream.
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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

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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 ___ ___?

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A pro-Verb Story for Gapping

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

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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

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Coordinated TPs and the CSC

• Joe eats cookies and Sam drinks tea.

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Coordinated TPs and the CSC

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

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Coordinated TPs and the CSC

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

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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 . . . ???

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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.

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Thank you
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Relating Coordination and Movement
A parallel between elements that can be extracted
and elements that can be coordinated (Dowty 1988).
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Gapping

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

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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.

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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
• Ellipsis ?Sal is a talented forger, but Holly
  cant ___ at all.
• Gapping Sal may be a forger of passports and
  Holly may forge paintings.

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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