Linguistics 187 Week 3

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Linguistics 187 Week 3
Coordination and Functional Uncertainty
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Coordination

• Illustrates engineering interaction of
• Linguistic phenomena
• Description
• Representation

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Coordination phenomena

• Constituent Coordinated elements are otherwise
  motivated constituents.
• S A girl saw Mary and S a girl heard
  Bill. (Unreduced)
• A girl VP saw Mary and VP heard
  Bill. (Reduced)
• A girl V saw and V heard Mary.
• Nonconstituent Coordinated elements look like
  fragments
• Bill went to ? Chicago on Wednesday and ? New
  York on Thursday.

(What motivates constituency?
Transformations? Phonology? Semantics?
Coordination? Well deal only with constituent
coordination)
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Descriptive problems

• First cut Conjoin phrases of like category
  Assign expanded-form interpretation (?)

• A girl VP saw Mary and VP heard Bill.

interpreted like
(2) S A girl saw Mary and S a girl heard
Bill.
see(girl,Mary) hear(girl, Bill)
But Can coordinate some unlike
categories Bush is NP a Republican and AP
proud of it. Cant coordinate some like
categories Bad John V keeps and V
polishes his car in the garage. OK John V
washes and V polishes his car in the garage.
And semantic entailments differ One girl in (1)
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Theoretical/engineering goal

• Get right syntactic and semantic results
• Without obscuring other generalizations
• One account of passives, relatives,
  subcategorizationwhether conjoined or not.

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Coordination in LFG/XLE

• Functional representation
• A coordinate phrase corresponds to an f-structure
  set
• (Bresnan/Kaplan/Peterson Kaplan/Maxwell)
• For unreduced, add alternative to other S
  expansions
• S --gt NP VP S ! CONJ S !
  .

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Coordinate reduction

• Also sets, but must distribute external
  elements across all set members
• E.g. single SUBJ satisfies conjoined VPs
• A girl VP saw Mary and VP
  heard Bill.
• VP --gt V NP VP ! CONJ
  VP ! .

How does SUBJ distribute without modifying normal
SUBJ equation?
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Distribution

• If denotes an f-structure f, then ( SUBJ)!
  Holds iff f has an attribute SUBJ with value !
• What if denotes a set f?
• Without further specification, ( SUBJ)! is
  false.
• Distribution a formal/theoretical extension
• For any (distributive) property P and set s,
  P(s) holds iff P(f) holds for all f in s.
• ( SUBJ)! is a (distributive) property, so
• If s f1 f2 and !g, then (s SUBJ)g iff
• (f1 SUBJ)g and (f2 SUBJ)g

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(s SUBJ)g
Note For defining equations, distribution is
equivalent to generalization (Kaplan Maxwell)
distribution is better for existentials
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Further consequences
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Wheres the conjunction?

• Lexical entry and CONJ ( COORD)and.

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Solution Nondistributives

• Observe Coordination itself has properties
• NUM, PERS, GEND of coordination different from
  any/all conjuncts
• sg and sg ? pl fem masc ?
  masc
• Coordination f-structure is hybrid
• Elements and attributes
• Attributes declared in grammar configuration
• NONDISTRIBUTIVES NUM PERS GEND COORD.

PRED see SUBJ girl
COORD and
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Nondistributives NP example
Mary
I
Mary and I
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METARULEMACRO

• Right-hand side of each grammar rule is the
  result of applying the macro to the rule
• METARULEMACRO(_CAT _BASECAT _RHS)
• _RHS.

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Coordination without METARULEMACRO

• Want to coordinate any constituent
• Coordination macro (Same Category
  COORD)
• SCCOORD(_CAT)
• _CAT !
• COMMA
• _CAT !
• CONJ
• _CAT ! .
• Put invocation in each rule
• NP (DET) AP N PP
• _at_(SCCOORD NP).
• Engineering problem
• forget to invoke
• put in wrong category

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Coordination with METARULEMACRO

• Call SCCOORD as part of MRM
• METARULEMACRO(_CAT _BASECAT _RHS)
• _RHS _at_(SCCOORD _CAT).
• Base NP rule NP (DET) AP N PP.
• Expanded NP (DET) AP N PP
• _at_(SCCOORD NP.
  MRM

_CAT
_RHS
NP (DET) AP N PP NP !
COMMA SCOORD NP !
CONJ NP ! .
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Ambiguity with coordination

• Boys and girls jumped.

3 c-structures NP coord, NPadj coord, N coord
NP
NP
NP
NP
NP
NPadj
NPadj
NPadj
NPadj
NPadj
NPadj
N
N
N
N
N
N
N
C
C
C
girls
girls
girls
boys
and
boys
and
boys
and
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Solution, as before PUSHUP

• If non-branching, push up to highest node.
• METARULEMACRO(_CAT _BASECAT _RHS)
• _RHS _CAT _at_PUSHUP .
• Recall
• Designator to test existence of sister nodes
• MOTHER SISTER

PUSHUP ( MOTHER LEFT_SISTER)
( MOTHER RIGHT_SISTER)
( MOTHER LEFT_SISTER)
( MOTHER MOTHER) .
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Different categories

• Republican and proud of it.

• MCATS Mixable categories
• MCATS VP S AP NP PP.
• MCOORD _at_MCATS !
• COMMA
• _at_MCATS !
• CONJ
• _at_MCATS ! .

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Functional Uncertainty

• Linguistic Issue Long distance dependencies
• Questions
• Who do you think Mary saw?
• Relative Clauses
• The boy who I think Mary saw jumped.
• Topicalization
• The little boy, I think Mary saw.

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The Problem

• What is Mary's within clause function or role
• Mary, John saw.
• Mary, John said Bill saw.
• Mary, John said Bill claimed Henry saw.
• Mary is the argument/function of a distant
  predicate/clause.
• Not just any distant predicate though
• Mary, John said the man who saw surprised Ken.
• (relative clause island)
• How to characterize such dependencies?

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Phrase structure solutions Guess a tree

• TG, GPSG, ATN, PATR, original LFG
• Link fronted phrase with trace/gap
• Infer role from trace position
• Node configuration gives island constraints

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Example Kaplan/Bresnan 82
?
M
TOPIC Mary1 PRED seeltJohn,Marygt TENSE
past SUBJ John OBJ 1
?
Long-distance path in c-str (M) induces
long-distance identity in f-str via c-str to
f-str correspondence f
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Categorial generalizations?

• Perhaps bad category mismatches
• She'll grow that tall/height.
• She'll reach that height/tall.
• The girl wondered how tall she would grow/reach.
• The girl wondered what height she would
  reach/grow.
• But these differ in function and control as well
  as category

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Grow vs. Reach

• grow ( PRED)'growlt( SUBJ)( XCOMP)gt'
• ( XCOMP SUBJ)( SUBJ)
• reach ( PRED)'reachlt( SUBJ)( OBJ)gt'

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But some mismatches are required

• He didn't think of that problem.
  (oblique NP)
• He didn't think that he might be wrong. (S
  complement)
• He didn't think of that he might be wrong.
  (mismatch)
• That he might be wrong he didn't think.
  (match!)
• That he might be wrong he didn't think of.
  (mismatch!)
• Simple functional account
• Think takes either of-oblique (1) or S complement
  (2)
• Sentences cannot be PP objects in English (3)
• English doesn't permit complement extraction (4)
• But fronted S can be "linked" to oblique object
  (5)

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Functional solution guess a function

• Directly encode functional relations via f-str
  description language
• S' --gt NP ( TOPIC)! (
  TOPIC)( OBJ) S

?
TOPIC Mary1 PRED seeltJohn,Marygt TENSE
past SUBJ John OBJ 1
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Problem Infinite role uncertainty

• Infinite role uncertainty gives infinite
  disjunction
• Mary, John saw. ( TOPIC)( OBJ)
• Mary, John said Bill saw. ( TOPIC)( COMP OBJ)
• Mary, John said Bill claimed Henry saw.
• ( TOPIC)(
  COMP COMP OBJ)
• etc.
• Can't have direct functional encoding in a finite
  grammar.

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Functional Uncertainty

• Extend description language to characterize, not
  enumerate, infinite role possibilities.
• Normal LFG function application
• (f s)v iff f is an f-str, s is a symbol, and
  lts,vgt ? f
• Extended to strings
• (f sy)((f s) y) for sy a string of symbols
• (f ?)f (? denotes the empty
  string)

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• Extended to sets of strings (possibly infinite)
• (f ?)v iff (f x)v for some string x in
  string-set ?
• (choice of x gives uncertainty)
• If ? is regular, can be defined by regular
  predicates
• ( TOPIC)( COMP OBJ) hold iff one of
• ( TOPIC)( OBJ)
• ( TOPIC)( COMP OBJ)
• ( TOPIC)( COMP COMP
  OBJ)
• holds.
• Regular predicates define accessibility and
  islands in functional terms.

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Possible Paths

• The paths can be any of the regular expressions
  that are used for the c-structure (see the XLE
  documentation)
• Some common ones
• Kleene ( XCOMP OBJ)! (0 or or
  more)
• Kleene ( COMP OBJ) ! (1 or more)
• ( COMP XCOMP OBJ) !
  (disjunction)
• These can be combined
• ( ACOMP NCOMP SUBJ OBL OBJ ) !

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Subcategorization

• Subcategorization eliminates possibilities
• Mary, he told/failed to stop.
• Topicalization uncertainty
• ( TOPIC)( XCOMP SUBJ OBJ )
• Satisfactory uncertainty strings
• intransitive stop OBJ (only
  with told)
• transitive stop XCOMP OBJ (only with
  failed)

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Intransitive stop
TOPIC Mary 1 SUBJ he PRED
'telllthe,Mary,stopgt' OBJ 1 XCOMP SUBJ 1
PRED 'stopltMarygt'
TOPICOBJ
Mary he told to stop.
TOPIC Mary 1 SUBJ he 2 PRED
'faillthe,stopgt' OBJ 1 XCOMP SUBJ 2
PRED 'stopltMarygt'
TOPICOBJ failed is Incoherent TOPICXCOMP OBJ
stop is Incoherent TOPICXCOMP SUBJ Inconsistent
Mary he failed to stop.
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Transitive stop
TOPIC Mary 1 SUBJ he PRED
'telllthe,---,stopgt' OBJ ---2 XCOMP SUBJ
2 PRED 'stoplt---.Marygt'
OBJ 1
TOPICOBJ stop is Incomplete TOPICXCOMP OBJ
told is Incomplete
Mary he told to stop.
TOPIC Mary 1 SUBJ he 2 PRED
'faillthe,stopgt' XCOMP SUBJ 2
PRED 'stopltMarygt' OBJ 1
TOPICXCOMP OBJ failed
Mary he failed to stop.
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Uncertainty for English topics

• ( TOPIC)( COMPXCOMP GF-COMP)
• Topic clause can be OBJ but not COMP
• He didn't think of that problem.
• He didn't think that he might be wrong.
• He didn't think of that he might be wrong.
• That he might be wrong he didn't think.
• That he might be wrong he didn't think of.

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No need for empty nodes

• S' --gt NP ( TOPIC)! ( TOPIC)( COMP GF) S
• where GFSUBJOBJOBJ2OBL
• VP --gt V (NP ( OBJ)!)

?
?
TOPIC Mary1 PRED seeltJohn,Marygt TENSE
past SUBJ John OBJ 1
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No empty nodes cont.

• Object NP is independently optional (for
  intransitives)
• Long-distance identity in f-structure is directly
  specified
• C-structure is closer to concrete phonology

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Satisfiability

• Given a system of equations with functional
  uncertainty, there is an algorithm that
• determines if the system is satisfiable
• finds all minimal solutions
• Problems
• Strings chosen from different uncertainties can
  interact
• Infinite choices gt Finite case analysis doesnt
  work

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Satisfiability example

• Which strings produce a satisfiable system?
• (f XCOMP SUBJOBJ)c1
• (f XCOMP SUBJOBJOBJ2)c2 c2?c1
• Satisfiability depends on the particular strings
  chosen
• satisfiable (f XCOMP SUBJ)c1
• (f OBJ)c2
• not satisfiable (f XCOMP SUBJ)c1
• (f XCOMP SUBJ)c2

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Satisfiability example cont.

• Solution A finite characterization of
  dependencies

(f XCOMP)g ?
(g SUBJOBJ) c1 (g XCOMP
SUBJOBJOBJ2)c2 ? (g XCOMP SUBJOBJc1
(g SUBJOBJOBJ2)c2 ? (g SUBJ)c1 (g
OBJOBJ2)c2 ? (g OBJ)c1 (g SUBJOBJ2)c2
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Inside-out functional uncertainty

• Just saw "outside-in" for (f ?)v
• The uncertainty can be anchored on v and lead
  outside it to an enclosing f.
• (? g)f iff (f ?)g for some f-structure f
• iff (f x)g for some f-structure
  f and some
• string x in ?
• Used for
• quantifier scope
• anaphora
• in-situ wh words

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Inside-out FU example

• ((XCOMP OBJ ) SUBJ NUM)sg

SUBJ NUM sg XCOMP XCOMP OBJ

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Functional Uncertainty Summary

• Characterizes long-distance dependencies
• Basic form ( PATH GF)
• XLE implements both outside-in (typical) and
  inside-out functional uncertainty
• Functional uncertainty can be inefficient,
  especially when multiple uncertainties interact

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