linguistics 187 week 3 coordination and functional uncertainty
DESCRIPTION
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? We’ll deal only with constituent coordination)TRANSCRIPT
Linguistics 187 Week 3Linguistics 187 Week 3
Coordination and Functional UncertaintyCoordination and Functional Uncertainty
CoordinationCoordination
Illustrates engineering interaction of– Linguistic phenomena– Description– Representation
Coordination phenomenaCoordination 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 fragmentsBill went to [? Chicago on Wednesday] and [? New York on Thursday].
(What motivates constituency? Transformations? Phonology? Semantics? Coordination?We’ll deal only with constituent coordination)
Descriptive problemsDescriptive problemsFirst cut: Conjoin phrases of like category
Assign expanded-form interpretation (?)
(1) 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]. Can’t 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)
Theoretical/engineering goalTheoretical/engineering goal
Get right syntactic and semantic results Without obscuring other generalizations:
One account of passives, relatives, subcategorization…whether conjoined or not.
Coordination in LFG/XLECoordination in LFG/XLEFunctional representation:
– A coordinate phrase corresponds to an f-structure set(Bresnan/Kaplan/Peterson; Kaplan/Maxwell)
– For unreduced, add alternative to other S expansions S --> { NP VP | … | S: ! $ ^; CONJ S: ! $ ^ }.
Coordinate reductionCoordinate 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 --> { V NP … | VP: ! $ ^; CONJ VP: ! $ ^ }.
How does SUBJ distribute without modifying normal SUBJ equation?
DistributionDistribution
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, soIf ^=s= {f1 f2} and !=g, then (s SUBJ)=g iff
(f1 SUBJ)=g and (f2 SUBJ)=g
(s SUBJ)=g
s
g
Note: For defining equations, distribution is equivalent to generalization (Kaplan & Maxwell); distribution is better for existentials
Further consequencesFurther consequences
Where’s the conjunction?Where’s the conjunction?Lexical entry: and CONJ * (^ COORD)=and.
VP -> VP: !$^; CONJ: !$^; VP: !$^.
PRED seeSUBJ girl
COORD andSUBJ girl
PRED hearSUBJ girl
VP -> VP: !$^; CONJ: !=^; VP: !$^.
PRED seeSUBJ girlCOORD and
PRED hearSUBJ girlCOORD and
PRED seeSUBJ girlCOORD and
PRED hearSUBJ girlCOORD *and/or
PRED smellSUBJ girlCOORD *and/or
see and hear or smell
Solution: NondistributivesSolution: 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 seeSUBJ girl
COORD and
PRED smellSUBJ girl
COORD or
PRED hearSUBJ girl
Nondistributives: NP exampleNondistributives: NP example
Mary I
PRED 'Mary'NUM sgPERS 3
PRED 'I'NUM sgPERS 1
Mary and I
PRED 'Mary'NUM sgPERS 3
PRED 'I'NUM sgPERS 1
NUM pl, PERS 1, COORD and
METARULEMACROMETARULEMACRO
Right-hand side of each grammar rule is the result of applying the macro to the rule
METARULEMACRO(_CAT _BASECAT _RHS) = _RHS.
Coordination without METARULEMACROCoordination 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* |@(SCCOORD NP)}.
Engineering problem: – forget to invoke– put in wrong category
Coordination with METARULEMACROCoordination with METARULEMACRO Call SCCOORD as part of MRM
METARULEMACRO(_CAT _BASECAT _RHS) = { _RHS | @(SCCOORD _CAT)}.
Base NP rule: NP: (DET) AP* N PP*.Expanded: NP: { (DET) AP* N PP* |@(SCCOORD NP}. MRM
= NP: { (DET) AP* N PP* | [ NP: ! $ ^; COMMA]* SCOORD NP: ! $ ^; CONJ NP: ! $ ^. }
_CAT _RHS
Ambiguity with coordinationAmbiguity with coordination Boys and girls jumped.
3 c-structures: NP coord, NPadj coord, N coord
boys and girls
NP
NPadj
N
NP
NPadj
N
NP
boys and girls
NPadj
N
NPadj
N
NP
NPadj
boys and girls
N N
NP
NPadj
N
C C C
Solution, as before: PUSHUPSolution, as before: PUSHUP If non-branching, push up to highest node.
METARULEMACRO(_CAT _BASECAT _RHS) = { _RHS | _CAT: @PUSHUP }.
Recall– Designator to test existence of sister nodes: * MOTHER SISTER
PUSHUP = { (* MOTHER LEFT_SISTER) |(* MOTHER RIGHT_SISTER) ~(* MOTHER LEFT_SISTER)
|~(* MOTHER MOTHER) }.
Different categoriesDifferent categories
… Republican and proud of it.
MCATS: Mixable categories MCATS = {VP S AP NP PP}.
MCOORD = [ @MCATS: ! $ ^; COMMA]* @MCATS: ! $ ^; CONJ @MCATS: ! $ ^.
Functional UncertaintyFunctional 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.
The ProblemThe 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?
Phrase structure solutions: Phrase structure solutions: Guess a tree 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
Example: Kaplan/Bresnan 82Example: Kaplan/Bresnan 82
NPMary
S'
S
NPJohn
VP
Vsaw
NP:objt
TOPIC Mary1PRED see<John,Mary>TENSE pastSUBJ JohnOBJ 1
M*
Long-distance path in c-str (M*) induces long-distanceidentity in f-str via c-str to f-str correspondence φ
Categorial generalizations?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
Grow vs. ReachGrow vs. Reach
grow: (^ PRED)='grow<(^ SUBJ)(^ XCOMP)>' (^ XCOMP SUBJ)=(^ SUBJ)
reach: (^ PRED)='reach<(^ SUBJ)(^ OBJ)>'
PRED 'grow<girl,tall>'SUBJ [ girl ] 1XCOMP PRED 'tall<girl>' SUBJ 1
PRED 'reach<girl,height>'SUBJ [ girl ]OBJ [ height ]
But: some mismatches are requiredBut: some mismatches are required
1) He didn't think of that problem. (oblique NP)2) He didn't think that he might be wrong. (S complement)3) *He didn't think of that he might be wrong. (mismatch)4) *That he might be wrong he didn't think. (match!)5) 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)
Functional solution: guess a functionFunctional solution: guess a function Directly encode functional relations via f-str description
language S' --> NP: (^ TOPIC)=! (^ TOPIC)=(^ OBJ); S
NPMary
S'
S
NPJohn
VP
Vsaw
TOPIC Mary1PRED see<John,Mary>TENSE pastSUBJ JohnOBJ 1
Problem: Infinite role uncertaintyProblem: 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.
Functional UncertaintyFunctional 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 <s,v> ∈ f
Extended to strings:(f sy)=((f s) y) for sy a string of symbols(f )=f ( denotes the empty string)
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.
Possible PathsPossible 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 }) = !
SubcategorizationSubcategorization
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)
Intransitive Intransitive stopstop
TOPIC [ Mary ] 1SUBJ [ he ]PRED 'tell<he,Mary,stop>'OBJ 1XCOMP SUBJ 1 PRED 'stop<Mary>'
TOPIC [ Mary ] 1SUBJ [ he ] 2PRED 'fail<he,stop>'OBJ 1XCOMP SUBJ 2 PRED 'stop<Mary>'
TOPIC=OBJ: failed is IncoherentTOPIC=XCOMP OBJ: stop is IncoherentTOPIC=XCOMP SUBJ: Inconsistent
TOPIC=OBJ
“Mary he failed to stop.”
“Mary he told to stop.”
Transitive Transitive stopstopTOPIC [ Mary ] 1SUBJ [ he ]PRED 'tell<he,---,stop>'OBJ [---]2XCOMP SUBJ 2 PRED 'stop<---.Mary>' OBJ 1
TOPIC [ Mary ] 1SUBJ [ he ] 2PRED 'fail<he,stop>'XCOMP SUBJ 2 PRED 'stop<Mary>' OBJ 1
TOPIC=XCOMP OBJfailed
TOPIC=OBJ: stop is IncompleteTOPIC=XCOMP OBJ: told is Incomplete
“Mary he failed to stop.”
“Mary he told to stop.”
Uncertainty for English topicsUncertainty for English topics
(^ TOPIC)=(^ {COMP|XCOMP}* [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.
No need for empty nodesNo need for empty nodesS' --> NP: (^ TOPIC)=! (^ TOPIC)=(^ COMP* GF); S where GF={SUBJ|OBJ|OBJ2|OBL}
VP --> V (NP: (^ OBJ)=!) …
TOPIC Mary1PRED see<John,Mary>TENSE pastSUBJ JohnOBJ 1
NP
Mary
S'
S
NPJohn
VP
Vsaw
No empty nodes cont.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
SatisfiabilitySatisfiability
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 ==> Finite case analysis doesn’t work
Satisfiability exampleSatisfiability example
Which strings produce a satisfiable system? (f XCOMP* {SUBJ|OBJ})=c1 (f XCOMP* {SUBJ|OBJ|OBJ2})=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
Satisfiability example cont.Satisfiability example cont.
Solution: A finite characterization of dependencies:
(f XCOMP*)=g ∧
(g {SUBJ|OBJ})= c1 ^ (g XCOMP+ {SUBJ|OBJ|OBJ2})=c2 (g XCOMP+ {SUBJ|OBJ}=c1 ^ (g {SUBJ|OBJ|OBJ2})=c2 (g SUBJ)=c1 ^ (g {OBJ|OBJ2})=c2 (g OBJ)=c1 ^ (g {SUBJ|OBJ2})=c2
Inside-out functional uncertaintyInside-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
Inside-out FU exampleInside-out FU example
((XCOMP* OBJ ^) SUBJ NUM)=sg
SUBJ [NUM sg]XCOMP [XCOMP [OBJ ^[…] ]
Functional Uncertainty SummaryFunctional 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