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