october 25, 2006

October 25, 2006

11-721: Grammars and Lexicons

Lori Levin

Lexical Functional Grammar

• History:– Joan Bresnan (linguist, MIT and Stanford)– Ron Kaplan (computational psycholinguist,

Xerox PARC)– Around 1978

What is Linguistic Theory• Delimit the range of possible human languages.

– What do all languages have in common?• Semantic roles, grammatical relations, pragmatic relations, some

constituent structure; only subjects can be controllees in matrix coding as subject constructions; etc.

– What are the ways in which they can differ from each other?

• Relative prominence of grammatical or pragmatic relations: word order reflects grammatical relations in English and reflects focus (new information) in Hungarian; Topic takes precedence over subject in Chinese in determining antecedent of null pronouns; Subject is more prominent in English.

– What never happens in a human language?• Make a question by saying the sentence backwards.

Universalist view of language

• There is “a common organizing structure of all languages that underlies their superficial variations in modes of expression” (Bresnan)– E.g., Passives that look very different in

different languages can be described by a universal passive rule.

• The common organizing structure is part of human biology.

Some differences between English and Warlpiri

The two small children are chasing that dog.

Aux V NP

NP VP

VP’ S

Wita-jarra-rlu ka-pala wajili-pi-nyi yalumpu kurdu-jarra-rlu maliki.Small-DU-ERG pres-3duSUBJ chase-NPAST that.ABS child-DU-ERG dog.ABS

NP AUX V NP NP NP

S

Possible word orders in Warlpiri that are not possible in English

• *The two small are chasing that children dog.

• *The two small are dog chasing that children.

• *Chasing are the two small that dog children.

• *That are children chasing the two small dog.

Non-configurational languages

• Free word order.

• May have discontinuous constituents.

• Tests for constituency do not yield evidence for VP constituent.

Something that English and Warlpiri have in common

• Lucy is hitting herself.• *Herself is hitting Lucy.• Napaljarri-rli ka-nyanu paka-rni Napaljarri-ERG PRES-REFL hit-NONPAST

“Napaljarri is hitting herself.”

• *Napaljarri ka-nyanu paka-rni Napaljarri.ABS PRES-REFL hit-NONPAST

“Herself is hitting Napaljarri.”

What English and Warlpiri have in common according to Chomsky

NP VP

VP’ S

Aux V NP

Deep structure

NP VP

VP’ S

Aux V NP

Surface Structure

English

What English and Warlpiri have in common according to Chomsky

NP VP

VP’ S

Aux V NP

Deep structure

Surface Structure

Warlpiri

S

NP Aux V NP NP NP

What English and Warlpiri have in common according to Bresnan

• Same grammatical relations and semantic roles– SUBJECT: the two small children: AGENT

– PREDICATE: are chasing

– OBJECT: that dog: PATIENT

• Different codings of grammatical relations:– English subject: NP immediately under S

– Warlpiri subject: Ergative case marked NP (if verb is transitive)

Strength of Chomsky’s approach

• Proposing that there is a VP in all languages explains why there are subject-object asymmetries in all languages.

Strength of Bresnan’s approach

• Doesn’t propose non-existent VPs: – phrase structure is used for representing

constituency– A different representation is used for

grammatical relations

Challenges for Bresnan and Chomsky

• Bresnan: – explain subject-object asymmetries in the absence of a

VP– Explain in a principled way the range of possible

coding properties of grammatical relations

• Chomsky: – explain in a principled way how the words get

scrambled out of VP; – The phrase structure tree has to represent both

grammatical relations and constituent structure, which may conflict with each other.

Levels of Representation in LFG[s [np The bear] [vp ate [np a sandwich]]] constituent structure

SUBJ PRED OBJ functional structure

Agent eat patient thematic roles

Grammatical encoding

Lexical mapping

Eat < agent patient > lexical mapping

SUBJ OBJ

SNP

SUBJ

VP

V NP

OBJ

VP

V PP

OBL

Grammatical Encoding

For English!!!

Syntax

• Syntax is not about the form (phrase structure) of sentences.

• It is about how strings of words are associated with their semantic roles.– Phrase structure is only part of the solution.

• Sam saw Sue– Sam: perceiver– Sue: perceived

Syntax• Syntax is also about how to tell that two

sentences are thematic paraphrases of each other (same phrases filling the same semantic roles).– It seems that Sam ate the sandwich.– It seems that the sandwich was eaten by Sam.– Sam seems to have eaten the sandwich.– The sandwich seems to have been eaten by Sam.

How to associate phrases with their semantic roles in LFG

• Starting from a constituent structure tree:• Grammatical encoding tells you how to find

the subject.– The bear is the subject.

• Lexical mapping tells you what semantic role the subject has.– The subject is the agent.– Therefore, the bear is the agent.

Levels of Representation in LFG[s [np The sandwich ] [vp was eaten [pp by the bear]]] constituent structure

SUBJ PRED OBL functional structure

patient eat agent thematic roles

Grammatical encoding

Lexical mapping

Eat < agent patient > lexical mapping

OBL SUBJ

SNP

SUBJ

VP

V NP

OBJ

VP

V PP

OBL

Grammatical Encoding

For English!!!

Active and Passive

• Active:– Patient is mapped to OBJ in lexical mapping.

• Passive– Patient is mapped to SUBJ in lexical mapping.

• Notice that the grammatical encodings are the same for active and passive sentences!!!

Passive mappings• Starting from the constituent structure tree.• The grammatical encoding tells you that the

sandwich is the subject.• The lexical mapping tells you that the subject is the

patient.– Therefore, the sandwich is the patient.

• The grammatical encoding tells you that the bear is oblique.

• The lexical mapping tells you that the oblique is the agent.– Therefore, the bear is the agent.

How you know that the active and passive have the same meaning

• In both sentences, the mappings connect the bear to the agent role.

• In both sentences, the mappings connect the sandwich to the patient role (roll?)

• In both sentences, the verb is eat.

Levels of Representation in LFG[s-bar [np what ] [s did [np the bear] eat ]] constituent structure

OBJ SUBJ PRED functional structure

patient agent eat thematic roles

Grammatical encoding

Lexical mapping

Eat < agent patient > lexical mapping

SUBJ OBJ

VP

V PP

OBL

Grammatical Encoding

For English!!!

SNP

SUBJ

S-barNP

OBJ

S

Wh-question

• Different grammatical encoding:– In this example, the OBJ is encoded as the NP

immediately dominated by S-bar

• Same lexical mappings are used for:– What did the bear eat?– The bear ate the sandwich.

Principles

• Variability:– Phrase structures and grammatical encodings

vary across languages.

• Universality– Functional structures are largely invariant

across languages.

Functional StructureSUBJ PRED ‘bear’ NUM sg PERS 3 DEF +PRED ‘eat< agent patient > SUBJ OBJTENSE pastOBJ PRED ‘sandwich’ NUM sg PERS 3 DEF -

Functional Structure

• Pairs of attributes (features) and values– Attributes (in this example): SUBJ, PRED,

OBJ, NUM, PERS, DEF, TENSE– Values:

• Atomic: sg, past, +, etc.

• Feature structure:

[num sg, pred `bear’, def +, person 3]

• Semantic form: ‘eat<subj ob>’, ‘bear’, ‘sandwich’

Semantic Forms

• Why are they values of a feature called PRED?– In some approaches to semantics, even nouns

like bear are predicates (function) that take one argument and returns true or false.

– Bear(x) is true when the variable x is bound to a bear.

– Bear(x) is false when x is not bound to a bear.

Why is it called a Functional Structure?

X squared

1 1

2 4

3 9

4 16

5 25

Each feature has a unique value.

features values

Also, another term for grammtical relation is grammatical function.

We will use the terms functional structure, f-structure and feature structure interchangeably.

Give a name to each function

SUBJ PRED ‘bear’ NUM sg PERS 3 DEF +PRED ‘eat< agent patient > SUBJ OBJTENSE pastOBJ PRED ‘sandwich’ NUM sg PERS 3 DEF -

f1

f2

f3

How to describe an f-structure

• F1(TENSE) = past– Function f1 applied to TENSE gives the value past.

• F1(SUBJ) = [PRED ‘bear’, NUM sg, PERS 3, DEF +]

• F2(NUM) = sg

Descriptions can be true or false

• F(a) = v – Is true if the feature-value pair [a v] is in f.– Is false if the feature-value pair [a v] is not in f.

This is the notation we really use

• (f1 TENSE) = past

• Read it this way:

f1’s tense is past.

• (f1 SUBJ) = [PRED ‘bear’, NUM sg, PERS 3, DEF +]

• (f2 NUM) = sg

Chains of function application

• (f1 SUBJ) = f2

• (f2 NUM) = sg

• ((f1 SUBJ) NUM) = sg

• Write it this way.

(f1 SUBJ NUM) = sg

• Read it this way.

“f1’s subject’s number is sg.”

More f-descriptions

• (f a) = v– f is something that evaluates to a function.

– a is something that evaluates to an attribute.

– v is something that evaluates to a function, symbol, or semantic form.

• (f1 subj) = (f1 xcomp subj)– Used for matrix coding as subject. A subject is shared by

the main clause and the complement clause (xcomp).

• (f1 (f6 case)) = f6– Used for obliques

Lions seem to live in the forest

DET N

P NP

V PP

COMP VP

N V VP-bar

NP VP

S

SUBJ PRED ‘lion’ NUM pl PERS 3PRED ‘seem < theme > SUBJ’ XCOMPTENSE presVFORM finXCOMP SUBJ [ ] VFORM INF PRED ‘live< theme loc >’ SUBJ OBL-loc OBJ

OBL-loc CASE OBL-loc PRED ‘in<OBJ>’ OBJ PRED ‘forest’ NUM sg PERS 3 DEF +

Lions seem to live in the forest

DET N

P NP

V PP

COMP VP

N V VP-bar

NP VP

S

SUBJ PRED ‘lion’ NUM pl PERS 3PRED ‘seem < theme > SUBJ’ XCOMPTENSE presVFORM finXCOMP SUBJ [ ] VFORM INF PRED ‘live< theme loc >’ SUBJ OBL-loc OBJ

OBL-loc CASE OBL-loc PRED ‘in<OBJ>’ OBJ PRED ‘forest’ NUM sg PERS 3 DEF +

f1

f3

f2

f4

f5 f6

n7

n6n5

n4

n3

n2

n1

n10n9

n8

n11n13

n12

n14

Lions seem to live in the forest

DET N

P NP

V PP

COMP VP

N V VP-bar

NP VP

S

SUBJ PRED ‘lion’ NUM pl PERS 3PRED ‘seem < theme > SUBJ’ XCOMPTENSE presVFORM finXCOMP SUBJ [ ] VFORM INF PRED ‘live< theme loc >’ SUBJ OBL-loc OBJ

OBL-loc CASE OBL-loc PRED ‘in<OBJ>’ OBJ PRED ‘forest’ NUM sg PERS 3 DEF +

f1

f3

f2

f4

f5 f6

n7

n6n5

n4

n3

n2

n1

n10n9

n8

n11n13

n12

n14

Properties of the mapping from c-structure to f-structure

• Each c-structure node maps onto at most one f-structure node.

• More than one c-structure node can map onto the same f-structure node.

• An f-structure node does not have to correspond to any c-structure node. (But the information it contains does come from somewhere – either a grammar rule or lexical entry.)

• Φ is a mapping from c-structure nodes to f-structure nodes. – There are other mappings to semantic structures,

argument structures, discourse structures,etc.

• * is the “current” c-structure node (me).• Φ(*) is “my f-structure” ()• m(*) is “my c-structure mother”• Φ(m(*)) is “my c-structure mother’s f-structure” ()

The formalism for grammatical encoding :Local co-description of partial structures

Local co-description of partial structures

• S NP VP ( SUBJ) = = NP says: My mother’s f-structure has a SUBJ

feature whose value is my f-structure.VP says: My mother’s f-structure is my f-structure.This rule simultaneously describes a piece of c-

structure and a piece of f-structure.It is local because each equation refers only to the

current node and its mother. (page 119-120)

Other types of equations

• F-structure composition– ( SUBJ NUM) = sg– My f-structure has a subj feature, whose value is another

f-structure, which has a num feature, whose value is sg.– Usually, path names are not longer than two.

• Two features pointing to the same value:– ( SUBJ) = ( XCOMP SUBJ)– ( SUBJ) = ( TOPIC)

• ( ( CASE)) = (Dalrymple pages 152-153)– Sam walked in the park.– ( CASE) = OBL-loc– ( OBL-loc) =

The minimal solution

• The f-structure for a sentence is the minimal f-structure that satisfies all of the equations. (page 101).

Building an F-structure: informal, for linguists• Annotate

– Assign a variable name to the f-structure corresponding to each c-structure node.

– May find out later that some of them are the same.

• Instantiate – Replace the arrows with the variable names.

• Solve– Locate the f-structure named on the left side of the equation.– Locate the f-structure named on the right side of the equation– Unify them.– Replace both of them with the result of unification.

Unification• [], empty feature structure, is identity

element– [] U x = x

• Atomic value unified with an atomic value:– x U x = x– x U y = fail

• Atomic value unified with a non empty feature structure: fail

Unification• Feature structure f1 unified with feature

structure f2 to make feature structure f3:– The set of features is the union of the features in

f1 and f2.– The value of each feature in f3 is the value of

that feature in f1 unified with the value of that feature in f2.

– Keep going recursively if there are embedded feature structures.

– If any unification fails, then the whole thing fails.

Unification and Grammaticality

• Grammatical sentence:– All unifications succeed and– Phrase structure derivation succeeds

• Ungrammatical sentence:– At least one unification fails or– Phrase structure derivation fails

Unification Example

f1 [ num sg gender masc person 3]f2 [ case nom def + person 3]

f3 [ num sg gender masc person 3 case nom def +]

Unification Example

f1 [ num sg gender masc person 3]f2 [ case nom def + person 2]

Unification fails. No f-structure is produced.

Unification Example

f1 [ subj [num sg gender masc person 3] tense pres]

f2 [ subj [case nom def + person 3] tense pres neg +]

f3 [ subj [num sg gender masc person 3 case nom def +] tense pres neg +]

Unification Example

f1 [ subj [num sg gender masc person 2] tense pres]

f2 [ subj [case nom def + person 3] tense pres neg +]

Unification fails. No f-structure is produced.

Lions seem to live in the forest

DET N

P NP

V PP

COMP VP

N V VP-bar

NP f2 VP f3

S f1

SUBJ PRED ‘lion’ NUM pl PERS 3PRED ‘seem < theme > SUBJ’ XCOMPTENSE presVFORM finXCOMP SUBJ [ ] VFORM INF PRED ‘live< theme loc >’ SUBJ OBL-loc OBJ

OBL-loc CASE OBL-loc PRED ‘in<OBJ>’ OBJ PRED ‘forest’ NUM sg PERS 3 DEF +

Rule:S → NP VP (↑ SUBJ) = ↓ ↑=↓ (↑VFORM) = fin

Instantiated equations: (f1 SUBJ) = f2f1 = f3

f1f2

f3

Lions seem to live in the forest

DET N

P NP

V PP

COMP VP

f4 N f5 V VP-bar

NP VP

S

SUBJ PRED ‘lion’ NUM pl PERS 3PRED ‘seem < theme > SUBJ’ XCOMPTENSE presVFORM finXCOMP SUBJ [ ] VFORM INF PRED ‘live< theme loc >’ SUBJ OBL-loc OBJ

OBL-loc CASE OBL-loc PRED ‘in<OBJ>’ OBJ PRED ‘forest’ NUM sg PERS 3 DEF +

lion: N seem: V(↑ PRED) = `lion’ (↑ PRED) =

‘seem < theme > SUBJ’ XCOMP (↑ SUBJ) = (↑ XCOMP SUBJ) -s (suffix for nouns) (↑ NUM) = pl - Ø (suffix for verbs)(↑ PERS) = 3 (↑ VFORM) = fin (↑ SUBJ NUM) = pl

f5

f4

Lions seem to live in the forest

DET N

P NP

V PP

COMP VP

f4 N f5 V VP-bar

NP VP

S

SUBJ PRED ‘lion’ NUM pl PERS 3PRED ‘seem < theme > SUBJ’ XCOMPTENSE presVFORM finXCOMP SUBJ [ ] VFORM INF PRED ‘live< theme loc >’ SUBJ OBL-loc OBJ

OBL-loc CASE OBL-loc PRED ‘in<OBJ>’ OBJ PRED ‘forest’ NUM sg PERS 3 DEF +

lion: N seem: V(f4 PRED) = `lion’ (f5 PRED) =

‘seem < theme > SUBJ’ XCOMP (f5 SUBJ) = (f5 XCOMP SUBJ) -s (suffix for nouns) (f4 NUM) = pl - Ø (suffix for verbs)(f4 PERS) = 3 (f5 VFORM) = fin (f5 SUBJ NUM) = pl

f5

f4

What is an XCOMP• A non-finite clause, predicate nominal, predicate adjective, or predicate PP– Sam seemed to be happy (VP)– Sam seemed happy (AP)– Sam became a teacher (NP)– We had them arrested (VP)– We kept them in the drawer (PP)

• Has to be an argument of a verb:– Arrested by the police, Sam had no alternative but to give up

his life of crime. • This is an adjunct, not an XCOMP

• Gets its subject by sharing with another verb:– I think that Sam is happy.

• This is a COMP, not an XCOMP

Lions seem to live in the forest

DET N

P NP

f7V PP

f6COMP VP f9

N f5 V f8 VP-bar

NP VP f3

S

SUBJ PRED ‘lion’ NUM pl PERS 3PRED ‘seem < theme > SUBJ’ XCOMPTENSE presVFORM finXCOMP SUBJ [ ] VFORM INF PRED ‘live< theme loc >’ SUBJ OBL-loc OBJ

OBL-loc CASE OBL-loc PRED ‘in<OBJ>’ OBJ PRED ‘forest’ NUM sg PERS 3 DEF +

seem: V

(↑ PRED) = ‘seem < theme > SUBJ’ XCOMP

(↑ SUBJ) = (↑ XCOMP SUBJ)

(↑ XCOMP VFORM) = INF

- Ø (suffix for verbs)

(↑ VFORM) = fin

(↑ SUBJ NUM) = pl

to: COMP - Ø (suffix for verbs)

(↑ VFORM) = INF (↑ VFORM) = INF

live: V

(↑ PRED) = `live<theme loc>’ SUBJ OBL

VP → V VP ↑=↓ (↑ XCOMP) = ↓

f3

f5

f9

f8

f7

f6

Lions seem to live in the forest

DET N

P NP

f7V PP

f6COMP VP f9

N f5 V f8 VP-bar

NP VP f3

S

SUBJ PRED ‘lion’ NUM pl PERS 3PRED ‘seem < theme > SUBJ’ XCOMPTENSE presVFORM finXCOMP SUBJ [ ] VFORM INF PRED ‘live< theme loc >’ SUBJ OBL-loc OBJ

OBL-loc CASE OBL-loc PRED ‘in<OBJ>’ OBJ PRED ‘forest’ NUM sg PERS 3 DEF +

seem: V

(f5 PRED) = ‘seem < theme > SUBJ’ XCOMP(f5 SUBJ) = (f5 XCOMP SUBJ) (f5 XCOMP VFORM) = INF

- Ø (suffix for verbs)(f5 VFORM) = fin (f5 SUBJ NUM) = pl

to: COMP - Ø (suffix for verbs)(f6 VFORM) = INF (f7 VFORM) = INF

live: V(f7 PRED) = `live<theme loc>’ SUBJ OBL

VP → V VP f3=f5 (f3 XCOMP) = f8

f3

f5

f9

f8

f7

f6

Lions try to live in the forest

DET N

P NP

V PP

COMP VP

N V VP-bar

NP VP

S

SUBJ PRED ‘lion’ NUM pl PERS 3PRED ‘try < agent theme >’ SUBJ XCOMPTENSE presVFORM finXCOMP SUBJ [ ] VFORM INF PRED ‘live< theme loc >’ SUBJ OBL-loc OBJ

OBL-loc CASE OBL-loc PRED ‘in<OBJ>’ OBJ PRED ‘forest’ NUM sg PERS 3 DEF +

Lions have lived in the forest

DET N

P NP

V PP

VP

N V

NP VP

S

SUBJ PRED ‘lion’ NUM pl PERS 3PRED ‘have < theme > SUBJ’ XCOMPTENSE presVFORM finXCOMP SUBJ [ ] VFORM PASTPART PRED ‘live< theme loc >’ SUBJ OBL-loc OBJ

OBL-loc CASE OBL-loc PRED ‘in<OBJ>’ OBJ PRED ‘forest’ NUM sg PERS 3 DEF +

have: V

(↑ PRED) = ‘have < theme > SUBJ’ XCOMP

(↑ SUBJ) = (↑ XCOMP SUBJ)

(↑ XCOMP VFORM) = PASTPART

- Ø (suffix for verbs)

(↑ VFORM) = fin

(↑ SUBJ NUM) = pl

Lions were hunted in the forest

DET N

P NP

V PP

VP

N V

NP VP

S

SUBJ PRED ‘lion’ NUM pl PERS 3PRED ‘be < theme > SUBJ’ XCOMPTENSE presVFORM finXCOMP SUBJ [ ] VFORM PASSIVE PRED ‘hunt<agent theme loc >’ Ø SUBJ OBL-loc OBJ

OBL-loc CASE OBL-loc PRED ‘in<OBJ>’ OBJ PRED ‘forest’ NUM sg PERS 3 DEF +

were : V

(↑ PRED) = ‘be < theme > SUBJ’ XCOMP

(↑ SUBJ) = (↑ XCOMP SUBJ)

(↑ XCOMP VFORM) = PASSIVE

(↑ VFORM) = fin

(↑ SUBJ NUM) = pl